2004_Kothari_Research Methodology

Multivariate Analysis Techniques 327 First centroid First Matrix of Factor Cross Product (Q ) factor A 1 .693 .618 .642 .641 .629 .694 .679 .683 .693 .480 .428 .445 .444 .436 .481 .471 .473 .618 .428 .382 .397 .396 .389 .429 .420 .422 .642 .445 .397 .412 .412 .404 .446 .436 .438 .641 .444 .396 .412 .411 .403 .445 .435 .438 .629 .436 .389 .404 .403 .396 .437 .427 .430 .694 .481 .429 .446 .445 .437 .482 .471 .474 .679 .471 .420 .436 .435 .427 .471 .461 .464 .683 .473 .422 .438 .438 .430 .474 .464 .466 Now we obtain first matrix of residual coefficient (R1) by subtracting Q1 from R as shown below: First Matrix of Residual Coefficient (R ) 1 Variables 12 3 4 56 7 8 Variables 1 .520 .281 – .241 – .363 .190 – .368 – .316 .301 2 .281 .618 –.346 –.307 .192 – .331 – .337 .230 3 –.241 –.346 .588 .259 – .281 .243 .146 – .366 4 – .363 – .307 .259 .589 – .381 .353 .178 – .327 5 .190 .192 – .281 – .381 .604 – .390 – .217 .294 6 – .368 – .331 .243 .353 – .390 .518 .330 – .354 7 –.316 – .337 .146 .178 – .226 .330 .539 – .312 8 .301 .230 – .366 – .327 .294 – .354 – .312 .534 Reflecting the variables 3, 4, 6 and 7, we obtain reflected matrix of residual coefficient (R'1) as under and then we can extract the second centroid factor (B) from it as shown on the next page. Reflected Matrix of Residual Coefficients (R'1) and Extraction of 2nd Centroid Factor (B) Variables 1 2 3* 4* 5 6* 7* 8 1 .520 .281 .241 .363 .190 .368 .316 .301 2 .281 .618 .346 .307 .192 .331 .337 .230 3* .241 .346 .588 .259 .281 .243 .146 .366 Variables 4* .363 .307 .259 .589 .381 .353 .178 .327 5 .190 .192 .281 .381 .604 .390 .217 .294 6* .368 .331 .243 .353 .390 .518 .330 .354 7* .316 .337 .146 .178 .226 .330 .539 .312 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ Contd.

328 Research Methodology 8 1 Variables 4* 5 6* 7* 8 Column sums: .301 2 3* .327 .294 .354 .312 .534 2.580 .230 .366 2.757 2.558 2.887 2.375 2.718 2.642 2.470 Sum of column sums (T) = 20.987 ∴ T = 4.581 Second centroid factor B = .563 .577 –.539 –.602 .558 –.630 –.518 .593 *These variables were reflected. Now we can write the matrix of factor loadings as under: Variables Factor loadings 1 Centroid Factor Centroid Factor 2 A B 3 4 .693 .563 5 .618 .577 6 .642 –.539 7 .641 –.602 8 .629 .558 .694 –.630 .679 –.518 .683 .593 Illustration 2 Work out the communality and eigen values from the final results obtained in illustration No. 1 of this chapter. Also explain what they (along with the said two factors) indicate. Solution: We work out the communality and eigen values for the given problem as under: Table 13.2 Variables Factor loadings Communality (h2) Centroid Factor Centroid Factor A B 1 .693 .563 (.693)2 + (.563)2 = .797 2 .618 .577 (.618)2 + (.577)2 = .715 3 .642 –.539 (.642)2 + (–.539)2 = .703 4 .641 –.602 (.641)2 + (–.602)2 = .773 5 .629 .558 (.629)2 + (.558)2 = .707 6 .694 –.630 (.694)2 + (–.630)2 = .879 7 .679 –.518 (.679)2 + (–.518)2 = .729 8 .683 .593 (.683)2 + (.593)2 = .818 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ Contd.

Multivariate Analysis Techniques 329 Variables Factor loadings Communality (h2) Eigen value Centroid Factor Centroid Factor 6.121 (Variance A B .77 accounted for i.e., (77%) common variance) 3.490 2.631 1.00 Proportion of total (100%) variance .44 .33 Proportion of (44%) (33%) common variance .57 .43 (57%) (43%) Each communality in the above table represents the proportion of variance in the corresponding (row) variable and is accounted for by the two factors (A and B). For instance, 79.7% of the variance in variable one is accounted for by the centroid factor A and B and the remaining 20.3% of the total variance in variable one scores is thought of as being made up of two parts: a factor specific to the attribute represented by variable one, and a portion due to errors of measurement involved in the assessment of variable one (but there is no mention of these portions in the above table because we usually concentrate on common variance in factor analysis). It has become customary in factor analysis literature for a loading of 0.33 to be the minimum absolute value to be interpreted. The portion of a variable’s variance accounted for by this minimum loading is approximately 10%. This criterion, though arbitrary, is being used more or less by way of convention, and as such must be kept in view when one reads and interprets the multivariate research results. In our example, factor A has loading in excess of 0.33 on all variables; such a factor is usually called “the general factor” and is taken to represent whatever it is that all of the variables have in common. We might consider all the eight variables to be product of some unobserved variable (which can be named subjectively by the researcher considering the nature of his study). The factor name is chosen in such a way that it conveys what it is that all variables that correlate with it (that “load on it”) have in common. Factor B in our example has all loadings in excess of 0.33, but half of them are with negative signs. Such a factor is called a “bipolar factor” and is taken to represent a single dimension with two poles. Each of these poles is defined by a cluster of variables—one pole by those with positive loadings and the other pole with negative loadings. We can give different names to the said two groups to help us interpret and name factor B. The rows at the bottom of the above table give us further information about the usefulness of the two factors in explaining the relations among the eight variables. The total variance (V) in the analysis is taken as equal to the number of variables involved (on the presumption that variables are standardized). In this present example, then V = 8.0. The row labeled “Eigen value” or “Common variance” gives the numerical value of that portion of the variance attributed to the factor in the concerning column above it. These are found by summing up the squared values of the corresponding factor loadings. Thus the total value, 8.0, is partitioned into 3.490 as eigen value for factor A and 2.631 as eigen value for factor B and the total 6.121 as the sum of eigen values for these two factors. The corresponding proportion of the total variance, 8.0, are shown in the next row; there we can notice that 77% of the

330 Research Methodology total variance is related to these two factors, i.e., approximately 77% of the total variance is common variance whereas remaining 23% of it is made up of portions unique to individual variables and the techniques used to measure them. The last row shows that of the common variance approximately 57% is accounted for by factor A and the other 43% by factor B. Thus it can be concluded that the two factors together “explain” the common variance. (B) Principal-components Method of Factor Analysis Principal-components method (or simply P.C. method) of factor analysis, developed by H. Hotelling, seeks to maximize the sum of squared loadings of each factor extracted in turn. Accordingly PC factor explains more variance than would the loadings obtained from any other method of factoring. The aim of the principal components method is the construction out of a given set of variables Xj’s (j = 1, 2, …, k) of new variables (pi), called principal components which are linear combinations of the Xs p1 = a11 X1 + a12 X2 + ... + a1k Xk p =a X +a X +…+a X 2 21 1 22 2 2k k . . .. . . . .. . pk = ak1 X1 + ak2 X2 + … + akk Xk 2 d iThe method is being applied mostly by using standardized variables, i.e., z j = X j − X j /σ j . The aij’s are called loadings and are worked out in such a way that the extracted principal components satisfy two conditions: (i) principal components are uncorrelated (orthogonal) and (ii) the first principal component (p1) has the maximum variance, the second principal component (p2) has the next maximum variance and so on. Following steps are usually involved in principal components method (i) Estimates of aij’s are obtained with which X’s are transformed into orthogonal variables i.e., the principal components. A decision is also taken with regard to the question: how many of the components to retain into the analysis? (ii) We then proceed with the regression of Y on these principal components i.e., b gY = y$1 p1 + y$2 p2 + ... + y$m pm m < k (iii) From the a$ij and y$ij , we may find bij of the original model, transferring back from the p’s into the standardized X’s. Alternative method for finding the factor loadings is as under: (i) Correlation coefficients (by the product moment method) between the pairs of k variables are worked out and may be arranged in the form of a correlation matrix, R, as under:

Multivariate Analysis Techniques 331 Correlation Matrix, R Variables Variables X1 X1 X2 X3 …. Xk X2 X3 r11 r12 r13 …. r1k . r21 r22 r23 …. r3k r31 r32 r33 …. r3k . . . . . . . Xk rk1 rk2 rk3 …. rkk The main diagonal spaces include unities since such elements are self-correlations. The correlation matrix happens to be a symmetrical matrix. (ii) Presuming the correlation matrix to be positive manifold (if this is not so, then reflections as mentioned in case of centroid method must be made), the first step is to obtain the sum of coefficients in each column, including the diagonal element. The vector of column sums is referred to as Ua1 and when Ua1 is normalized, we call it Va1. This is done by squaring and summing the column sums in Ua1 and then dividing each element in Ua1 by the square root of the sum of squares (which may be termed as normalizing factor). Then elements in Va1 are accumulatively multiplied by the first row of R to obtain the first element in a new vector Ua2. For instance, in multiplying Va1 by the first row of R, the first element in Va1 would be multiplied by the r11 value and this would be added to the product of the second element in Va1 multiplied by the r12 value, which would be added to the product of third element in Va1 multiplied by the r13 value, and so on for all the corresponding elements in Va1 and the first row of R. To obtain the second element of Ua2, the same process would be repeated i.e., the elements in Va1 are accumulatively multiplied by the 2nd row of R. The same process would be repeated for each row of R and the result would be a new vector Ua2. Then Ua2 would be normalized to obtain Va2. One would then compare Va1 and Va2. If they are nearly identical, then convergence is said to have occurred (If convergence does not occur, one should go on using these trial vectors again and again till convergence occurs). Suppose the convergence occurs when we work out Va8 in which case Va7 will be taken as Va (the characteristic vector) which can be converted into loadings on the first principal component when we multiply the said vector (i.e., each element of Va) by the square root of the number we obtain for normalizing Ua8. (iii) To obtain factor B, one seeks solutions for Vb, and the actual factor loadings for second component factor, B. The same procedures are used as we had adopted for finding the first factor, except that one operates off the first residual matrix, R1 rather than the original correlation matrix R (We operate on R1 in just the same way as we did in case of centroid method stated earlier). (iv) This very procedure is repeated over and over again to obtain the successive PC factors (viz. C, D, etc.).

332 Research Methodology Other steps involved in factor analysis (a) Next the question is: How many principal components to retain in a particular study? Various criteria for this purpose have been suggested, but one often used is Kaiser’s criterion. According to this criterion only the principal components, having latent root greater than one, are considered as essential and should be retained. (b) The principal components so extracted and retained are then rotated from their beginning position to enhance the interpretability of the factors. (c) Communality, symbolized, h2, is then worked out which shows how much of each variable is accounted for by the underlying factors taken together. A high communality figure means that not much of the variable is left over after whatever the factors represent is taken into consideration. It is worked out in respect of each variable as under: h2 of the ith variable = (ith factor loading of factor A)2 + (ith factor loading of factor B)2 + … Then follows the task of interpretation. The amount of variance explained (sum of squared loadings) by each PC factor is equal to the corresponding characteristic root. When these roots are divided by the number of variables, they show the characteristic roots as proportions of total variance explained. (d) The variables are then regressed against each factor loading and the resulting regression coefficients are used to generate what are known as factor scores which are then used in further analysis and can also be used as inputs in several other multivariate analyses. Illustration 3 Take the correlation matrix, R, for eight variables of illustration 1 of this chapter and then compute: (i) the first two principal component factors; (ii) the communality for each variable on the basis of said two component factors; (iii) the proportion of total variance as well as the proportion of common variance explained by each of the two component factors. Solution: Since the given correlation matrix is a positive manifold, we work out the first principal component factor (using trial vectors) as under: Table 13.3 Variables 1 2 3 4 5678 1 1.000 .709 .204 .081 .626 .113 .155 .774 2 .709 1.000 .051 .089 .581 .098 .083 .652 3 .204 .051 1.000 .671 .123 .689 .582 .072 4 .081 .089 .671 1.000 .022 .798 .613 .111 Variables 5 .626 .581 .123 .022 1.000 .047 .201 .724 6 .113 .098 .689 .798 .047 1.000 .801 .120 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ Contd.

Multivariate Analysis Techniques 333 7 1 2 3 45 678 8 .155 .083 .582 .613 .201 .801 1.000 .152 Column .774 .652 .072 .111 .724 .120 .152 1.000 sums Ua1 3.662 3.263 3.392 3.385 3.324 3.666 3.587 3.605 Normalizing Ua1 we .371 .331 .344 .343 .337 .372 .363 .365 obtain Va1 i.e., Va1 = Ua /Nor- malizing factor* b g b g b g b g b g b g b g b g*Normalizing factor = 3.662 2 + 3.263 2 + 3.392 2 + 3.385 2 + 3.324 2 + 3.666 2 + 3.587 2 + 3.605 2 = 97.372 = 9.868 Then we obtain U by accumulatively multiplying V row by row into R and the result comes as a2 a1 under: Ua2 : [1.296, 1.143, 1.201, 1.201, 1.165, 1.308, 1.280, 1.275] Normalizing it we obtain (normalizing factor for Ua2 will be worked out as above and will be = 3.493): V : [.371, .327, .344, .344, .334, .374, .366, .365] a2 Comparing Va1 and Va2, we find the two vectors are almost equal and this shows convergence has occurred. Hence Va1 is taken as the characteristic vector, Va. Finally, we compute the loadings on the first principal component by multiplying Va by the square root of the number that we obtain for normalizing Ua2. The result is as under: Variables (Characteristic × normalizing factor of Ua2 = Principal Component I 1 vector Va ) × 1.868 2 × 1.868 = .69 3 .371 × 1.868 = .62 4 .331 × 1.868 = .64 5 .344 × 1.868 = .64 6 .343 × 1.868 = .63 7 .337 × 1.868 = .70 8 .372 × 1.868 = .68 .363 = .68 .365

334 Research Methodology For finding principal component II, we have to proceed on similar lines (as stated in the context of obtaining centroid factor B earlier in this chapter) to obtain the following result*: Variables Principal Component II 1 +.57 2 +.59 3 –.52 4 –.59 5 +.57 6 –.61 7 –.49 8 –.61 The other parts of the question can now be worked out (after first putting the above information in a matrix form) as given below: Variables Principal Components Communality, h2 I II 1 (.69)2 + (.57)2 = .801 2 .69 +.57 (.62)2 + (.59)2 = .733 3 .62 +.59 (.64)2 + (–.52)2 = .680 4 .64 –.52 (.64)2 + (–.59)2 = .758 5 .64 –.59 (.63)2 + (.57)2 = .722 6 .63 +.57 (.70)2 + (–.61)2 = .862 7 .70 –.61 (.68)2 + (–.49)2 = .703 8 .68 –.49 (.68)2 + (–.61)2 = .835 .68 –.61 Eigen value 6.0921 i.e., common 3.4914 2.6007 variance .761 .436 .325 (76%) Proportion (43.6%) (32.5%) of total 1.000 variance .573 .427 (100%) (57%) (43%) Proportion of common variance All these values can be interpreted in the same manner as stated earlier. *This can easily be worked out. Actual working has been left as an exercise for the students.

Multivariate Analysis Techniques 335 (C) Maximum Likelihood (ML) Method of Factor Analysis The ML method consists in obtaining sets of factor loadings successively in such a way that each, in turn, explains as much as possible of the population correlation matrix as estimated from the sample correlation matrix. If Rs stands for the correlation matrix actually obtained from the data in a sample, Rp stands for the correlation matrix that would be obtained if the entire population were tested, then the ML method seeks to extrapolate what is known from Rs in the best possible way to estimate Rp (but the PC method only maximizes the variance explained in Rs). Thus, the ML method is a statistical approach in which one maximizes some relationship between the sample of data and the population from which the sample was drawn. The arithmetic underlying the ML method is relatively difficult in comparison to that involved in the PC method and as such is understandable when one has adequate grounding in calculus, higher algebra and matrix algebra in particular. Iterative approach is employed in ML method also to find each factor, but the iterative procedures have proved much more difficult than what we find in the case of PC method. Hence the ML method is generally not used for factor analysis in practice.* The loadings obtained on the first factor are employed in the usual way to obtain a matrix of the residual coefficients. A significance test is then applied to indicate whether it would be reasonable to extract a second factor. This goes on repeatedly in search of one factor after another. One stops factoring after the significance test fails to reject the null hypothesis for the residual matrix. The final product is a matrix of factor loadings. The ML factor loadings can be interpreted in a similar fashion as we have explained in case of the centroid or the PC method. ROTATION IN FACTOR ANALYSIS One often talks about the rotated solutions in the context of factor analysis. This is done (i.e., a factor matrix is subjected to rotation) to attain what is technically called “simple structure” in data. Simple structure according to L.L. Thurstone is obtained by rotating the axes** until: (i) Each row of the factor matrix has one zero. (ii) Each column of the factor matrix has p zeros, where p is the number of factors. (iii) For each pair of factors, there are several variables for which the loading on one is virtually zero and the loading on the other is substantial. (iv) If there are many factors, then for each pair of factors there are many variables for which both loadings are zero. (v) For every pair of factors, the number of variables with non-vanishing loadings on both of them is small. All these criteria simply imply that the factor analysis should reduce the complexity of all the variables. * The basic mathematical derivations of the ML method are well explained in S.A. Mulaik’s, The Foundations of Factor Analysis. ** Rotation constitutes the geometric aspects of factor analysis. Only the axes of the graph (wherein the points representing variables have been shown) are rotated keeping the location of these points relative to each other undisturbed.

336 Research Methodology There are several methods of rotating the initial factor matrix (obtained by any of the methods of factor analysis) to attain this simple structure. Varimax rotation is one such method that maximizes (simultaneously for all factors) the variance of the loadings within each factor. The variance of a factor is largest when its smallest loadings tend towards zero and its largest loadings tend towards unity. In essence, the solution obtained through varimax rotation produces factors that are characterized by large loadings on relatively few variables. The other method of rotation is known as quartimax rotation wherein the factor loadings are transformed until the variance of the squared factor loadings throughout the matrix is maximized. As a result, the solution obtained through this method permits a general factor to emerge, whereas in case of varimax solution such a thing is not possible. But both solutions produce orthogonal factors i.e., uncorrelated factors. It should, however, be emphasised that right rotation must be selected for making sense of the results of factor analysis. R-TYPE AND Q-TYPE FACTOR ANALYSES Factor analysis may be R-type factor analysis or it may be Q-type factor analysis. In R-type factor analysis, high correlations occur when respondents who score high on variable 1 also score high on variable 2 and respondents who score low on variable 1 also score low on variable 2. Factors emerge when there are high correlations within groups of variables. In Q-type factor analysis, the correlations are computed between pairs of respondents instead of pairs of variables. High correlations occur when respondent 1’s pattern of responses on all the variables is much like respondent 2’s pattern of responses. Factors emerge when there are high correlations within groups of people. Q-type analysis is useful when the object is to sort out people into groups based on their simultaneous responses to all the variables. Factor analysis has been mainly used in developing psychological tests (such as IQ tests, personality tests, and the like) in the realm of psychology. In marketing, this technique has been used to look at media readership profiles of people. Merits: The main merits of factor analysis can be stated thus: (i) The technique of factor analysis is quite useful when we want to condense and simplify the multivariate data. (ii) The technique is helpful in pointing out important and interesting, relationships among observed data that were there all the time, but not easy to see from the data alone. (iii) The technique can reveal the latent factors (i.e., underlying factors not directly observed) that determine relationships among several variables concerning a research study. For example, if people are asked to rate different cold drinks (say, Limca, Nova-cola, Gold Spot and so on) according to preference, a factor analysis may reveal some salient characteristics of cold drinks that underlie the relative preferences. (iv) The technique may be used in the context of empirical clustering of products, media or people i.e., for providing a classification scheme when data scored on various rating scales have to be grouped together. Limitations: One should also be aware of several limitations of factor analysis. Important ones are as follows:

Multivariate Analysis Techniques 337 (i) Factor analysis, like all multivariate techniques, involves laborious computations involving heavy cost burden. With computer facility available these days, there is no doubt that factor analysis has become relatively faster and easier, but the cost factor continues to be the same i.e., large factor analyses are still bound to be quite expensive. (ii) The results of a single factor analysis are considered generally less reliable and dependable for very often a factor analysis starts with a set of imperfect data. “The factors are nothing but blurred averages, difficult to be identified.”4 To overcome this difficulty, it has been realised that analysis should at least be done twice. If we get more or less similar results from all rounds of analyses, our confidence concerning such results increases. (iii) Factor-analysis is a complicated decision tool that can be used only when one has thorough knowledge and enough experience of handling this tool. Even then, at times it may not work well and may even disappoint the user. To conclude, we can state that in spite of all the said limitations “when it works well, factor analysis helps the investigator make sense of large bodies of intertwined data. When it works unusually well, it also points out some interesting relationships that might not have been obvious from examination of the input data alone”.5 (vi) Cluster Analysis Cluster analysis consists of methods of classifying variables into clusters. Technically, a cluster consists of variables that correlate highly with one another and have comparatively low correlations with variables in other clusters. The basic objective of cluster analysis is to determine how many mutually and exhaustive groups or clusters, based on the similarities of profiles among entities, really exist in the population and then to state the composition of such groups. Various groups to be determined in cluster analysis are not predefined as happens to be the case in discriminant analysis. Steps: In general, cluster analysis contains the following steps to be performed: (i) First of all, if some variables have a negative sum of correlations in the correlation matrix, one must reflect variables so as to obtain a maximum sum of positive correlations for the matrix as a whole. (ii) The second step consists in finding out the highest correlation in the correlation matrix and the two variables involved (i.e., having the highest correlation in the matrix) form the nucleus of the first cluster. (iii) Then one looks for those variables that correlate highly with the said two variables and includes them in the cluster. This is how the first cluster is formed. (iv) To obtain the nucleus of the second cluster, we find two variables that correlate highly but have low correlations with members of the first cluster. Variables that correlate highly with the said two variables are then found. Such variables along the said two variables thus constitute the second cluster. (v) One proceeds on similar lines to search for a third cluster and so on. 4 Srinibas Bhattacharya, Psychometrics and Behavioural Research, p. 177. 5 William D. Wells and Jagdish N. Sheth in their article on “Factor Analysis” forming chapter 9 in Robert Ferber, (ed.), Handbook of Marketing Research, p. 2–471.

338 Research Methodology From the above description we find that clustering methods in general are judgemental and are devoid of statistical inferences. For problems concerning large number of variables, various cut-and- try methods have been proposed for locating clusters. McQuitty has specially developed a number of rather elaborate computational routines* for that purpose. In spite of the above stated limitation, cluster analysis has been found useful in context of market research studies. Through the use of this technique we can make segments of market of a product on the basis of several characteristics of the customers such as personality, socio-economic considerations, psychological factors, purchasing habits and like ones. (vii) Multidimensional Scaling** Multidimensional scaling (MDS) allows a researcher to measure an item in more than one dimension at a time. The basic assumption is that people perceive a set of objects as being more or less similar to one another on a number of dimensions (usually uncorrelated with one another) instead of only one. There are several MDS techniques (also known as techniques for dimensional reduction) often used for the purpose of revealing patterns of one sort or another in interdependent data structures. If data happen to be non-metric, MDS involves rank ordering each pair of objects in terms of similarity. Then the judged similarities are transformed into distances through statistical manipulations and are consequently shown in n-dimensional space in a way that the interpoint distances best preserve the original interpoint proximities. After this sort of mapping is performed, the dimensions are usually interpreted and labeled by the researcher. The significance of MDS lies in the fact that it enables the researcher to study “The perceptual structure of a set of stimuli and the cognitive processes underlying the development of this structure.... MDS provides a mechanism for determining the truly salient attributes without forcing the judge to appear irrational.”6 With MDS, one can scale objects, individuals or both with a minimum of information. The MDS analysis will reveal the most salient attributes which happen to be the primary determinants for making a specific decision. (viii) Latent Structure Analysis This type of analysis shares both of the objectives of factor analysis viz., to extract latent factors and express relationship of observed (manifest) variables with these factors as their indicators and to classify a population of respondents into pure types. This type of analysis is appropriate when the variables involved in a study do not possess dependency relationship and happen to be non-metric. In addition to the above stated multivariate techniques, we may also describe the salient features of what is known as “Path analysis”, a technique useful for decomposing the total correlation between any two variables in a causal system. * These are beyond the scope of this book and hence have been omitted. Readers interested in such methods are referred to “Cluster Analysis” by R. C. Tryon and D. E. Bailey. ** See, Chapter No. 5 of this book for other details about MDS. 6 Robert Ferber, ed., Handbook of Marketing Research, p. 3–52.

Multivariate Analysis Techniques 339 PATH ANALYSIS The term ‘path analysis’ was first introduced by the biologist Sewall Wright in 1934 in connection with decomposing the total correlation between any two variables in a causal system. The technique of path analysis is based on a series of multiple regression analyses with the added assumption of causal relationship between independent and dependent variables. This technique lays relatively heavier emphasis on the heuristic use of visual diagram, technically described as a path diagram. An illustrative path diagram showing interrelationships between Fathers’ education, Fathers’ occupation, Sons’ education, Sons’ first and Sons’ present occupation can be shown in the Fig. 13.2. Path analysis makes use of standardized partial regression coefficients (known as beta weights) as effect coefficients. In linear additive effects are assumed, then through path analysis a simple set of equations can be built up showing how each variable depends on preceding variables. “The main principle of path analysis is that any correlation coefficient between two variables, or a gross or overall measure of empirical relationship can be decomposed into a series of parts: separate paths of influence leading through chronologically intermediate variable to which both the correlated variables have links.”7 The merit of path analysis in comparison to correlational analysis is that it makes possible the assessment of the relative influence of each antecedent or explanatory variable on the consequent or criterion variables by first making explicit the assumptions underlying the causal connections and then by elucidating the indirect effect of the explanatory variables. Father’s Son’s education education Son’s present occupation Father’s Son’s occupation first occupation Path analysis makes Fig.13.2 “The use of the path analysis technique requires the assumption that there are linear additive, a symmetric relationships among a set of variables which can be measured at least on a quasi-interval scale. Each dependent variable is regarded as determined by the variables preceding it in the path diagram, and a residual variable, defined as uncorrelated with the other variables, is postulated to account for the unexplained portion of the variance in the dependent variable. The determining variables are assumed for the analysis to be given (exogenous in the model).”8 7 K. Takeuchi, et al. op. cit., The Foundations of Multivariate Analysis, p. 122. 8 Ibid., p. 121–122.

340 Research Methodology We may illustrate the path analysis technique in connection with a simple problem of testing a causal model with three explicit variables as shown in the following path diagram: Path Diagram (with the variables) X1 p21 X2 p p31 32 X3 Fig. 13.3 The structural equation for the above can be written as: L O L OX1 =e1 M P M PX2 = NMM PPQ NMM PQPX3 = p31X2 + p32 X2 + e3 p21 X1 + e2 = pX + e where the X variables are measured as deviations from their respective means. p21 may be estimated from the simple regression of X2 on X1 i.e., X2 = b21Xl and p31 and p32 may be estimated from the regression of X3 on X2 and X1 as under: X$ 3 = b31.2 X1 + b2.1 X 2 where b31.2 means the standardized partial regression coefficient for predicting variable 3 from variable 1 when the effect of variable 2 is held constant. In path analysis the beta coefficient indicates the direct effect of Xj (j = 1, 2, 3, ..., p) on the dependent variable. Squaring the direct effect yields the proportion of the variance in the dependent variable Y which is due to each of the p number of independent variables Xj (i = 1, 2, 3, ..., p). After calculating the direct effect, one may then obtain a summary measure of the total indirect effect of Xj on the dependent variable Y by subtracting from the zero correlation coefficient ryxj, the beta coefficient bj i.e., Indirect effect of X on Y = c = r – b j jy yxj j for all j = 1, 2, ..., p. Such indirect effects include the unanalysed effects and spurious relationships due to antecedent variables. In the end, it may again be emphasised that the main virtue of path analysis lies in making explicit the assumptions underlying the causal connections and in elucidating the indirect effects due to antecedent variables of the given system. CONCLUSION From the brief account of multivariate techniques presented above, we may conclude that such techniques are important for they make it possible to encompass all the data from an investigation in one analysis. They in fact result in a clearer and better account of the research effort than do the piecemeal analyses of portions of data. These techniques yield more realistic probability statements

Multivariate Analysis Techniques 341 in hypothesis testing and interval estimation studies. Multivariate analysis (consequently the use of multivariate techniques) is specially important in behavioural sciences and applied researches for most of such studies involve problems in which several response variables are observed simultaneously. The common source of each individual observation generally results into dependence or correlation among the dimensions and it is this feature that distinguishes multivariate data and techniques from their univariate prototypes. In spite of all this, multivariate techniques are expensive and involve laborious computations. As such their applications in the context of research studies have been accelerated only with the advent of high speed electronic computers since 1950’s. Questions 1. What do you mean by multivariate techniques? Explain their significance in context of research studies. 2. Write a brief essay on “Factor analysis” particularly pointing out its merits and limitations. 3. Name the important multivariate techniques and explain the important characteristic of each one of such techniques. 4. Enumerate the steps involved in Thurstone’s centroid method of factor analysis. 5. Write a short note on ‘rotation’ in context of factor analysis. 6. Work out the first two centroid factors as well as first two principal components from the following correlation matrix, R, relating to six variables: Variables 56 1 2 34 Variables 1 1.00 .55 .43 .32 .28 .36 2 1.00 .50 .25 .31 .32 3 1.00 .39 .25 .33 4 1.00 .43 .49 5 1.00 .44 6 1.00 Answers: Variables Centroid factors Principal Components I II I II 1 2 .71 .40 .71 .39 3 .70 .46 .71 .48 4 .70 .37 .70 .32 5 .69 –.41 .69 –.42 6 .65 –.43 .64 –.45 .71 –.39 .71 –.38 7. Compute communality for each of the variable based on first two centroid factors in question six above and state what does it indicate.

342 Research Methodology 8. Compute the proportion of total variance explained by the two factors worked out in question six above by the principal components method. Also point out the proportion of common variance explained by each of the two factors. ‘ 9. What is the significance of using multiple discriminant analysis? Explain in brief the technical details involved in such a technique. 10. Write short notes on: (i) Cluster analysis; (ii) Multidimensional scaling; (iii) Reflections in context of factor analysis; (iv) Maximum likelihood method of factor analysis; (v) Path analysis.

Appendix: Summary Chart 343 Appendix Summary Chart: Showing the Appropriateness of a Particular Multivariate Technique Techniques of Number of multivariate analysis Explanatory Criterion variables 1. Multiple regression variables analysis (along with path analysis) many one (to be classified one many into many groups) 2. Multiple discriminant many analysis many many many*1 many*2 many 3. Multivariate analysis many many of variance many many 4. Canonical A correlation analysis A A A Non-metric 5. Factor analysis metric Non-metric metric 6. Cluster analysis 7. Multidimensional scaling (MDS) 8. Latent structure analysis Nature of data *1 Any one of the two. *2 Any one of the two.

344 Research Methodology 14 Interpretation and Report Writing After collecting and analyzing the data, the researcher has to accomplish the task of drawing inferences followed by report writing. This has to be done very carefully, otherwise misleading conclusions may be drawn and the whole purpose of doing research may get vitiated. It is only through interpretation that the researcher can expose relations and processes that underlie his findings. In case of hypotheses testing studies, if hypotheses are tested and upheld several times, the researcher may arrive at generalizations. But in case the researcher had no hypothesis to start with, he would try to explain his findings on the basis of some theory. This may at times result in new questions, leading to further researches. All this analytical information and consequential inference(s) may well be communicated, preferably through research report, to the consumers of research results who may be either an individual or a group of individuals or some public/private organisation. MEANING OF INTERPRETATION Interpretation refers to the task of drawing inferences from the collected facts after an analytical and/or experimental study. In fact, it is a search for broader meaning of research findings. The task of interpretation has two major aspects viz., (i) the effort to establish continuity in research through linking the results of a given study with those of another, and (ii) the establishment of some explanatory concepts. “In one sense, interpretation is concerned with relationships within the collected data, partially overlapping analysis. Interpretation also extends beyond the data of the study to include the results of other research, theory and hypotheses.”1 Thus, interpretation is the device through which the factors that seem to explain what has been observed by researcher in the course of the study can be better understood and it also provides a theoretical conception which can serve as a guide for further researches. WHY INTERPRETATION? Interpretation is essential for the simple reason that the usefulness and utility of research findings lie in proper interpretation. It is being considered a basic component of research process because of the following reasons: 1 C. William Emory, Business Research Methods, p. 336.

Interpretation and Report Writing 345 (i) It is through interpretation that the researcher can well understand the abstract principle that works beneath his findings. Through this he can link up his findings with those of other studies, having the same abstract principle, and thereby can predict about the concrete world of events. Fresh inquiries can test these predictions later on. This way the continuity in research can be maintained. (ii) Interpretation leads to the establishment of explanatory concepts that can serve as a guide for future research studies; it opens new avenues of intellectual adventure and stimulates the quest for more knowledge. (iii) Researcher can better appreciate only through interpretation why his findings are what they are and can make others to understand the real significance of his research findings. (iv) The interpretation of the findings of exploratory research study often results into hypotheses for experimental research and as such interpretation is involved in the transition from exploratory to experimental research. Since an exploratory study does not have a hypothesis to start with, the findings of such a study have to be interpreted on a post-factum basis in which case the interpretation is technically described as ‘post factum’ interpretation. TECHNIQUE OF INTERPRETATION The task of interpretation is not an easy job, rather it requires a great skill and dexterity on the part of researcher. Interpretation is an art that one learns through practice and experience. The researcher may, at times, seek the guidance from experts for accomplishing the task of interpretation. The technique of interpretation often involves the following steps: (i) Researcher must give reasonable explanations of the relations which he has found and he must interpret the lines of relationship in terms of the underlying processes and must try to find out the thread of uniformity that lies under the surface layer of his diversified research findings. In fact, this is the technique of how generalization should be done and concepts be formulated. (ii) Extraneous information, if collected during the study, must be considered while interpreting the final results of research study, for it may prove to be a key factor in understanding the problem under consideration. (iii) It is advisable, before embarking upon final interpretation, to consult someone having insight into the study and who is frank and honest and will not hesitate to point out omissions and errors in logical argumentation. Such a consultation will result in correct interpretation and, thus, will enhance the utility of research results. (iv) Researcher must accomplish the task of interpretation only after considering all relevant factors affecting the problem to avoid false generalization. He must be in no hurry while interpreting results, for quite often the conclusions, which appear to be all right at the beginning, may not at all be accurate. PRECAUTIONS IN INTERPRETATION One should always remember that even if the data are properly collected and analysed, wrong interpretation would lead to inaccurate conclusions. It is, therefore, absolutely essential that the task

346 Research Methodology of interpretation be accomplished with patience in an impartial manner and also in correct perspective. Researcher must pay attention to the following points for correct interpretation: (i) At the outset, researcher must invariably satisfy himself that (a) the data are appropriate, trustworthy and adequate for drawing inferences; (b) the data reflect good homogeneity; and that (c) proper analysis has been done through statistical methods. (ii) The researcher must remain cautious about the errors that can possibly arise in the process of interpreting results. Errors can arise due to false generalization and/or due to wrong interpretation of statistical measures, such as the application of findings beyond the range of observations, identification of correlation with causation and the like. Another major pitfall is the tendency to affirm that definite relationships exist on the basis of confirmation of particular hypotheses. In fact, the positive test results accepting the hypothesis must be interpreted as “being in accord” with the hypothesis, rather than as “confirming the validity of the hypothesis”. The researcher must remain vigilant about all such things so that false generalization may not take place. He should be well equipped with and must know the correct use of statistical measures for drawing inferences concerning his study. (iii) He must always keep in view that the task of interpretation is very much intertwined with analysis and cannot be distinctly separated. As such he must take the task of interpretation as a special aspect of analysis and accordingly must take all those precautions that one usually observes while going through the process of analysis viz., precautions concerning the reliability of data, computational checks, validation and comparison of results. (iv) He must never lose sight of the fact that his task is not only to make sensitive observations of relevant occurrences, but also to identify and disengage the factors that are initially hidden to the eye. This will enable him to do his job of interpretation on proper lines. Broad generalisation should be avoided as most research is not amenable to it because the coverage may be restricted to a particular time, a particular area and particular conditions. Such restrictions, if any, must invariably be specified and the results must be framed within their limits. (v) The researcher must remember that “ideally in the course of a research study, there should be constant interaction between initial hypothesis, empirical observation and theoretical conceptions. It is exactly in this area of interaction between theoretical orientation and empirical observation that opportunities for originality and creativity lie.”2 He must pay special attention to this aspect while engaged in the task of interpretation. SIGNIFICANCE OF REPORT WRITING Research report is considered a major component of the research study for the research task remains incomplete till the report has been presented and/or written. As a matter of fact even the most brilliant hypothesis, highly well designed and conducted research study, and the most striking generalizations and findings are of little value unless they are effectively communicated to others. The purpose of research is not well served unless the findings are made known to others. Research results must invariably enter the general store of knowledge. All this explains the significance of 2 Pauline V. Young, Scientific Social Surveys and Research, 4th ed., p. 488.

Interpretation and Report Writing 347 writing research report. There are people who do not consider writing of report as an integral part of the research process. But the general opinion is in favour of treating the presentation of research results or the writing of report as part and parcel of the research project. Writing of report is the last step in a research study and requires a set of skills somewhat different from those called for in respect of the earlier stages of research. This task should be accomplished by the researcher with utmost care; he may seek the assistance and guidance of experts for the purpose. DIFFERENT STEPS IN WRITING REPORT Research reports are the product of slow, painstaking, accurate inductive work. The usual steps involved in writing report are: (a) logical analysis of the subject-matter; (b) preparation of the final outline; (c) preparation of the rough draft; (d) rewriting and polishing; (c) preparation of the final bibliography; and (f) writing the final draft. Though all these steps are self explanatory, yet a brief mention of each one of these will be appropriate for better understanding. Logical analysis of the subject matter: It is the first step which is primarily concerned with the development of a subject. There are two ways in which to develop a subject (a) logically and (b) chronologically. The logical development is made on the basis of mental connections and associations between the one thing and another by means of analysis. Logical treatment often consists in developing the material from the simple possible to the most complex structures. Chronological development is based on a connection or sequence in time or occurrence. The directions for doing or making something usually follow the chronological order. Preparation of the final outline: It is the next step in writing the research report “Outlines are the framework upon which long written works are constructed. They are an aid to the logical organisation of the material and a reminder of the points to be stressed in the report.”3 Preparation of the rough draft: This follows the logical analysis of the subject and the preparation of the final outline. Such a step is of utmost importance for the researcher now sits to write down what he has done in the context of his research study. He will write down the procedure adopted by him in collecting the material for his study along with various limitations faced by him, the technique of analysis adopted by him, the broad findings and generalizations and the various suggestions he wants to offer regarding the problem concerned. Rewriting and polishing of the rough draft: This step happens to be most difficult part of all formal writing. Usually this step requires more time than the writing of the rough draft. The careful revision makes the difference between a mediocre and a good piece of writing. While rewriting and polishing, one should check the report for weaknesses in logical development or presentation. The researcher should also “see whether or not the material, as it is presented, has unity and cohesion; does the report stand upright and firm and exhibit a definite pattern, like a marble arch? Or does it resemble an old wall of moldering cement and loose brick.”4 In addition the researcher should give due attention to the fact that in his rough draft he has been consistent or not. He should check the mechanics of writing—grammar, spelling and usage. Preparation of the final bibliography: Next in order comes the task of the preparation of the final bibliography. The bibliography, which is generally appended to the research report, is a list of books 3 Elliott S.M. Gatner and Francesco Cordasco, Research and Report Writing, p. 37. 4 Ibid., p. 50.

348 Research Methodology in some way pertinent to the research which has been done. It should contain all those works which the researcher has consulted. The bibliography should be arranged alphabetically and may be divided into two parts; the first part may contain the names of books and pamphlets, and the second part may contain the names of magazine and newspaper articles. Generally, this pattern of bibliography is considered convenient and satisfactory from the point of view of reader, though it is not the only way of presenting bibliography. The entries in bibliography should be made adopting the following order: For books and pamphlets the order may be as under: 1. Name of author, last name first. 2. Title, underlined to indicate italics. 3. Place, publisher, and date of publication. 4. Number of volumes. Example Kothari, C.R., Quantitative Techniques, New Delhi, Vikas Publishing House Pvt. Ltd., 1978. For magazines and newspapers the order may be as under: 1. Name of the author, last name first. 2. Title of article, in quotation marks. 3. Name of periodical, underlined to indicate italics. 4. The volume or volume and number. 5. The date of the issue. 6. The pagination. Example Robert V. Roosa, “Coping with Short-term International Money Flows”, The Banker, London, September, 1971, p. 995. The above examples are just the samples for bibliography entries and may be used, but one should also remember that they are not the only acceptable forms. The only thing important is that, whatever method one selects, it must remain consistent. Writing the final draft: This constitutes the last step. The final draft should be written in a concise and objective style and in simple language, avoiding vague expressions such as “it seems”, “there may be”, and the like ones. While writing the final draft, the researcher must avoid abstract terminology and technical jargon. Illustrations and examples based on common experiences must be incorporated in the final draft as they happen to be most effective in communicating the research findings to others. A research report should not be dull, but must enthuse people and maintain interest and must show originality. It must be remembered that every report should be an attempt to solve some intellectual problem and must contribute to the solution of a problem and must add to the knowledge of both the researcher and the reader. LAYOUT OF THE RESEARCH REPORT Anybody, who is reading the research report, must necessarily be conveyed enough about the study so that he can place it in its general scientific context, judge the adequacy of its methods and thus

Interpretation and Report Writing 349 form an opinion of how seriously the findings are to be taken. For this purpose there is the need of proper layout of the report. The layout of the report means as to what the research report should contain. A comprehensive layout of the research report should comprise (A) preliminary pages; (B) the main text; and (C) the end matter. Let us deal with them separately. (A) Preliminary Pages In its preliminary pages the report should carry a title and date, followed by acknowledgements in the form of ‘Preface’ or ‘Foreword’. Then there should be a table of contents followed by list of tables and illustrations so that the decision-maker or anybody interested in reading the report can easily locate the required information in the report. (B) Main Text The main text provides the complete outline of the research report along with all details. Title of the research study is repeated at the top of the first page of the main text and then follows the other details on pages numbered consecutively, beginning with the second page. Each main section of the report should begin on a new page. The main text of the report should have the following sections: (i) Introduction; (ii) Statement of findings and recommendations; (iii) The results; (iv) The implications drawn from the results; and (v) The summary. (i) Introduction: The purpose of introduction is to introduce the research project to the readers. It should contain a clear statement of the objectives of research i.e., enough background should be given to make clear to the reader why the problem was considered worth investigating. A brief summary of other relevant research may also be stated so that the present study can be seen in that context. The hypotheses of study, if any, and the definitions of the major concepts employed in the study should be explicitly stated in the introduction of the report. The methodology adopted in conducting the study must be fully explained. The scientific reader would like to know in detail about such thing: How was the study carried out? What was its basic design? If the study was an experimental one, then what were the experimental manipulations? If the data were collected by means of questionnaires or interviews, then exactly what questions were asked (The questionnaire or interview schedule is usually given in an appendix)? If measurements were based on observation, then what instructions were given to the observers? Regarding the sample used in the study the reader should be told: Who were the subjects? How many were there? How were they selected? All these questions are crucial for estimating the probable limits of generalizability of the findings. The statistical analysis adopted must also be clearly stated. In addition to all this, the scope of the study should be stated and the boundary lines be demarcated. The various limitations, under which the research project was completed, must also be narrated. (ii) Statement of findings and recommendations: After introduction, the research report must contain a statement of findings and recommendations in non-technical language so that it can be easily understood by all concerned. If the findings happen to be extensive, at this point they should be put in the summarised form.

350 Research Methodology (iii) Results: A detailed presentation of the findings of the study, with supporting data in the form of tables and charts together with a validation of results, is the next step in writing the main text of the report. This generally comprises the main body of the report, extending over several chapters. The result section of the report should contain statistical summaries and reductions of the data rather than the raw data. All the results should be presented in logical sequence and splitted into readily identifiable sections. All relevant results must find a place in the report. But how one is to decide about what is relevant is the basic question. Quite often guidance comes primarily from the research problem and from the hypotheses, if any, with which the study was concerned. But ultimately the researcher must rely on his own judgement in deciding the outline of his report. “Nevertheless, it is still necessary that he states clearly the problem with which he was concerned, the procedure by which he worked on the problem, the conclusions at which he arrived, and the bases for his conclusions.”5 (iv) Implications of the results: Toward the end of the main text, the researcher should again put down the results of his research clearly and precisely. He should, state the implications that flow from the results of the study, for the general reader is interested in the implications for understanding the human behaviour. Such implications may have three aspects as stated below: (a) A statement of the inferences drawn from the present study which may be expected to apply in similar circumstances. (b) The conditions of the present study which may limit the extent of legitimate generalizations of the inferences drawn from the study. (c) Thc relevant questions that still remain unanswered or new questions raised by the study along with suggestions for the kind of research that would provide answers for them. It is considered a good practice to finish the report with a short conclusion which summarises and recapitulates the main points of the study. The conclusion drawn from the study should be clearly related to the hypotheses that were stated in the introductory section. At the same time, a forecast of the probable future of the subject and an indication of the kind of research which needs to be done in that particular field is useful and desirable. (v) Summary: It has become customary to conclude the research report with a very brief summary, resting in brief the research problem, the methodology, the major findings and the major conclusions drawn from the research results. (C) End Matter At the end of the report, appendices should be enlisted in respect of all technical data such as questionnaires, sample information, mathematical derivations and the like ones. Bibliography of sources consulted should also be given. Index (an alphabetical listing of names, places and topics along with the numbers of the pages in a book or report on which they are mentioned or discussed) should invariably be given at the end of the report. The value of index lies in the fact that it works as a guide to the reader for the contents in the report. 5 Selltiz, Jahoda, Deutsch and Cook, Research Methods in Social Relations, p. 448.

Interpretation and Report Writing 351 TYPES OF REPORTS Research reports vary greatly in length and type. In each individual case, both the length and the form are largely dictated by the problems at hand. For instance, business firms prefer reports in the letter form, just one or two pages in length. Banks, insurance organisations and financial institutions are generally fond of the short balance-sheet type of tabulation for their annual reports to their customers and shareholders. Mathematicians prefer to write the results of their investigations in the form of algebraic notations. Chemists report their results in symbols and formulae. Students of literature usually write long reports presenting the critical analysis of some writer or period or the like with a liberal use of quotations from the works of the author under discussion. In the field of education and psychology, the favourite form is the report on the results of experimentation accompanied by the detailed statistical tabulations. Clinical psychologists and social pathologists frequently find it necessary to make use of the case-history form. News items in the daily papers are also forms of report writing. They represent firsthand on-the- scene accounts of the events described or compilations of interviews with persons who were on the scene. In such reports the first paragraph usually contains the important information in detail and the succeeding paragraphs contain material which is progressively less and less important. Book-reviews which analyze the content of the book and report on the author’s intentions, his success or failure in achieving his aims, his language, his style, scholarship, bias or his point of view. Such reviews also happen to be a kind of short report. The reports prepared by governmental bureaus, special commissions, and similar other organisations are generally very comprehensive reports on the issues involved. Such reports are usually considered as important research products. Similarly, Ph.D. theses and dissertations are also a form of report-writing, usually completed by students in academic institutions. The above narration throws light on the fact that the results of a research investigation can be presented in a number of ways viz., a technical report, a popular report, an article, a monograph or at times even in the form of oral presentation. Which method(s) of presentation to be used in a particular study depends on the circumstances under which the study arose and the nature of the results. A technical report is used whenever a full written report of the study is required whether for record- keeping or for public dissemination. A popular report is used if the research results have policy implications. We give below a few details about the said two types of reports: (A) Technical Report In the technical report the main emphasis is on (i) the methods employed, (it) assumptions made in the course of the study, (iii) the detailed presentation of the findings including their limitations and supporting data. A general outline of a technical report can be as follows: 1. Summary of results: A brief review of the main findings just in two or three pages. 2. Nature of the study: Description of the general objectives of study, formulation of the problem in operational terms, the working hypothesis, the type of analysis and data required, etc. 3. Methods employed: Specific methods used in the study and their limitations. For instance, in sampling studies we should give details of sample design viz., sample size, sample selection, etc.

352 Research Methodology 4. Data: Discussion of data collected, their sources, characteristics and limitations. If secondary data are used, their suitability to the problem at hand be fully assessed. In case of a survey, the manner in which data were collected should be fully described. 5. Analysis of data and presentation of findings: The analysis of data and presentation of the findings of the study with supporting data in the form of tables and charts be fully narrated. This, in fact, happens to be the main body of the report usually extending over several chapters. 6. Conclusions: A detailed summary of the findings and the policy implications drawn from the results be explained. 7. Bibliography: Bibliography of various sources consulted be prepared and attached. 8. Technical appendices: Appendices be given for all technical matters relating to questionnaire, mathematical derivations, elaboration on particular technique of analysis and the like ones. 9. Index: Index must be prepared and be given invariably in the report at the end. The order presented above only gives a general idea of the nature of a technical report; the order of presentation may not necessarily be the same in all the technical reports. This, in other words, means that the presentation may vary in different reports; even the different sections outlined above will not always be the same, nor will all these sections appear in any particular report. It should, however, be remembered that even in a technical report, simple presentation and ready availability of the findings remain an important consideration and as such the liberal use of charts and diagrams is considered desirable. (B) Popular Report The popular report is one which gives emphasis on simplicity and attractiveness. The simplification should be sought through clear writing, minimization of technical, particularly mathematical, details and liberal use of charts and diagrams. Attractive layout along with large print, many subheadings, even an occasional cartoon now and then is another characteristic feature of the popular report. Besides, in such a report emphasis is given on practical aspects and policy implications. We give below a general outline of a popular report. 1. The findings and their implications: Emphasis in the report is given on the findings of most practical interest and on the implications of these findings. 2. Recommendations for action: Recommendations for action on the basis of the findings of the study is made in this section of the report. 3. Objective of the study: A general review of how the problem arise is presented along with the specific objectives of the project under study. 4. Methods employed: A brief and non-technical description of the methods and techniques used, including a short review of the data on which the study is based, is given in this part of the report. 5. Results: This section constitutes the main body of the report wherein the results of the study are presented in clear and non-technical terms with liberal use of all sorts of illustrations such as charts, diagrams and the like ones. 6. Technical appendices: More detailed information on methods used, forms, etc. is presented in the form of appendices. But the appendices are often not detailed if the report is entirely meant for general public.

Interpretation and Report Writing 353 There can be several variations of the form in which a popular report can be prepared. The only important thing about such a report is that it gives emphasis on simplicity and policy implications from the operational point of view, avoiding the technical details of all sorts to the extent possible. ORAL PRESENTATION At times oral presentation of the results of the study is considered effective, particularly in cases where policy recommendations are indicated by project results. The merit of this approach lies in the fact that it provides an opportunity for give-and-take decisions which generally lead to a better understanding of the findings and their implications. But the main demerit of this sort of presentation is the lack of any permanent record concerning the research details and it may be just possible that the findings may fade away from people’s memory even before an action is taken. In order to overcome this difficulty, a written report may be circulated before the oral presentation and referred to frequently during the discussion. Oral presentation is effective when supplemented by various visual devices. Use of slides, wall charts and blackboards is quite helpful in contributing to clarity and in reducing the boredom, if any. Distributing a board outline, with a few important tables and charts concerning the research results, makes the listeners attentive who have a ready outline on which to focus their thinking. This very often happens in academic institutions where the researcher discusses his research findings and policy implications with others either in a seminar or in a group discussion. Thus, research results can be reported in more than one ways, but the usual practice adopted, in academic institutions particularly, is that of writing the Technical Report and then preparing several research papers to be discussed at various forums in one form or the other. But in practical field and with problems having policy implications, the technique followed is that of writing a popular report. Researches done on governmental account or on behalf of some major public or private organisations are usually presented in the form of technical reports. MECHANICS OF WRITING A RESEARCH REPORT There are very definite and set rules which should be followed in the actual preparation of the research report or paper. Once the techniques are finally decided, they should be scrupulously adhered to, and no deviation permitted. The criteria of format should be decided as soon as the materials for the research paper have been assembled. The following points deserve mention so far as the mechanics of writing a report are concerned: 1. Size and physical design: The manuscript should be written on unruled paper 8 1 2″ × 11″ in size. If it is to be written by hand, then black or blue-black ink should be used. A margin of at least one and one-half inches should be allowed at the left hand and of at least half an inch at the right hand of the paper. There should also be one-inch margins, top and bottom. The paper should be neat and legible. If the manuscript is to be typed, then all typing should be double-spaced on one side of the page only except for the insertion of the long quotations. 2. Procedure: Various steps in writing the report should be strictly adhered (All such steps have already been explained earlier in this chapter). 3. Layout: Keeping in view the objective and nature of the problem, the layout of the report should be thought of and decided and accordingly adopted (The layout of the research report and various

354 Research Methodology types of reports have been described in this chapter earlier which should be taken as a guide for report-writing in case of a particular problem). 4. Treatment of quotations: Quotations should be placed in quotation marks and double spaced, forming an immediate part of the text. But if a quotation is of a considerable length (more than four or five type written lines) then it should be single-spaced and indented at least half an inch to the right of the normal text margin. 5. The footnotes: Regarding footnotes one should keep in view the followings: (a) The footnotes serve two purposes viz., the identification of materials used in quotations in the report and the notice of materials not immediately necessary to the body of the research text but still of supplemental value. In other words, footnotes are meant for cross references, citation of authorities and sources, acknowledgement and elucidation or explanation of a point of view. It should always be kept in view that footnote is not an end nor a means of the display of scholarship. The modern tendency is to make the minimum use of footnotes for scholarship does not need to be displayed. (b) Footnotes are placed at the bottom of the page on which the reference or quotation which they identify or supplement ends. Footnotes are customarily separated from the textual material by a space of half an inch and a line about one and a half inches long. (c) Footnotes should be numbered consecutively, usually beginning with 1 in each chapter separately. The number should be put slightly above the line, say at the end of a quotation. At the foot of the page, again, the footnote number should be indented and typed a little above the line. Thus, consecutive numbers must be used to correlate the reference in the text with its corresponding note at the bottom of the page, except in case of statistical tables and other numerical material, where symbols such as the asterisk (*) or the like one may be used to prevent confusion. (d) Footnotes are always typed in single space though they are divided from one another by double space. 6. Documentation style: Regarding documentation, the first footnote reference to any given work should be complete in its documentation, giving all the essential facts about the edition used. Such documentary footnotes follow a general sequence. The common order may be described as under: (i) Regarding the single-volume reference 1. Author’s name in normal order (and not beginning with the last name as in a bibliography) followed by a comma; 2. Title of work, underlined to indicate italics; 3. Place and date of publication; 4. Pagination references (The page number). Example John Gassner, Masters of the Drama, New York: Dover Publications, Inc. 1954, p. 315. (ii) Regarding multivolumed reference 1. Author’s name in the normal order;

Interpretation and Report Writing 355 2. Title of work, underlined to indicate italics; 3. Place and date of publication; 4. Number of volume; 5. Pagination references (The page number). (iii) Regarding works arranged alphabetically For works arranged alphabetically such as encyclopedias and dictionaries, no pagination reference is usually needed. In such cases the order is illustrated as under: Example 1 “Salamanca,” Encyclopaedia Britannica, 14th Edition. Example 2 “Mary Wollstonecraft Godwin,” Dictionary of national biography. But if there should be a detailed reference to a long encyclopedia article, volume and pagination reference may be found necessary. (iv) Regarding periodicals reference 1. Name of the author in normal order; 2. Title of article, in quotation marks; 3. Name of periodical, underlined to indicate italics; 4. Volume number; 5. Date of issuance; 6. Pagination. (v) Regarding anthologies and collections reference Quotations from anthologies or collections of literary works must be acknowledged not only by author, but also by the name of the collector. (vi) Regarding second-hand quotations reference In such cases the documentation should be handled as follows: 1. Original author and title; 2. “quoted or cited in,”; 3. Second author and work. Example J.F. Jones, Life in Ploynesia, p. 16, quoted in History of the Pacific Ocean area, by R.B. Abel, p. 191. (vii) Case of multiple authorship If there are more than two authors or editors, then in the documentation the name of only the first is given and the multiple authorship is indicated by “et al.” or “and others”. Subsequent references to the same work need not be so detailed as stated above. If the work is cited again without any other work intervening, it may be indicated as ibid, followed by a comma and

356 Research Methodology the page number. A single page should be referred to as p., but more than one page be referred to as pp. If there are several pages referred to at a stretch, the practice is to use often the page number, for example, pp. 190ff, which means page number 190 and the following pages; but only for page 190 and the following page ‘190f’. Roman numerical is generally used to indicate the number of the volume of a book. Op. cit. (opera citato, in the work cited) or Loc. cit. (loco citato, in the place cited) are two of the very convenient abbreviations used in the footnotes. Op. cit. or Loc. cit. after the writer’s name would suggest that the reference is to work by the writer which has been cited in detail in an earlier footnote but intervened by some other references. 7. Punctuation and abbreviations in footnotes: The first item after the number in the footnote is the author’s name, given in the normal signature order. This is followed by a comma. After the comma, the title of the book is given: the article (such as “A”, “An”, “The” etc.) is omitted and only the first word and proper nouns and adjectives are capitalized. The title is followed by a comma. Information concerning the edition is given next. This entry is followed by a comma. The place of publication is then stated; it may be mentioned in an abbreviated form, if the place happens to be a famous one such as Lond. for London, N.Y. for New York, N.D. for New Delhi and so on. This entry is followed by a comma. Then the name of the publisher is mentioned and this entry is closed by a comma. It is followed by the date of publication if the date is given on the title page. If the date appears in the copyright notice on the reverse side of the title page or elsewhere in the volume, the comma should be omitted and the date enclosed in square brackets [c 1978], [1978]. The entry is followed by a comma. Then follow the volume and page references and are separated by a comma if both are given. A period closes the complete documentary reference. But one should remember that the documentation regarding acknowledgements from magazine articles and periodical literature follow a different form as stated earlier while explaining the entries in the bibliography. Certain English and Latin abbreviations are quite often used in bibliographies and footnotes to eliminate tedious repetition. The following is a partial list of the most common abbreviations frequently used in report-writing (the researcher should learn to recognise them as well as he should learn to use them): anon., anonymous ante., before art., article aug., augmented bk., book bull., bulletin cf., compare ch., chapter col., column diss., dissertation ed., editor, edition, edited. ed. cit., edition cited e.g., exempli gratia: for example eng., enlarged et.al., and others

Interpretation and Report Writing 357 et seq., et sequens: and the following ex., example f., ff., and the following fig(s)., figure(s) fn., footnote ibid., ibidem: in the same place (when two or more successive footnotes refer to the same work, it is not necessary to repeat complete reference for the second id., idem: footnote. Ibid. may be used. If different pages are referred to, pagination ill., illus., or must be shown). illust(s). the same Intro., intro., l, or ll, illustrated, illustration(s) loc. cit., introduction loco citato: line(s) MS., MSS., in the place cited; used as op.cit., (when new reference N.B., nota bene: is made to the same pagination as cited in the previous note) n.d., Manuscript or Manuscripts n.p., note well no pub., no date no(s)., no place o.p., no publisher op. cit: number(s) opera citato out of print in the work cited (If reference has been made to a work p. or pp., and new reference is to be made, ibid., may be used, if intervening passim: reference has been made to different works, op.cit. must be used. The post: name of the author must precede. rev., page(s) tr., trans., here and there vid or vide: after viz., revised vol. or vol(s)., translator, translated, translation vs., versus: see, refer to namely volume(s) against 8. Use of statistics, charts and graphs: A judicious use of statistics in research reports is often considered a virtue for it contributes a great deal towards the clarification and simplification of the material and research results. One may well remember that a good picture is often worth more than

358 Research Methodology a thousand words. Statistics are usually presented in the form of tables, charts, bars and line-graphs and pictograms. Such presentation should be self explanatory and complete in itself. It should be suitable and appropriate looking to the problem at hand. Finally, statistical presentation should be neat and attractive. 9. The final draft: Revising and rewriting the rough draft of the report should be done with great care before writing the final draft. For the purpose, the researcher should put to himself questions like: Are the sentences written in the report clear? Are they grammatically correct? Do they say what is meant’? Do the various points incorporated in the report fit together logically? “Having at least one colleague read the report just before the final revision is extremely helpful. Sentences that seem crystal-clear to the writer may prove quite confusing to other people; a connection that had seemed self evident may strike others as a non-sequitur. A friendly critic, by pointing out passages that seem unclear or illogical, and perhaps suggesting ways of remedying the difficulties, can be an invaluable aid in achieving the goal of adequate communication.”6 10. Bibliography: Bibliography should be prepared and appended to the research report as discussed earlier. 11. Preparation of the index: At the end of the report, an index should invariably be given, the value of which lies in the fact that it acts as a good guide, to the reader. Index may be prepared both as subject index and as author index. The former gives the names of the subject-topics or concepts along with the number of pages on which they have appeared or discussed in the report, whereas the latter gives the similar information regarding the names of authors. The index should always be arranged alphabetically. Some people prefer to prepare only one index common for names of authors, subject-topics, concepts and the like ones. PRECAUTIONS FOR WRITING RESEARCH REPORTS Research report is a channel of communicating the research findings to the readers of the report. A good research report is one which does this task efficiently and effectively. As such it must be prepared keeping the following precautions in view: 1. While determining the length of the report (since research reports vary greatly in length), one should keep in view the fact that it should be long enough to cover the subject but short enough to maintain interest. In fact, report-writing should not be a means to learning more and more about less and less. 2. A research report should not, if this can be avoided, be dull; it should be such as to sustain reader’s interest. 3. Abstract terminology and technical jargon should be avoided in a research report. The report should be able to convey the matter as simply as possible. This, in other words, means that report should be written in an objective style in simple language, avoiding expressions such as “it seems,” “there may be” and the like. 4. Readers are often interested in acquiring a quick knowledge of the main findings and as such the report must provide a ready availability of the findings. For this purpose, charts, 6 Claire Selltiz and others, Research Methods in Social Relations rev., Methuen & Co. Ltd., London, 1959, p. 454.

Interpretation and Report Writing 359 graphs and the statistical tables may be used for the various results in the main report in addition to the summary of important findings. 5. The layout of the report should be well thought out and must be appropriate and in accordance with the objective of the research problem. 6. The reports should be free from grammatical mistakes and must be prepared strictly in accordance with the techniques of composition of report-writing such as the use of quotations, footnotes, documentation, proper punctuation and use of abbreviations in footnotes and the like. 7. The report must present the logical analysis of the subject matter. It must reflect a structure wherein the different pieces of analysis relating to the research problem fit well. 8. A research report should show originality and should necessarily be an attempt to solve some intellectual problem. It must contribute to the solution of a problem and must add to the store of knowledge. 9. Towards the end, the report must also state the policy implications relating to the problem under consideration. It is usually considered desirable if the report makes a forecast of the probable future of the subject concerned and indicates the kinds of research still needs to be done in that particular field. 10. Appendices should be enlisted in respect of all the technical data in the report. 11. Bibliography of sources consulted is a must for a good report and must necessarily be given. 12. Index is also considered an essential part of a good report and as such must be prepared and appended at the end. 13. Report must be attractive in appearance, neat and clean, whether typed or printed. 14. Calculated confidence limits must be mentioned and the various constraints experienced in conducting the research study may also be stated in the report. 15. Objective of the study, the nature of the problem, the methods employed and the analysis techniques adopted must all be clearly stated in the beginning of the report in the form of introduction. CONCLUSION In spite of all that has been stated above, one should always keep in view the fact report-writing is an art which is learnt by practice and experience, rather than by mere doctrination. Questions 1. Write a brief note on the ‘task of interpretation’ in the context of research methodology. 2. “Interpretation is a fundamental component of research process”, Explain. Why so? 3. Describe the precautions that the researcher should take while interpreting his findings. 4. “Interpretation is an art of drawing inferences, depending upon the skill of the researcher”. Elucidate the given statement explaining the technique of interpretation.

360 Research Methodology 5. “It is only through interpretation the researcher can expose the relations and processes that underlie his findings”. Explain, giving examples. 6. Explain the significance of a research report and narrate the various steps involved in writing such a report. 7. Describe, in brief, the layout of a research report, covering all relevant points. 8. Write a short note on ‘Documentation’ in the context of a research report. 9. Mention the different types of report, particularly pointing out the difference between a technical report and a popular report. 10. Explain the technique and importance of oral presentation of research findings. Is only oral presentation sufficient? If not, why? 11. (a) What points will you keep in mind while preparing a research report? Explain. (b)What are the different forms in which a research work may be reported. Describe. (M. Phil. Exam. (EAFM) 1979, Uni. of Rajasthan) 12. “We can teach methods of analysis, yet any extensive research... requires something equally important: an organisation or synthesis which provides the essential structure into which the pieces of analysis fit.” Examine this statement and show how a good research report may be prepared. (M. Phil. Exam. (EAFM) 1978, Uni. of Rajasthan) 13. Write short notes on the following: (a) The techniques of writing report; (b) Characteristics of a good research report; (c) Bibliography and its importance in context of research report; (d) Rewriting and polishing of report. 14. “Report writing is more an art that hinges upon practice and experience”. Discuss.

The Computer: Its Role in Research 361 15 The Computer: Its Role in Research INTRODUCTION Problem solving is an age old activity. The development of electronic devices, specially the computers, has given added impetus to this activity. Problems which could not be solved earlier due to sheer amount of computations involved can now be tackled with the aid of computers accurately and rapidly. Computer is certainly one of the most versatile and ingenious developments of the modern technological age. Today people use computers in almost every walk of life. No longer are they just big boxes with flashing lights whose sole purpose is to do arithmetic at high speed but they make use of studies in philosophy, psychology, mathematics and linguistics to produce output that mimics the human mind. The sophistication in computer technology has reached the stage that it will not be longer before it is impossible to tell whether you are talking to man or machine. Indeed, the advancement in computers is astonishing. To the researcher, the use of computer to analyse complex data has made complicated research designs practical. Electronic computers have by now become an indispensable part of research students in the physical and behavioural sciences as well as in the humanities. The research student, in this age of computer technology, must be exposed to the methods and use of computers. A basic understanding of the manner in which a computer works helps a person to appreciate the utility of this powerful tool. Keeping all this in view, the present chapter introduces the basics of computers, especially it. answers questions like: What is a computer? How does it function? How does one communicate with it? How does it help in analysing data? THE COMPUTER AND COMPUTER TECHNOLOGY A computer, as the name indicates, is nothing but a device that computes. In this sense, any device, however crude or sophisticated, that enables one to carry out mathematical manipulations becomes a computer. But what has made this term conspicuous today and, what we normally imply when we speak of computers, are electronically operating machines which are used to carry out computations.

362 Research Methodology In brief, computer is a machine capable of receiving, storing, manipulating and yielding information such as numbers, words, pictures. The computer can be a digital computer or it can be a analogue computer. A digital computer is one which operates essentially by counting (using information, including letters and symbols, in coded form) where as the analogue computer operates by measuring rather than counting. Digital computer handles information as strings of binary numbers i.e., zeros and ones, with the help of counting process but analogue computer converts varying quantities such as temperature and pressure into corresponding electrical voltages and then performs specified functions on the given signals. Thus, analogue computers are used for certain specialised engineering and scientific applications. Most computers are digital, so much so that the word computer is generally accepted as being synonymous with the term ‘digital computer’. Computer technology has undergone a significant change over a period of four decades. The present day microcomputer is far more powerful and costs very little, compared to the world’s first electronic computer viz. Electronic Numerical Integrator and Calculator (ENIAC) completed in 1946. The microcomputer works many times faster, is thousands of times more reliable and has a large memory. The advances in computer technology are usually talked in terms of ‘generations’.* Today we have the fourth generation computer in service and efforts are being made to develop the fifth generation computer, which is expected to be ready by 1990. The first generation computer started in 1945 contained 18000 small bottle-sized valves which constituted its central processing unit (CPU). This machine did not have any facility for storing programs and the instructions had to be fed into it by a readjustment of switches and wires. The second generation computer found the way for development with the invention of the transistor in 1947. The transistor replaced the valve in all electronic devices and made them much smaller and more reliable. Such computers appeared in the market in the early sixties. The third generation computer followed the invention of integrated circuit (IC) in 1959. Such machines, with their CPU and main store made of IC chips, appeared in the market in the second half of the sixties. The fourth generation computers owe their birth to the advent of microprocessor—the king of chips—in 1972. The use of microprocessor as CPU in a computer has made real the dream of ‘computer for the masses’. This device has enabled the development of microcomputers, personal computers, portable computers and the like. The fifth generation computer, which is presently in the developing stage, may use new switch (such as the High Electron Mobility Transistor) instead of the present one and it may herald the era of superconducting computer. It is said that fifth generation computer will be 50 times or so more faster than the present day superfast machines. So far as input devices in computers are concerned, the card or tape-based data entry system has almost been replaced by direct entry devices, such as Visual Display Unit (VDU) which consist of a TV-like screen and a typewriter-like key board which is used for feeding data into the computer. Regarding output devices, the teleprinter has been substituted by various types of low-cost high speed printers. VDU is also used as an output device. For storing data, the magnetic tapes and discs * (i) First generation computers were those produced between 1945–60 such as IBM 650, IBM 701. (ii) Second generation computers were those produced between 1960–65 such as IBM 1401 Honeywell 40. (iii) Third generation computers were those produced between 1965–70 such as IBM System 360, 370. (iv) Fourth generation computers are those produced between 1971 to this date such as IBM 3033, HP 3000, Burroughs B 7700.

The Computer: Its Role in Research 363 are being replaced by devices such as bubble memories and optical video discs. In brief, computer technology has become highly sophisticated and is being developed further at a very rapid speed. THE COMPUTER SYSTEM In general, all computer systems can be described as containing some kind of input devices, the CPU and some kind of output devices. Figure 15.1 depicts the components of a computer system and their inter-relationship: Central Processing Unit (CPU) Control Unit (Interprets the computer programme. Directs the operation of all components and units of the system) Input Devices Internal Storage Output Devices (Enters the computer (Holds the computer programme (Records result programme and data and data, and makes them received from into internal storage) available for processing) internal storage) Arithmetic-Logical Unit (Performs all arithmetic operations and logical comparisons) Instruction or data flow Control function Fig. 15.1 The function of the input-output devices is to get information into, and out of, the CPU. The input devices translate the characters into binary, understandable by the CPU, and the output devices retranslate them back into the familiar character i.e., in a human readable form. In other words, the purpose of the input-output devices is to act as translating devices between our external world and the internal world of the CPU i.e., they act as an interface between man and the machine. So far as CPU is concerned, it has three segments viz. (i) internal storage, (ii) control unit, and (iii) arithmetic logical unit. When a computer program or data is input into the CPU, it is in fact input into the internal storage of the CPU. The control unit serves to direct the sequence of computer system operation. Its function extends to the input and output devices as well and does not just remain confined to the sequence of operation within the CPU. The arithmetic logical unit is concerned with performing the arithmetic operations and logical comparisons designated in the computer program. In terms of overall sequence of events, a computer program is input into the internal storage and then transmitted to the control unit, where it becomes the basis for overall sequencing and control of computer system operations. Data that is input into the internal storage of the CPU is available for

364 Research Methodology processing by the arithmetic logical unit, which conveys the result of the calculations and comparisons back to the internal storage. After the designated calculations and comparisons have been completed, output is obtained from the internal storage of the CPU. It would be appropriate to become familiar with the following terms as well in context of computers: (a) Hardware: All the physical components (such as CPU, Input-output devices, storage devices, etc.) of computer are collectively called hardware. (b) Software: It consists of computer programs written by the user which allow the computer to execute instructions. (c) Firmware: It is that software which is incorporated by the manufacturer into the electronic circuitry of computer. (d) System software: It is that program which tells the computer how to function. It is also known as operating software and is normally supplied by the computer manufacturer. (e) Application software: It is that program which tells the computer how to perform specific tasks such as preparation of company pay roll or inventory management. This software is either written by the user himself or supplied by ‘software houses’, the companies whose business is to produce and sell software. (f) Integrated circuit (IC): It is a complete electronic circuit fabricated on a single piece of pure silicon. Silicon is the most commonly used semiconductor—a material which is neither a good conductor of electricity nor a bad one. An IC may be small-scale, medium-scale or a large-scale depending upon the number of electronic components fabricated on the chip. (g) Memory chips: These ICs form the secondary memory or storage of the computer. They hold data and instructions not needed immediately by the main memory contained in the CPU. (h) Two-state devices: The transistors on an IC Chip take only two states—they are either on or off, conducting or non-conducting. The on-state is represented by 1 and the off-state by zero. These two binary digits are called bits. A string of eight bits is termed byte and a group of bits constitute a word. A chip is called 8-bit, 16-bit, 32-bit and so on, depending on the number of bits contained in its standard word. IMPORTANT CHARACTERISTICS The following characteristics of computers are note worthy: (i) Speed: Computers can perform calculations in just a few seconds that human beings would need weeks to do by hand. This has led to many scientific projects which were previously impossible. (ii) Diligence: Being a machine, a computer does not suffer from the human traits of tireness and lack of concentration. If two million calculations have to be performed, it will perform the two millionth with exactly the same accuracy and speed as the first. (iii) Storage: Although the storage capacity of the present day computer is much more than its earlier counterpart but even then the internal memory of the CPU is only large enough to retain a certain amount of information just as the human brain selects and retains what it feels to be important and relegates unimportant details to the back of the mind or just

The Computer: Its Role in Research 365 forgets them. Hence, it is impossible to store all types of information inside the computer records. If need be, all unimportant information/data can be stored in auxiliary storage devices and the same may be brought into the main internal memory of the computer, as and when required for processing. (iv) Accuracy: The computer’s accuracy is consistently high. Errors in the machinery can occur but, due to increased efficiency in error-detecting techniques, these seldom lead to false results. Almost without exception, the errors in computing are due to human rather than to technological weaknesses, i.e., due to imprecise thinking by the programmer or due to inaccurate data or due to poorly designed systems. (v) Automation: Once a program is in the computer’s memory, all that is needed is the individual instructions to it which are transferred one after the other, to the control unit for execution. The CPU follows these instructions until it meets a last instruction which says ‘stop program execution’. (vi) Binary digits: Computers use only the binary number system (a system in which all the numbers are represented by a combination of two digits—one and zero) and thus operates to the base of two, compared to the ordinary decimal arithmetic which operates on a base of ten. (Binary system has been described in further details under separate heading in this chapter.) Computers use binary system because the electrical devices can understand only ‘on’ (1) or ‘off’ (0). THE BINARY NUMBER SYSTEM An arithmetic concept which uses two levels, instead of ten, but operates on the same logic is called the binary system. The binary system uses two symbols ‘0’ and ‘1’, known as bits, to form numbers. The base of this number system is 2. The system is called binary because it allows only two symbols for the formation of numbers. Binary numbers can be constructed just like decimal numbers except that the base is 2 instead of 10. For example, 523 (decimal) = 5 × 102 + 2 × 101 + 3 × 100 Similarly, 111 (binary) = 1 × 22 + 1 × 21 + 1 × 20 = 7 (decimal) Thus, in the example, we see that in the decimal system, the first place is for 1s, 2nd place is for 10s and the 3rd place is for 100. On the other hand, in the binary system, the factor being 2 instead of 10, the first place is still for 1s but the 2nd place is for 2s, the 3rd for 4s, the 4th for 8s and so on. Decimal to Binary Conversion: A positive decimal integer can be easily converted to equivalent binary form by repeated division by 2. The method works as follows: Start by dividing the given decimal integer by 2. Let R1 be the remainder and ql the quotient. Next, divide q by 2 and let R and q be the remainder and quotient respectively. Continue this l 22 process of division by 2 until a 0 is obtained as quotient. The equivalent binary number can be formed by arranging the remainders as Rk Rk –1 ... R1 where Rk and R1 are the last and the first remainders respectively, obtained by the division process.

366 Research Methodology Illustration 1 Remainder Find the binary equivalents of 26 and 45. 0 Solution: Table for conversion of 26 into its Binary equivalent: 1 0 Number to be Quotient 1 divided by 2 1 26 13 13 6 63 31 10 Collecting the remainders obtained in the above table we find that 26(decimal) =11010 (binary) or (26)10 = (11010)2 Similarly, we can find the binary equivalent of 45 as under: Table 15.1 Number to be Quotient Remainder divided by 2 22 1 45 11 0 22 5 1 11 2 1 5 1 0 2 0 1 1 Thus, we have (45)10 = (101101)2 i.e., the binary equivalent of 45 is 101101. Alternative method: Another simple method for decimal to binary conversion is to first express the given integer as a sum of powers of 2, written in ascending order. For example, 26 = 16 + 8 + 0 + 2 + 0 = 1 × 24 + 1 × 23 + 0 × 22 + 1 × 21 + 0 × 20 Then collect the multipliers of the powers to form the binary equivalent. For 26, we get, from the above mentioned expansion 11010 as the binary equivalent. This alternative method is convenient for converting small decimal integers by hand. Binary to Decimal Conversion: A simple method for converting a binary number to its decimal equivalent is known as double-babble method. This can be described as follows:

The Computer: Its Role in Research 367 Begin the conversion process by doubling the leftmost bit of the given number and add to it the bit at its right. Then again double the sum and add to it the third bit from the left. Proceed in this manner till all the bits have been considered. The final sum obtained by repeated doubling and adding is the desired decimal equivalent. Illustration 2 Convert 1101 to its decimal equivalent using the double-babble method. Solution: 1. Doubling the leftmost bit we get 2. 2. Adding to it the bit on its right we get 2 + 1 = 3 3. Doubling again the number obtained we get 6 4. Adding to it the next bit we get 6 + 0 = 6 5. Again doubling we get 12 6. Finally adding the last bit we get 12 + 1 = 13 Thus, we have (1101)2 = (13)10 In other words, the decimal equivalent of binary 1101 is 13. (Conversion of real number to binary number is also possible but it involves little bit more complicated conversion process. Those interested may read any binary system book.) Computations in Binary System (a) Binary addition: Binary addition is just like decimal addition except that the rules are much simpler. The binary addition rules are as shown below: 0011 +0 +1 +0 +1 0 1 1 10 Note that sum of 1 and 1 is written as ‘10’ (a zero sum with a 1 carry) which is the equivalent of decimal digit ‘2’. We can now look at two examples of binary additions which make use of the above rules. Illustration 3 Add 1010 and 101. Solution: Binary Decimal equivalent 1010 (10) +101 +(5) 1111 (15) Illustration 4 Add 10111000 and 111011.

368 Research Methodology Solution: Carry 111 Carry 11 10111000 184 + 111011 + 59 11110011 243 In Illustration 4, we find a new situation (1 + 1 + 1) brought about by the 1 carry. However, we can still handle this by using the four combinations already mentioned. We add the digits in turn. 1 + 1 = 10 (a zero sum with a 1 carry). The third 1 is now added to this result to obtain 11 (a 1 sum with a 1 carry). The computer performs all the other arithmetical operations (viz. ×, –, +) by a form of addition. This is easily seen in the case of multiplication, e.g., 6 × 8 may be thought of as essentially being determined by evaluating, with necessary carry overs, 8 + 8 + 8 + 8 + 8 + 8. This idea of repeated addition may seem to be a longer way of doing things, but remember that computer is well suited to carry out the operation at great speed. Subtraction and division are handled essentially by addition using the principle of complementing. (b) Complementary subtraction: Three steps are involved in this method: Step 1. Find the ones complement of the number you are subtracting; Step 2. Add this to number from which you are taking away; Step 3. If there is a carry of 1 add it to obtain the result; if there is no carry, add 0, recomplement and attach a negative sign to obtain the result. Following two examples illustrate this method. Illustration 5 Subtract 10 from 25. Solution: Decimal Binary number According to complementary method number 11001 + 10101 (Ones complement of 01010) 25 11001 Subtract 10 01010 Step 1 15 Step 2 101110 Step 3 1 (add the carry of 1) Result 1111 Its decimal equivalent is 15. Illustration 6 Subtract 72 from 14.

The Computer: Its Role in Research 369 Solution: Binary According to complementary method Decimal number number 0001110 Step 1. 0001110 14 1001000 + 0110111 (ones complement of 1001000) Subtract 72 –58 Step 2. 01000101 Step 3. 0 (add 0 as no carry) Result 1000101 (recomplement and attach a – 0111010 negative sign). Its decimal equivalent is –58. The computer performs the division operation essentially by repeating this complementary subtraction method. For example, 45 ÷ 9 may be thought of as 45 – 9 = 36 – 9 = 27 – 9 = 18 – 9 = 9 – 9 = 0 (minus 9 five times). Binary Fractions Just as we use a decimal point to separate the whole and decimal fraction parts of a decimal number, we can use a binary point in binary numbers to separate the whole and fractional parts. The binary fraction can be converted into decimal fraction as shown below: 0.101 (binary) = (1 × 2–1) + (0 × 2–2)+ (1 × 2–3) = 0.5 + 0.0 + 0.125 = 0.625 (decimal) To convert the decimal fraction to binary fraction, the following rules are applied: (i) Multiply the decimal fraction repeatedly by 2. The whole number part of the first multiplication gives the first 1 or 0 of the binary fraction; (ii) The fractional part of the result is carried over and multiplied by 2; (iii) The whole number part of the result gives the second 1 or 0 and so on. Illustration 7 Convert 0.625 into its equivalent binary fraction. Solution: Applying the above rules, this can be done as under: 0.625 × 2 = 1.250 → 1 0.250 × 2 = 0.500 → 0 0.500 × 2 = 1.000 → 1 Hence, 0.101 is the required binary equivalent.

370 Research Methodology Illustration 8 Convert 3.375 into its equivalent binary number. Solution: This can be done in two stages. First (3)10 = (11)2 as shown earlier. Secondly, (0.375)10 = (0.011)2 as shown above. Hence, the required binary equivalent is 11.011. From all this above description we find how computer arithmetic is based on addition. Exactly how this simplifies matters can only be understood in the context of binary (not in decimal). The number of individual steps may indeed be increased because all computer arithmetic is reduced to addition, but the computer can carry out binary additions at such great speed that this is not a disadvantage. COMPUTER APPLICATIONS At present, computers are widely used for varied purposes. Educational, commercial, industrial, administrative, transport, medical, social financial and several other organisations are increasingly depending upon the help of computers to some degree or the other. Even if our work does not involve the use of computers in our everyday work, as individuals, we are affected by them. “The motorists, the air passenger, hospital patients and those working in large departmental stores, are some of the people for whom computers process information. Everyone who pays for electricity or telephone has their bills processed by computers. Many people who are working in major organisations and receive monthly salary have their salary slips prepared by computers. Thus, it is difficult to find anyone who in some way or the other does not have some information concerning them processed by computer”.1 “Computers can be used by just about anyone: doctors, policemen, pilots, scientists, engineers and recently even house-wives. Computers are used not only in numeric applications but also in non- numeric applications such as proving theorems, playing chess, preparing menu, matrimonial match- making and so on. Without computers we might not have achieved a number of things. For example, man could not have landed on the moon nor could he have launched satellites. We might not have built 100 storied buildings or high speed trains and planes.”2 The following table depicts some of the important applications and uses of computers: Table 15.2 Applications in Some of the various uses 1. Education (i) Provide a large data bank of information; (ii) Aid to time-tabling; (iii) Carry out lengthy or complex calculations; (iv) Assist teaching and learning processes; (v) Provide students’ profiles; (vi) Assist in career guidance. ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ Contd. 1 N. Subramanian, “Introduction to Computers”, Tata McGraw-Hill Publishing Company Ltd., New Delhi, 1986, p. 192. 2 Ibid., p. 192–93.

The Computer: Its Role in Research 371 Applications in Some of the various uses 2. Commerce (i) Assist the production of text material (known as word processing) 3. Banks and Financial such as reports, letters, circulars etc. institutions (ii) Handle payroll of personnel, office accounts, invoicing, records 4. Management keeping, sales analysis, stock control and financial forecasting. 5. Industry (i) Cheque handling; (ii) Updating of accounts; 6. Communications (iii) Printing of customer statements; and Transportation (iv) Interest calculations. (i) Planning of new enterprises; 7. Scientific Research (ii) Finding the best solution from several options; 8. The homes (iii) Helpful in inventory management, sales forecasting and production planning; (iv) Useful in scheduling of projects. (i) In process control; (ii) In production control; (iii) Used for load control by electricity authorities; (iv) Computer aided designs to develop new products. (i) Helpful in electronic mail; (ii) Useful in aviation: Training of pilots, seat reservations, provide information to pilots about weather conditions; (iii) Facilitate routine jobs such as crew schedules, time-tables, maintenance schedules, safety systems, etc.; (iv) Helpful to railways, shipping companies; (v) Used in traffic control and also in space flight. (i) Model processing; (ii) Performing computations; (iii) Research and data analysis. (i) Used for playing games such as chess, draughts, etc.; (ii) Can be used as an educational aid; (iii) Home management is facilitated. COMPUTERS AND RESEARCHERS Performing calculations almost at the speed of light, the computer has become one of the most useful research tools in modern times. Computers are ideally suited for data analysis concerning large research projects. Researchers are essentially concerned with huge storage of data, their faster retrieval when required and processing of data with the aid of various techniques. In all these operations, computers are of great help. Their use, apart expediting the research work, has reduced human drudgery and added to the quality of research activity.

372 Research Methodology Researchers in economics and other social sciences have found, by now, electronic computers to constitute an indispensable part of their research equipment. The computers can perform many statistical calculations easily and quickly. Computation of means, standard deviations, correlation coefficients, ‘t’ tests, analysis of variance, analysis of covariance, multiple regression, factor analysis and various nonparametric analyses are just a few of the programs and subprograms that are available at almost all computer centres. Similarly, canned programs for linear programming, multivariate analysis, monte carlo simulation etc. are also available in the market. In brief, software packages are readily available for the various simple and complicated analytical and quantitative techniques of which researchers generally make use of. The only work a researcher has to do is to feed in the data he/she gathered after loading the operating system and particular software package on the computer. The output, or to say the result, will be ready within seconds or minutes depending upon the quantum of work. Techniques involving trial and error process are quite frequently employed in research methodology. This involves lot of calculations and work of repetitive nature. Computer is best suited for such techniques, thus reducing the drudgery of researchers on the one hand and producing the final result rapidly on the other. Thus. different scenarios are made available to researchers by computers in no time which otherwise might have taken days or even months. The storage facility which the computers provide is of immense help to a researcher for he can make use of stored up data whenever he requires to do so. Thus, computers do facilitate the research work. Innumerable data can be processed and analyzed with greater ease and speed. Moreover, the results obtained are generally correct and reliable. Not only this, even the design, pictorial graphing and report are being developed with the help of computers. Hence, researchers should be given computer education and be trained in the line so that they can use computers for their research work. Researchers interested in developing skills in computer data analysis, while consulting the computer centers and reading the relevant literature, must be aware of the following steps: (i) data organisation and coding; (ii) storing the data in the computer; (iii) selection of appropriate statistical measures/techniques; (iv) selection of appropriate software package; (v) execution of the computer program. A brief mention about each of the above steps is appropriate and can be stated as under: First of all, researcher must pay attention toward data organisation and coding prior to the input stage of data analysis. If data are not properly organised, the researcher may face difficulty while analysing their meaning later on. For this purpose the data must be coded. Categorical data need to be given a number to represent them. For instance, regarding sex, we may give number 1 for male and 2 for female; regarding occupation, numbers 1, 2, and 3 may represent Farmer, Service and Professional respectively. The researcher may as well code interval or ratio data. For instance, I.Q. Level with marks 120 and above may be given number 1, 90–119 number 2, 60–89 number 3, 30–59 number 4 and 29 and below number 5. Similarly, the income data classified in class intervals such as Rs. 4000 and above, Rs. 3000–3999, Rs. 2000–2999 and below Rs. 2000 may respectively be represented or coded as 1, 2, 3 and 4. The coded data are to be put in coding forms (most systems

The Computer: Its Role in Research 373 call for a maximum of 80 columns per line in such forms) at the appropriate space meant for each variable. Once the researcher knows how many spaces each variable will occupy, the variables can be assigned to their column numbers (from 1 to 80). If more than 80 spaces are required for each subject, then two or more lines will need to be assigned. The first few columns are generally devoted for subject identity number. Remaining columns are used for variables. When large number of variables are used in a study, separating the variables with spaces make the data easier to comprehend and easier for use with other programs. Once the data is coded, it is ready to be stored in the computer. Input devices may be used for the purpose. After this, the researcher must decide the appropriate statistical measure(s) he will use to analyse the data. He will also have to select the appropriate program to be used. Most researchers prefer one of the canned programs easily available but others may manage to develop it with the help of some specialised agency. Finally, the computer may be operated to execute instructions. The above description indicates clearly the usefulness of computers to researchers in data analysis. Researchers, using computers, can carry on their task at faster speed and with greater reliability. The developments now taking place in computer technology will further enhance and facilitate the use of computers for researchers. Programming knowledge would no longer remain an obstacle in the use of a computer. In spite of all this sophistication we should not forget that basically computers are machines that only compute, they do not think. The human brain remains supreme and will continue to be so for all times. As such, researchers should be fully aware about the following limitations of computer-based analysis: 1. Computerised analysis requires setting up of an elaborate system of monitoring, collection and feeding of data. All these require time, effort and money. Hence, computer based analysis may not prove economical in case of small projects. 2. Various items of detail which are not being specifically fed to computer may get lost sight of. 3. The computer does not think; it can only execute the instructions of a thinking person. If poor data or faulty programs are introduced into the computer, the data analysis would not be worthwhile. The expression “garbage in, garbage out” describes this limitation very well. Questions 1. What is a computer? Point out the difference between a digital computer and analogue computer. 2. How are computers used as a tool in research? Explain giving examples. 3. Explain the meaning of the following terms in context of computers: (a) Hardware and Software (b) The binary number system (c) Computer generations (d) Central Processing Unit. 4. Describe some of the important applications and uses of computers in present times.

374 Research Methodology 5. “The advancement in computers is astonishing”. Do you agree? Answer pointing out the various characteristics of computers. 6. Write a note on “Computers and Researchers”. 7. “Inspite of the sophistication achieved in computer technology, one should not forget that basically computers are machines that only compute, they do not think”. Comment. 8. Add 110011 and 1011. State the decimal equivalent of the sum you arrive at. 9. Explain the method of complementary subtraction. Subtract 15 from 45 and 85 from 68 through this method using the binary equivalents of the given decimal numbers. 10. Workout the decimal equivalents of the following binary numbers: (a) 111.110 (b) 0.111 and binary equivalents of the following decimal numbers: (a) 4.210 (b) 0.745 11. Convert 842 to binary and 10010101001 to decimal. Why binary system is being used in computer? 12. What do you understand by storage in a computer and how is that related to the generations?

Appendix 375 Appendix (Selected Statistical Tables)

376 Research Methodology Table 1: Area Under Normal Curve 1 An entry in the table is the proportion under the 02 entire curve which is between z = 0 and a positive value of z. Areas for negative values for z are obtained by symmetry. Areas of a standard normal distribution z .0 0.01 .02 .03 .04 .05 .06 .07 .08 .09 .0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359 .1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753 .2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141 .3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517 .4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879 .5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224 .6 .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2517 .2549 .7 .2580 .2611 .2642 .2673 .2903 .2734 .2764 .2794 .2823 .2852 .8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133 .9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 .3389 1.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 .3577 .3599 .3621 1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830 1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015 1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177 1.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319 1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441 1.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545 1.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633 1.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706 1.9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767 2.0 .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .4817 2.1 .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857 2.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .4890 2.3 .4893 .4896 .4898 .4901 .4904 .4906 .4909 .4911 .4913 .4916 2.4 .4918 .4920 .4922 .4925 .4927 .4929 .4931 .4932 .4934 .4936 2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .4952 2.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964 2.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974 2.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .4981 2.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .4986 3.0 .4987 .4987 ..4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990