RESEARCH METHODOLOGY-Final with alighment

and then the superior one (i.e., one with a higher percentage) with R. For example, A market survey was conducted to find out consumer’s preference for the network service provider brands, A and B. The outcome of the survey was as follows:  Brand ‘A’ = 57%  Brand ‘B’ = 43% Thus, it is visible that the consumers prefer brand ‘A’, over brand ‘B’. c. Rank Order In rank order scaling the respondent needs to rank or arrange the given objects according to his or her preference. For example, A soap manufacturing company conducted a rank order scaling to find out the orderly preference of the consumers. It asked the respondents to rank the following brands in the sequence of their choice: SOAP BRANDS RANK Brand V 4 Brand X 2 Brand Y 1 Brand Z 3 The above scaling shows that soap ‘Y’ is the most preferred brand, followed by soap ‘X’, then soap ‘Z’ and the least preferred one is the soap ‘V’. d. Constant Sum It is a scaling technique where a continual sum of units like dollars, points, chits, chips, etc. is given to the features, attributes and importance of a particular product or service by the respondents. For example, the respondents belonging to 3 different segments were asked to allocate 50 points to the following attributes of a cosmetic product ‘P’: ATTRIBUTES SEGMENT 1 SEGMENT 2 SEGMENT 3 Finish 11 8 9 Skin Friendly 11 12 12 Fragrance 7 11 8 Packaging 9 8 10 Price 12 11 11 101 CU IDOL SELF LEARNING MATERIAL (SLM)

From the above constant sum scaling analysis, we can see that:  Segment 1 considers product ‘P’ due to its competitive price as a major factor.  But segment 2 and segment 3, prefers the product because it is skin-friendly. e. Q-Sort Scaling Q-sort scaling is a technique used for sorting the most appropriate objects out of a large number of given variables. It emphasizes on the ranking of the given objects in a descending order to form similar piles based on specific attributes. It is suitable in the case where the number of objects is not less than 60 and more than 140, the most appropriate of all ranging between 60 to 90. For example, The marketing manager of a garment manufacturing company sorts the most efficient marketing executives based on their past performance, sales revenue generation, dedication and growth. The Q-sort scaling was performed on 60 executives, and the marketing head creates three piles based on their efficiency as follows: Figure 9.3 Q-Sort Scaling In the above diagram, the initials of the employees are used to denote their names. f. Non-Comparative Scales A non-comparative scale is used to analyses the performance of an individual product or object on different parameters. Following are some of its most common types: g. Continuous Rating Scales It is a graphical rating scale where the respondents are free to place the object at a position of their choice. It is done by selecting and marking a point along the vertical or horizontal line which ranges between two extreme criteria. 102 CU IDOL SELF LEARNING MATERIAL (SLM)

For example, A mattress manufacturing company used a continuous rating scale to find out the level of customer satisfaction for its new comfy bedding. The response can be taken in the following different ways (stated as versions here): Figure 9.4 Continuous Rating Scale The above diagram shows a non-comparative analysis of one particular product, i.e. comfy bedding. Thus, making it very clear that the customers are quite satisfied with the product and its features. h. Itemized Rating Scale Itemized scale is another essential technique under the non-comparative scales. It emphasizes on choosing a particular category among the various given categories by the respondents. Each class is briefly defined by the researchers to facilitate such selection. The three most commonly used itemized rating scales are as follows: i. Likert Scale: In the Likert scale, the researcher provides some statements and ask the respondents to mark their level of agreement or disagreement over these statements by selecting any one of the options from the five given alternatives. For example, A shoes manufacturing company adopted the Likert scale technique for its new sports shoe range named Z sports shoes. The purpose is to know the agreement or disagreement of the respondents. For this, the researcher asked the respondents to circle a number representing the most suitable answer according to them, in the following representation:  1 - Strongly Disagree  2 - Disagree  3 - Neither Agree Nor Disagree 103 CU IDOL SELF LEARNING MATERIAL (SLM)

 4 - Agree  5 - Strongly Agree ii. Semantic Differential Scale: A bi-polar seven-point non-comparative rating scale is where the respondent can mark on any of the seven points for each given attribute of the object as per personal choice. Thus, depicting the respondent’s attitude or perception towards the object. For example, A well-known brand for watches, carried out semantic differential scaling to understand the customer’s attitude towards its product. The pictorial representation of this technique is as follows: Figure 9.5 Semantic Differential Scale From the above diagram, we can analyze that the customer finds the product of superior quality; however, the brand needs to focus more on the styling of its watches. iii. Staple Scale: A Stapel scale is that itemized rating scale which measures the response, perception or attitude of the respondents for a particular object through a unipolar rating. The range of a Stapel scale is between -5 to +5 eliminating 0, thus confining to 10 units. For example, A tours and travel company asked the respondent to rank their holiday package in terms of value for money and user-friendly interface as follows: 104 CU IDOL SELF LEARNING MATERIAL (SLM)

Figure 9.6 Stapel Scale With the help of the above scale, we can say that the company needs to improve its package in terms of value for money. However, the decisive point is that the interface is quite user-friendly for the customers. RATING AND RANKING SCALES RATING SCALE Rating scale is defined as a closed-ended survey question used to represent respondent feedback in a comparative form for specific particular features/products/services. It is one of the most established question types for online and offline surveys where survey respondents are expected to rate an attribute or feature. Rating scale is a variant of the popular multiple-choice question which is widely used to gather information that provides relative information about a specific topic. Researchers use a rating scale in research when they intend to associate a qualitative measure with the various aspects of a product or feature. Generally, this scale is used to evaluate the performance of a product or service, employee skills, customer service performances, processes followed for a particular goal etc. Rating scale survey question can be compared to a checkbox question but rating scale provides more information than merely Yes/No. Types of Rating Scale Broadly speaking, rating scales can be divided into two categories: Ordinal and Interval Scales.  An ordinal scale is a scale the depicts the answer options in an ordered manner. The difference between the two-answer option may not be calculable but the answer options will always be in a certain innate order. Parameters such as attitude or feedback can be presented 105 CU IDOL SELF LEARNING MATERIAL (SLM)

using an ordinal scale.  An interval scale is a scale where not only is the order of the answer variables established but the magnitude of difference between each answer variable is also calculable. Absolute or true zero value is not present in an interval scale. Temperature in Celsius or Fahrenheit is the most popular example of an interval scale. Net Promoter Score, Likert Scale, Bipolar Matrix Table are some of the most effective types of interval scale. There are four primary types of rating scales which can be suitably used in an online survey:  Graphic Rating Scale  Numerical Rating Scale  Descriptive Rating Scale  Comparative Rating Scale (a) Graphic Rating Scale: Graphic rating scale indicates the answer options on a scale of 1-3, 1-5, etc. Likert Scale is a popular graphic rating scale example. Respondents can select a particular option on a line or scale to depict rating. This rating scale is often implemented by HR managers to conduct employee evaluation.5 point Likert scale for satisfaction (b) Numerical Rating Scale: Numerical rating scale has numbers as answer options and not each number corresponds to a characteristic or meaning. For instance, a Visual Analog Scale or a Semantic Differential Scale can be presented using a numerical rating scale (c) Descriptive Rating Scale: In a descriptive rating scale, each answer option is elaborately explained for the respondents. A numerical value is not always related to the answer options in the descriptive rating scale. There are certain surveys, for example, a customer satisfaction survey, which needs to describe all the answer options in detail so that every customer has thoroughly explained information about what is expected from the survey. (d) Comparative Rating Scale: Comparative rating scale, as the name suggests, expects respondents to answer a particular question in terms of comparison, i.e. on the basis of relative measurement or keeping other organizations/products/features as a reference. RANKING SCALE A ranking scale is a survey question tool that measures people’s preferences by asking them to rank their views on a list of related items. Using these scales can help your business establish what matters and what doesn’t matter to either external or internal stakeholders. You could use ranking scale questions to evaluate customer satisfaction or to assess ways to motivate your employees, for example. Ranking scales can be a source of useful information, but they do have some disadvantages. Businesses typically use ranking scales when they want to establish preferences or levels of 106 CU IDOL SELF LEARNING MATERIAL (SLM)

importance in a group of items. A respondent completing a scale with five items, for example, will assign a number 1 through 5 to each individual one. Typically, the number 1 goes to the item that is most important to the respondent; the number 5 goes to the one that is of least importance. In some cases, scales do not force respondents to rank all items, asking them to choose their top three out of the five, for example. Online surveys may remove the need to key in numbers, allowing respondents to drag and drop items into order. Advantages of Ranking Scales Ranking scales give you an insight into what matters to your respondents. Each response to an item has an individual value, giving results that you can easily average and rank numerically. This can be a valuable business tool, as it gives a statistical breakdown of your audience’s preferences based on what you need to know. If you are making business decisions and have various options to choose from, data from a ranking scale might give you a clearer insight into how to satisfy your audience based on what is important to them. SCALE CONSTRUCTION TECHNIQUES Scale construction techniques in research methodology helps in social science studies, while measuring attitudes of the people we generally follow the technique of preparing the opinionnaire* (or attitude scale) in such a way that the score of the individual responses assigns him a place on a scale. Under this approach, the respondent expresses his agreement or disagreement with a number of statements relevant to the issue. While developing such statements, the researcher must note the following two points:  That the statements must elicit responses which are psychologically related to the attitude being measured;  That the statements need be such that they discriminate not merely between extremes of attitude but also among individuals who differ slightly. Researchers must as well be aware that inferring attitude from what has been recorded in opinionnaires has several limitations. People may conceal their attitudes and express socially acceptable opinions. They may not really know how they feel about a social issue. People may be unaware of their attitude about an abstract situation; until confronted with a real situation, they may be unable to predict their reaction. Even behavior itself is at times not a true indication of attitude. For instance, when politicians kiss babies, their behavior may not be a true expression of affection toward infants. Thus, there is no sure method of measuring attitude; we only try to measure the expressed opinion and then draw inferences from it about people’s real feelings or attitudes. With all these limitations in mind, psychologists and sociologists have developed several scale construction techniques for the 107 CU IDOL SELF LEARNING MATERIAL (SLM)

purpose. The researcher should know these techniques so as to develop an appropriate scale for his own study. Some of the important approaches, along with the corresponding scales developed under each approach to measure attitude are as follows: Different Scales for Measuring Attitudes of People Figure 9.7 Different Scales for Measuring Attitudes of People Arbitrary scale in Research Methodology Arbitrary scales are developed on ad hoc basis and are designed largely through the researcher’s own subjective selection of items. The researcher first collects few statements or items which he believes are unambiguous and appropriate to a given topic. Some of these are selected for inclusion in the measuring instrument and then people are asked to check in a list the statements with which they agree. The chief merit of such scales is that they can be developed very easily, quickly and with relatively less expense. They can also be designed to be highly specific and adequate. Because of these benefits, such scales are widely used in practice. Differential Scales (or Thurstone-type Scales) The name of L.L. Thurstone is associated with differential scales which have been developed using consensus scale approach. Under such an approach the selection of items is made by a panel of judges who evaluate the items in terms of whether they are relevant to the topic area and unambiguous in implication. The detailed procedure is as under:  The researcher gathers a large number of statements, usually twenty or more, that express various points of view toward a group, institution, idea, or practice (i.e., statements belonging to the topic area).  These statements are then submitted to a panel of judges, each of whom arranges them in 108 CU IDOL SELF LEARNING MATERIAL (SLM)

eleven groups or piles ranging from one extreme to another in position. Each of the judges is requested to place generally in the first pile the statements which he thinks are most unfavorable to the issue, in the second pile to place those statements which he thinks are next most unfavorable and he goes on doing so in this manner till in the eleventh pile he puts the statements which he considers to be the most favorable.  This sorting by each judge yields a composite position for each of the items. In case of marked disagreement between the judges in assigning a position to an item, that item is discarded.  For items that are retained, each is given its median scale value between one and eleven as established by the panel. In other words, the scale value of any one statement is computed as the ‘median’ position to which it is assigned by the group of judges.  A final selection of statements is then made. For this purpose a sample of statements, whose median scores are spread evenly from one extreme to the other is taken. The statements so selected, constitute the final scale to be administered to respondents. The position of each statement on the scale is the same as determined by the judges. After developing the scale as stated above, the respondents are asked during the administration of the scale to check the statements with which they agree. The median value of the statements that they check is worked out and this establishes their score or quantifies their opinion. It may be noted that in the actual instrument the statements are arranged in random order of scale value. If the values are valid and if the opinionnaire deals with only one attitude dimension, the typical respondent will choose one or several contiguous items (in terms of scale values) to reflect his views. However, at times divergence may occur when a statement appears to tap a different attitude dimension. The Thurstone method has been widely used for developing differential scales which are utilized to measure attitudes towards varied issues like war, religion, etc. Such scales are considered most appropriate and reliable when used for measuring a single attitude. But an important deterrent to their use is the cost and effort required to develop them. Another weakness of such scales is that the values assigned to various statements by the judges may reflect their own attitudes. The method is not completely objective; it involves ultimately subjective decision process. Critics of this method also opine that some other scale designs give more information about the respondent’s attitude in comparison to differential scales. Summated Scales (or Likert-type Scales) Summated scales (or Likert-type scales) are developed by utilizing the item analysis approach wherein a particular item is evaluated on the basis of how well it discriminates between those persons whose total score is high and those whose score is low. Those items or statements that best meet this sort of discrimination test are included in the final instrument. 109 CU IDOL SELF LEARNING MATERIAL (SLM)

Thus, summated scales consist of a number of statements which express either a favorable or unfavorable attitude towards the given object to which the respondent is asked to react. The respondent indicates his agreement or disagreement with each statement in the instrument. Each response is given a numerical score, indicating its favorableness or unfavourableness, and the scores are totaled to measure the respondent’s attitude. In other words, the overall score represents the respondent’s position on the continuum of favorable-unfavourableness towards an issue. Most frequently used summated scales in the study of social attitudes follow the pattern devised by Likert. For this reason they are often referred to as Likert-type scales. In a Likert scale, the respondent is asked to respond to each of the statements in terms of several degrees, usually five degrees (but at times 3 or 7 may also be used) of agreement or disagreement. For example, when asked to express opinion whether one considers his job quite pleasant, the respondent may respond in any one of the following ways:  strongly agree,  agree,  undecided,  disagree,  strongly disagree. We find that these five points constitute the scale. At one extreme of the scale there is strong agreement with the given statement and at the other, strong disagreement, and between them lie intermediate points. We may illustrate this as under: Figure 9.8 Summated Scales (or Likert-type Scales) Each point on the scale carries a score. Response indicating the least favorable degree of job satisfaction is given the least score (say 1) and the most favorable is given the highest score (say 5). These score—values are normally not printed on the instrument but are shown here just to indicate the scoring pattern. The Likert scaling technique, thus, assigns a scale value to each of the five responses. The same thing is done in respect of each and every statement in the instrument. This way the instrument yields a total score for each respondent, which would then measure the respondent’s favorableness toward the given point of view. If the instrument consists of, say 30 statements, the following score values would be revealing. 110 CU IDOL SELF LEARNING MATERIAL (SLM)

 30 × 5 = 150 Most favorable response possible  30 × 3 = 90 A neutral attitude  30 × 1 = 30 Most unfavorable attitude. The scores for any individual would fall between 30 and 150. If the score happens to be above 90, it shows favorable opinion to the given point of view, a score of below 90 would mean unfavorable opinion and a score of exactly 90 would be suggestive of a neutral attitude. Procedure: The procedure for developing a Likert-type scale is as follows:  As a first step, the researcher collects a large number of statements which are relevant to the attitude being studied and each of the statements expresses definite favorableness or unfavourableness to a particular point of view or the attitude and that the number of favorable and unfavorable statements is approximately equal.  After the statements have been gathered, a trial test should be administered to a number of subjects. In other words, a small group of people, from those who are going to be studied finally, are asked to indicate their response to each statement by checking one of the categories of agreement or disagreement using a five point scale as stated above.  The response to various statements is scored in such a way that a response indicative of the most favorable attitude is given the highest score of 5 and that with the most unfavorable attitude is given the lowest score, say, of 1.  Then the total score of each respondent is obtained by adding his scores that he received for separate statements.  The next step is to array these total scores and find out those statements which have a high discriminatory power. For this purpose, the researcher may select some part of the highest and the lowest total scores, say the top 25 per cent and the bottom 25 per cent. These two extreme groups are interpreted to represent the most favorable and the least favorable attitudes and are used as criterion groups by which to evaluate individual statements. This way we determine which statements consistently correlate with low favorability and which with high favorability.  Only those statements that correlate with the total test should be retained in the final instrument and all others must be discarded from it. Advantages: The Likert-type scale has several advantages. Mention may be made of the important ones.  It is relatively easy to construct the Likert-type scale in comparison to Thurstone-type scale because Likert-type scale can be performed without a panel of judges. 111 CU IDOL SELF LEARNING MATERIAL (SLM)

 Likert-type scale is considered more reliable because under it respondents answer each statement included in the instrument. As such it also provides more information and data than does the Thurstone-type scale.  Each statement, included in the Likert-type scale, is given an empirical test for discriminating ability and as such, unlike Thurstone-type scale, the Likert-type scale permits the use of statements that are not manifestly related (to have a direct relationship) to the attitude being studied.  Likert-type scale can easily be used in respondent-centred and stimulus-centred studies i.e., through it we can study how responses differ between people and how responses differ between stimuli.  Likert-type scale takes much less time to construct, it is frequently used by the students of opinion research. Moreover, it has been reported in various research studies* that there is high degree of correlation between Likert-type scale and Thurstone-type scale. Limitations: There are several limitations of the Likert-type scale as well. One important limitation is that, with this scale, we can simply examine whether respondents are more or less favorable to a topic, but we cannot tell how much more or less they are. There is no basis for belief that the five positions indicated on the scale are equally spaced. The interval between ‘strongly agree’ and ‘agree’, may not be equal to the interval between “agree” and “undecided”. This means that Likert scale does not rise to a stature more than that of an ordinal scale, whereas the designers of Thurstone scale claim the Thurstone scale to be an interval scale. One further disadvantage is that often the total score of an individual respondent has little clear meaning since a given total score can be secured by a variety of answer patterns. It is unlikely that the respondent can validly react to a short statement on a printed form in the absence of real-life qualifying situations. Moreover, there “remains a possibility that people may answer according to what they think they should feel rather than how they do feel.” In spite of all the limitations, the Likert-type summated scales are regarded as the most useful in a situation wherein it is possible to compare the respondent’s score with a distribution of scores from some well-defined group. They are equally useful when we are concerned with a programme of change or improvement in which case we can use the scales to measure attitudes before and after the programme of change or improvement in order to assess whether our efforts have had the desired effects. We can as well correlate scores on the scale to other measures without any concern for the absolute value of what is favorable and what is unfavorable. All this accounts for the popularity of Likert-type scales in social studies relating to measuring of attitudes. Cumulative scales: Cumulative scales or Louis Guttman’s scalogram analysis, like other scales, consist of series of statements to which a respondent expresses his agreement or disagreement. The special feature of this type of scale is that statements in it form a cumulative series. This, in other words, means that the 112 CU IDOL SELF LEARNING MATERIAL (SLM)

statements are related to one another in such a way that an individual, who replies favorably to say item No. 3, also replies favorably to items No. 2 and 1, and one who replies favorably to item No. 4 also replies favorably to items No. 3, 2 and 1, and so on. This being so an individual whose attitude is at a certain point in a cumulative scale will answer favorably all the items on one side of this point, and answer unfavorably all the items on the other side of this point. The individual’s score is worked out by counting the number of points concerning the number of statements he answers favorably. If one knows this total score, one can estimate as to how a respondent has answered individual statements constituting cumulative scales. The major scale of this type of cumulative scales is the Guttman’s scalogram. We attempt a brief description of the same below. The technique developed by Louis Guttman is known as scalogram analysis, or at times simply ‘scale analysis’. Scalogram analysis refers to the procedure for determining whether a set of items forms a unidimensional scale. A scale is said to be unidimensional if the responses fall into a pattern in which endorsement of the item reflecting the extreme position results also in endorsing all items which are less extreme. Under this technique, the respondents are asked to indicate in respect of each item whether they agree or disagree with it, and if these items form a unidimensional scale, the response pattern will be as under: Response Pattern in Scalogram Analysis Figure 9.9 Response Pattern in Scalogram Analysis A score of 4 means that the respondent is in agreement with all the statements which is indicative of the most favorable attitude. But a score of 3 would mean that the respondent is not agreeable to item 4, but he agrees with all others. In the same way one can interpret other values of the respondents’ scores. This pattern reveals that the universe of content is scalable. Procedure: The procedure for developing a scalogram can be outlined as under:  The universe of content must be defined first of all. In other words, we must lay down in clear terms the issue we want to deal within our study.  The next step is to develop a number of items relating the issue and to eliminate by 113 CU IDOL SELF LEARNING MATERIAL (SLM)

inspection the items that are ambiguous, irrelevant or those that happen to be too extreme items.  The third step consists in pre-testing the items to determine whether the issue at hand is scalable (The pretest, as suggested by Guttman, should include 12 or more items, while the final scale may have only 4 to 6 items. Similarly, the number of respondents in a pretest may be small, say 20 or 25 but final scale should involve relatively more respondents, say 100 or more).  In a pretest the respondents are asked to record their opinions on all selected items using a Likert-type 5-point scale, ranging from ‘strongly agree’ to ‘strongly disagree’. The strongest favorable response is scored as 5, whereas the strongest unfavorable response as 1. The total score can thus range, if there are 15 items in all, from 75 for most favorable to 15 for the least favorable.  Respondent opinionnaires are then arrayed according to total score for analysis and evaluation. If the responses of an item form a cumulative scale, its response category scores should decrease in an orderly fashion as indicated in the above table. Failure to show the said decreasing pattern means that there is overlapping which shows that the item concerned is not a good cumulative scale item i.e., the item has more than one meaning. Sometimes the overlapping in category responses can be reduced by combining categories. After analyzing the pretest results, a few items, say 5 items, may be chosen.  The next step is again to total the scores for the various opinionnaires, and to re-array them to reflect any shift in order, resulting from reducing the items, say, from 15 in pretest to, say, 5 for the final scale. The final pretest results may be tabulated in the form of a table given in Table below. The Final Pretest Results in a Scalogram Analysis Pretest Results in a Scalogram Analysis Figure 9.10 The Final Pretest Results in a Scalogram Analysis Pretest Results in a Scalogram Analysis 114 CU IDOL SELF LEARNING MATERIAL (SLM)

The table shows that five items (numbering 5, 12, 3, 10 and 7) have been selected for the final scale. The number of respondents is 25 whose responses to various items have been tabulated along with the number of errors. Perfect scale types are those in which the respondent’s answers fit the pattern that would be reproduced by using the person’s total score as a guide. Non-scale types are those in which the category pattern differs from that expected from the respondent’s total score i.e., non-scale cases have deviations from one-dimensionality or errors. Whether the items (or series of statements) selected for final scale may be regarded a perfect cumulative (or a unidimensional scale), we have to examine on the basis of the coefficient of reproducibility. Guttman has set 0.9 as the level of minimum reproducibility in order to say that the scale meets the test of one-dimensionality. He has given the following formula for measuring the level of reproducibility: Guttman’s Coefficient of Reproducibility = 1 – e/n(N) where e = number of errors n = number of items N = number of cases For the above table figures, Coefficient of Reproducibility = 1 – 7/5(25) = .94 This shows that items number 5, 12, 3, 10 and 7 in this order constitute the cumulative or unidimensional scale, and with this we can reproduce the responses to each item, knowing only the total score of the respondent concerned. Scalogram, analysis, like any other scaling technique, has several advantages as well as limitations. One advantage is that it assures that only a single dimension of attitude is being measured. Researcher’s subjective judgement is not allowed to creep in the development of scale since the scale is determined by the replies of respondents. Then, we require only a small number of items that make such a scale easy to administer. Scalogram analysis can appropriately be used for personal, telephone or mail surveys. The main difficulty in using this scaling technique is that in practice perfect cumulative or unidimensional scales are very rarely found and we have only to use its approximation testing it through coefficient of reproducibility or examining it on the basis of some other criteria. This method is not a frequently used method for the simple reason that its development procedure is tedious and complex. Such scales hardly constitute a reliable basis for assessing attitudes of persons towards complex objects for predicting the behavioral responses of individuals towards such objects. Conceptually, this analysis is a bit more difficult in comparison to other scaling methods. Factor Scales Factor scales are developed through factor analysis or on the basis of intercorrelations of items which 115 CU IDOL SELF LEARNING MATERIAL (SLM)

indicate that a common factor accounts for the relationships between items. Factor scales are particularly “useful in uncovering latent attitude dimensions and approach scaling through the concept of multiple-dimension attribute space.” More specifically the two problems viz., how to deal appropriately with the universe of content which is multi-dimensional and how to uncover underlying (latent) dimensions which have not been identified, are dealt with through factor scales. An important factor scale based on factor analysis is Semantic Differential (S.D.) and the other one is Multidimensional Scaling. We give below a brief account of these factor scales. Semantic differential scale: Semantic differential scale or the S.D. scale developed by Charles E. Osgood, G.J. Suci and P.H. Tannenbaum (1957), is an attempt to measure the psychological meanings of an object to an individual. This scale is based on the presumption that an object can have different dimensions of connotative meanings which can be located in multidimensional property space, or what can be called the semantic space in the context of S.D. scale. This scaling consists of a set of bipolar rating scales, usually of 7 points, by which one or more respondents’ rate one or more concepts on each scale item. For instance, the S.D. scale items for analyzing candidates for leadership position may be shown as under: Figure 9.11 Factor Scales Candidates for leadership position (along with the concept—the ‘ideal’ candidate) may be compared and we may score them from +3 to –3 on the basis of the above stated scales. (The letters, E, P, A showing the relevant factor viz., evaluation, potency and activity respectively, written along the left side are not written in actual scale. Similarly the numeric values shown are also not written in actual scale.) 116 CU IDOL SELF LEARNING MATERIAL (SLM)

Osgood and others did produce a list of some adjective pairs for attitude research purposes and concluded that semantic space is multidimensional rather than unidimensional. They made sincere efforts and ultimately found that three factors, viz., evaluation, potency and activity, contributed most to meaningful judgements by respondents. The evaluation dimension generally accounts for 1/2 and 3/4 of the extractable variance and the other two factors account for the balance. Procedure: Various steps involved in developing S.D. scale are as follows:  First of all the concepts to be studied are selected. The concepts are usually chosen by personal judgement, keeping in view the nature of the problem.  The next step is to select the scales bearing in mind the criterion of factor composition and the criterion of scale’s relevance to the concepts being judged (it is common practice to use at least three scales for each factor with the help of which an average factor score has to be worked out). One more criterion to be kept in view is that scales should be stable across subjects and concepts.  Then a panel of judges are used to rate the various stimuli (or objects) on the various selected scales and the responses of all judges would then be combined to determine the composite scaling.  To conclude, “the S.D. has a number of specific advantages. It is an efficient and easy way to secure attitudes from a large sample. These attitudes may be measured in both direction and intensity. The total set of responses provides a comprehensive picture of the meaning of an object, as well as a measure of the subject doing the rating. It is a standardized technique that is easily repeated, but escapes many of the problems of response distortion found with more direct methods.” Multidimensional scaling: Multidimensional scaling (MDS) is relatively more complicated scaling device, but with this sort of scaling one can scale objects, individuals or both with a minimum of information. Multidimensional scaling (or MDS) can be characterized as a set of procedures for portraying perceptual or affective dimensions of substantive interest. It “provides useful methodology for portraying subjective judgements of diverse kinds.” MDS is used when all the variables (whether metric or non-metric) in a study are to be analyzed simultaneously and all such variables happen to be independent. The underlying assumption in MDS is that people (respondents) “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.” Through MDS techniques one can represent geometrically the locations and interrelationships among a set of points. In fact, these techniques attempt to locate the points, given the information about a set of interpoint distances, in space of one or more dimensions such as to best summarize the information contained in the interpoint distances. The distances in the solution space then optimally reflect the distances contained in the input data. For instance, if objects, say X and Y, 117 CU IDOL SELF LEARNING MATERIAL (SLM)

are thought of by the respondent as being most similar as compared to all other possible pairs of objects, MDS techniques will position objects X and Y in such a way that the distance between them in multidimensional space is shorter than that between any two other objects. Two approaches, viz., the metric approach and the non-metric approach, are usually talked about in the context of MDS, while attempting to construct a space containing m points such that m(m – 1)/2 interpoint distances reflect the input data. The metric approach to MDS treats the input data as interval scale data and solves applying statistical methods for the additive constant* which minimizes the dimensionality of the solution space. This approach utilizes all the information in the data in obtaining a solution. The data (i.e., the metric similarities of the objects) are often obtained on abipolar similarity scale on which pairs of objects are rated one at a time. If the data reflect exact distances between real objects in an r-dimensional space, their solution will reproduce the set of interpoint distances. But as the true and real data are rarely available, we require random and systematic procedures for obtaining a solution. Generally, the judged similarities among a set of objects are statistically transformed into distances by placing those objects in a multidimensional space of some dimensionality. The non-metric approach first gathers the non-metric similarities by asking respondents to rank order all possible pairs that can be obtained from a set of objects. Such non-metric data is then transformed into some arbitrary metric space and then the solution is obtained by reducing the dimensionality. In other words, this non-metric approach seeks “a representation of points in a space of minimum dimensionality such that the rank order of the interpoint distances in the solution space maximally corresponds to that of the data. This is achieved by requiring only that the distances in the solution be monotone with the input data.”9 The non-metric approach has come into prominence during the sixties with the coming into existence of high speed computers to generate metric solutions for ordinal input data. 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. Psychologists, for example, employ multidimensional scaling techniques in an effort to scale psychophysical stimuli and to determine appropriate labels for the dimensions along which these stimuli vary.” The MDS techniques, in fact, do away with the need in the data collection process to specify the attribute(s) along which the several brands, say of a particular product, may be compared as ultimately the MDS analysis itself reveals such attribute(s) that presumably underlie the expressed relative similarities among objects. Thus, MDS is an important tool in attitude measurement and the techniques falling under MDS promise “a great advance from a series of unidimensional measurements (e.g., a distribution of intensities of feeling towards single attribute such as color, taste or a preference ranking with indeterminate intervals), to a perceptual mapping in multidimensional space of objects ... company images, advertisement brands, etc.” In spite of all the merits stated above, the MDS is not widely used because of the computation 118 CU IDOL SELF LEARNING MATERIAL (SLM)

complications involved under it. Many of its methods are quite laborious in terms of both the collection of data and the subsequent analyses. However, some progress has been achieved (due to the pioneering efforts of Paul Green and his associates) during the last few years in the use of non- metric MDS in the context of market research problems. The techniques have been specifically applied in “finding out the perceptual dimensions, and the spacing of stimuli along these dimensions, that people, use in making judgments about the relative similarity of pairs of Stimuli.” But, “in the long run, the worth of MDS will be determined by the extent to which it advances the behavioral sciences.” SUMMARY  Scaling techniques provide a clear picture of the product life cycle and the market acceptability of the products offered. It facilitates product development and benchmarking through rigorous market research.  Scaling technique is a method of placing respondents in continuation of gradual change in the pre-assigned values, symbols or numbers based on the features of a particular object as per the defined rules. All the scaling techniques are based on four pillars, i.e., order, description, distance and origin.  Scaling is the procedure of measuring and assigning the objects to the numbers according to the specified rules. In other words, the process of locating the measured objects on the continuum, a continuous sequence of numbers to which the objects are assigned is called as scaling. The measurement is the process of assigning numbers or symbol to the characteristics of the object as per the specified rules. Here, the researcher assigns numbers, not to the object, but to its characteristics such as perceptions, attitudes, preferences, and other relevant traits.  In research, usually, the numbers are assigned to the qualitative traits of the object because the quantitative data helps in statistical analysis of the resulting data and further facilitates the communication of measurement rules and results.  All the scales used in scaling techniques can be explained in terms of four basic characteristics., Viz. Description, Order, Distance, and origin. These characteristics collectively define the Levels of Measurement of scale. The level of measurement indicates that what properties of an object are measured or not measured by the scale. KEYWORDS  Hypothesis - A formal statement made about the predicted relationship between variables in a research study, which is directly tested by the researcher. Generally linked to deductive reasoning.  Ideographic explanations - Only valid for a specific situation or ‘case’ and not 119 CU IDOL SELF LEARNING MATERIAL (SLM)

generalizable to others.  Individual fallacy - Taking an exception to a general rule and considering it as cancelling the rule.  Informants - A person who helps a researcher in a field study by helping them gain access to the setting, introduce them to the members of the setting, answer questions the researcher may have and provide clarifications. Often it is a member of the setting.  Interactions - Factors that influence each other within a system.  Inter-coder reliability - Recoding of (randomly selected) 10% of the units of analysis coded by one coder, by another in a content analysis, to examine the agreement between the two for reliability and consistency.  Interrelationships - Relationships between factors within a system LEARNING ACTIVITY 1. Explain using examples primary scaling techniques 2. Explain meaning of scaling. UNIT END QUESTIONS (MCQ AND DESCRIPTIVE) A. Descriptive Questions 1. Explain rating & ranking scales 2. State various scale construction techniques 3. Describe primary scaling techniques 4. Discuss important scaling techniques B. Multiple Choice Questions (MCQs) 120 CU IDOL SELF LEARNING MATERIAL (SLM)

1. In the concept of the relative position of the objects or labels based on the individual’s choice or preference a. Nominal b. Ordinal c. Interval d. Ratio 2. One of the most superior measurement technique is the a. Nominal b. Ordinal c. Interval d. Ratio 3. symbolizes two variables from which the respondent needs to select one a. Rank Order b. Paired comparison c. Q-sort d. Likert 4. symbolizes two variables from which the respondent needs to select one a. Rank Order b. Paired comparison c. Q-sort d. Likert 5. emphasizes on choosing a particular category among the various given categories by the respondents. a. Comparative scale b. Itemized rating scaling c. Raking scale d. Q-sort 121 CU IDOL SELF LEARNING MATERIAL (SLM)

Answers: 2. (d) 3. (c) 4. (b) 5. (b) 1. (b) REFERENCES  Donald, R. Cooper & Pamela S. Schindler (2014).  Business Research Methods. New Delhi: Tata McGraw-Hill Publishing Co. Ltd.  Gupta, S.C. (2010). Fundamentals of Statistics. 6th Ed. Mumbai: HPH.  Gupta, S. P. (2002). Statistical Methods. New Delhi: Sultan Chand & Sons.  Beri, G.C. (2012). Business Statistics. New Delhi: Tata McGraw-Hill Publishing Co. Ltd.  Zikmund. (2015). Business Research Methods. New Delhi: Cengage Learning  Abrams, M.A., Social Surveys and Social Action, London: Heinemann, 1951.  Arthur, Maurice, Philosophy of Scientific Investigation, Baltimore: John Hopkins University Press, 1943.  RS. Bhardwaj, Business Statistics, Excel Books, New Delhi, 2008.  S.N. Murthy and U. Bhojanna, Business Research Methods, Excel Books, 2007. 122 CU IDOL SELF LEARNING MATERIAL (SLM)

UNIT-10 DATA ANALYSIS Structure Learning Objectives Introduction Tabulation of Data Data Preparation –frequency tables, bar charts, pie charts, percentages Summary Keywords Learning Activity Unit End Questions (Mcq And Descriptive) References LEARNING OBJECTIVES After studying this Unit, you will be able to:  Explain data tabulation  State significance of tabulated data  Identify types of data analysis  Discuss the various data preparation methods INTRODUCTION According to LeCompte and Schensul, research data analysis is a process used by researchers for reducing data to a story and interpreting it to derive insights. The data analysis process helps in reducing a large chunk of data into smaller fragments, which makes sense. Three essential things take place during the data analysis process — the first data organization. Summarization and categorization together contribute to becoming the second known method used for data reduction. It helps in finding patterns and themes in the data for easy identification and linking. Third and the last way is data analysis – researchers do it in both top-down or bottom-up fashion. Marshall and Rossman, on the other hand, describe data analysis as a messy, ambiguous, and time- consuming, but a creative and fascinating process through which a mass of collected data is being brought to order, structure and meaning. 123 CU IDOL SELF LEARNING MATERIAL (SLM)

We can say that “the data analysis and interpretation is a process representing the application of deductive and inductive logic to the research and data analysis.” TABULATION OF DATA Tabulation comprises sorting of the data into different categories and counting the number of cases that belong to each category. The simplest way to tabulate is to count the number of responses to one question. This is also called univariate tabulation. The analysis based on just one variable is obviously meagre. Where two or more variables are involved in tabulation, it is called bivariate or multivariate tabulation in marketing research, projects generally both types of tabulation are used. Definition: Prof. Neiswanger has defined a statistical table as “In a systemic organisation of data in columns and rows.” L. K Connor has defined tabulation as the orderly and systematic presentation of numerical data in a form designed to elucidate the problem under consideration. The tabular presentation of data is one of the techniques of presentation of data. The tabular presentation means arranging the collected data in an orderly mariner in rows and in columns. The horizontal arrangement of the data is known as rows, whereas the vertical arrangement is called columns. The classified facts are recorded in rows and columns to give then tabular form. Objects of Tabulation: The following are the main objects of tabulation. a. To make the purpose of enquiry clear tabulation in the general scheme of statistics investigation is to arrange in easily accessible form. b. To make significance clear by arranging in form of table the significance of data, is made very clear. This is because table permits the observation of the whole data in one glance. The total information is clear to the view and the significance of different parts can easily be followed. c. To express the data in the least space table also permits the data to be represented in least possible space, making the whole information clear to the view. If it is expressed in form of a passage it would not only be difficult to follow, but would require more space too. d. To make comparison easy mainly because of the arrangement of figures in it. When two sets of figures are given side by side, it is much easier to form a comparative idea of their significance classification of tabulation: A. Simple Tabulation B. Complex Tabulation. A. Simple Tabulation: It gives information about one or more groups of independent questions. This 124 CU IDOL SELF LEARNING MATERIAL (SLM)

result, in one-way table, provides information of one characteristics of data. B. Complex Tabulation: In this type of tabulation, the data is divided in two or more categories which gives information regarding more sets of interrelated question. Importance of Tabulation a. Systematic Presentation of Data: Generally the collected data is in fragmented form. The mass of data is presented in a concise and simple manner by means of statistical tables. Thus, tabulation helps in presenting the data in an orderly manner. b. Facilitates Comparison of Data: If the data is in the raw form, it is very difficult to compare. Comparison is possible when the related items of data are presented in simple and concise form. The presentation of complete and unorganized data in the form of tables facilitates the comparison of the various aspects of the data. c. Identification of the Desired Values: In tabulation, data is presented in an orderly manner by arranging it in rows and columns. Therefore, the desired values can be identified without much difficulty. In the absence of tabulated data, it would be rather difficult to locate the required values. d. Provides a Basis for Analysis: Presentation of data in tabular form provides a basis for analysis of such data. The statistical methodology suggests that analysis follows presentation of data. A systematic presentation of data in tabular form is a prerequisite for the analysis of data Statistical tables are useful aids in analysis. e. Exhibits Trend of Data: By presenting data in a condensed form at one place, tabular presentation exhibits the trend of data. By looking at a statistical table, we can identify the overall pattern of the data. Data Analysis The data collected may or may not in numerical form. Even if data is not in numerical form still, we can carry out qualitative analysis based on the experiences of individual participants. When data is collected in numerical form than through descriptive statistics findings can be summarised. This includes measure of central tendency like mean range etc. Another way to summarised finding is by means of graphs and charts. In any of the research study there is experimental hypothesis or null hypothesis one the basis of data of both hypothesis, various test has 125 CU IDOL SELF LEARNING MATERIAL (SLM)

been devised to take decision. Where decision is taken on the basis statistical test, it is subject to error, and such correct decision is difficult. But some standard procedures followed to arrive at proper decision. Analysis involves estimating the values of unknown parameters of the population and testing hypothesis for drawing inferences. Types of Analysis:  Qualitative analysis  Content analysis  Quantitative analysis  Descriptive analysis  Bivariate analysis  Sequential analysis  Casual analysis  Multivariate analysis  Inferential analysis  Statistical analysis. a. Qualitative Analysis: It is less influenced by theoretical assumption. The limitation of this type of analysis is that the findings tend to be unrealisable. The information categories and interpreted after, differ considerable from one investigator to another one. In this system researcher to go through, research cycle, to increase reliability, repeating the research cycle is of value in some ways, but it does not ensure that the findings will have high reliability. Qualitative analyses are carried out in several different kinds of study like interview, case studies and observational studies. b. Content Analysis: Content analysis is used where originally qualitative information is reduced to numerical terms. It is a method of analysis media output includes articles published in new papers, speeches made in radio, television and various type of propaganda. This method of analysis is applied to all most all form of communications. c. Quantitative Analysis: The numerical data collected in study through descriptive statistics analysis can be conducted through measure of central tendency. d. Descriptive Analysis: This analysis of one variable is called one dimensional analysis. This analysis measures condition at particular time. e. Bivariate Analysis: The analysis in respect of two variables is called bivariate analysis. In this 126 CU IDOL SELF LEARNING MATERIAL (SLM)

analysis collected data in placed into tabular form, so that the meaning of the data can be derived. In this method simple dimensional data is developed and put into two or more categories. f. Sequential Analysis: When only factor is revel in the table at one time, this type of analysis is called sequential analysis is called sequential analysis. If we do the further analysis of the same data regard four going showed that person with leave travel concession facilities is more frequently going on tourism than those who are not gating facilities of casual analysis. It is concerned with study of one variable affecting another one. g. Causal Analysis: The purpose of causal analysis is trying to find the root cause of a problem instead of finding the symptoms. This technique helps to uncover the facts that lead to a certain situation. h. Multivariate Analysis: With an advancement of compute application there is fast development of multivariate analysis, in which statistical method simultaneously analysis more than two variables. i. Inferential Analysis: In order to decide the validity of data to indicate conclusion this analysis is concerned with tests for significance of hypothesis. One the basis of inferential analysis the task of interpretation is performed by estimating the population values. j. Statistical data analysis: Statistical data analysis is a procedure of performing various statistical operations. It is a kind of quantitative research, which seeks to quantify the data, and typically, applies some form of statistical analysis. Quantitative data basically involves descriptive data, such as survey data and observational data. DATA PREPARATION–FREQUENCY TABLES, BAR CHARTS, PIE CHARTS, PERCENTAGES Research shows that the data preparation process is estimated to take up to 80% of the overall analysis time. For businesses, this continues to be a major barrier to getting quick and accurate analysis. The data preparation process allows anyone to quickly turn any raw data from multiple sources into refined information assets so it can be used for accurate analysis and valuable business insights. The self-service data preparation process is quickly becoming a skill that is required for an increasing number of data analysts, data scientists and business users. These individuals have been learning and adopting this new skill to support their daily business intelligence activities and analytic initiatives. To date, the tools available for data preparation processing have been somewhat limited to Excel or other spreadsheet applications. As a result, it’s not always clear what a data preparation process should be, who’s responsible for it and how it fits with the current analytics practice. Frequency tables, pie charts, and bar charts can be used to display the distribution of a single categorical variable. These displays show all possible values of the variable along with either the 127 CU IDOL SELF LEARNING MATERIAL (SLM)

frequency (count) or relative frequency (percentage). Relative frequencies are more commonly used because they allow you to compare how often values occur relative to the overall sample size. They are calculated by dividing the number of responses for a specific category by the total number of responses. Pie charts represent relative frequencies by displaying how much of the whole pie each category represents. Frequency tables and bar charts can display either the raw frequencies or relative frequencies. If you wish to perform an inferential test on the distribution of a single categorical variable, see the chi-squared goodness-of-fit test. Example: A researcher asked her class to pick who would win in a battle of superheroes. Below is a frequency table and charts of the results: Out of a total of 128 responses, 41% (or 52/128) of students reported that Batman would win the battle, followed by Iron Man with 27%, Captain America with 19%, and Superman with 13%. A pie chart and bar chart of these results are shown below: 128 CU IDOL SELF LEARNING MATERIAL (SLM)

Percentage Frequency Table Example Percentage Cumulative Frequency Table 129 Example CU IDOL SELF LEARNING MATERIAL (SLM)

SUMMARY  Researchers rely heavily on data as they have a story to tell or problems to solve. It starts with a question, and data is nothing but an answer to that question. But, what if there is no question to ask? Well! It is possible to explore data even without a problem – we call it ‘Data Mining’ which often reveal some interesting patterns within the data that are worth exploring.  Irrelevant to the type of data, researchers explore, their mission, and audiences’ vision guide them to find the patterns to shape the story they want to tell. One of the essential things expected from researchers while analyzing data is to stay open and remain unbiased towards unexpected patterns, expressions, and results. Remember, sometimes, data analysis tells the most unforeseen yet exciting stories that were not expected at the time of initiating data analysis. Therefore, rely on the data you have at hand and enjoy the journey of exploratory research.  Qualitative data analysis is a process that seeks to reduce and make sense of vast amounts of information, often from different sources, so that impressions that shed light on a research question can emerge. It is a process where you take descriptive information and offer an explanation or interpretation. The information can consist of interview transcripts, documents, blogs, surveys, pictures, videos etc. You may have been in the situation where you have carried out 6 focus group discussions but then are not quite sure what to do with the 30 pages of notes you collected during the process. Do you just highlight what seems most relevant or is there a more systematic way of analyzing it? 130 CU IDOL SELF LEARNING MATERIAL (SLM)

 Qualitative data analysis ought to pay attention to the ‘spoken word’, context, consistency and contradictions of views, frequency and intensity of comments, their specificity as well as emerging themes and trends. We now explain three key components of qualitative data analysis.  Statistics help us turn quantitative data into useful information to help with decision making. We can use statistics to summarize our data, describing patterns, relationship and connections. Statistics can be descriptive or inferential. Descriptive statistics help us to summarize our data whereas inferential statistics are used to identify statistically significant differences between groups of data (such as intervention and control groups in a randomized control study). KEYWORDS  Hypothesis -- A formal statement made about the predicted relationship between variables in a research study, which is directly tested by the researcher. Generally linked to deductive reasoning.  Ideographic explanations - Only valid for a specific situation or ‘case’ and not generalizable to others.  Individual fallacy - Taking an exception to a general rule and considering it as cancelling the rule.  Informants - A person who helps a researcher in a field study by helping them gain access to the setting, introduce them to the members of the setting, answer questions the researcher may have and provide clarifications. Often it is a member of the setting.  Interactions - Factors that influence each other within a system. LEARNING ACTIVITY 1. Prepare a Pie Chart & Bar Charts for the following information. Student No. Marks in Chemistry Physics 40 1 48 2 30 30 3 49 30 4 25 30 131 CU IDOL SELF LEARNING MATERIAL (SLM)

UNIT END QUESTIONS (MCQ AND DESCRIPTIVE) A. Descriptive Questions 1. Explain the significance of data tabulation. 2. What do you mean by data analysis? 3. Explain the type of data analysis. Give examples. 4. Explain the importance of graphs, diagrams in data analysis. Give examples. B. Multiple Choice Questions (MCQs) 1. Which of the following is not a “Graphic representation”? a. Pie Chart b. Bar Chart c. Table d. Histogram 2. A pie chart is: a. A chart demonstrating the increasing incidence of obesity in society. b. Any form of pictorial representation of data. c. Only used in catering management research. d. An illustration where the data are divided into proportional segments according to the share each has of the total value of the data. 3. Qualitative data analysis is still a relatively new and rapidly developing branch of research methodology. a. True b. False 4. A graph that uses vertical bars to represent data is called a a. Line graph b. Bar graph c. Scatterplot d. Vertical graph Answers: 132 1. (c) 2. (d) 3. (a) 4. (b) CU IDOL SELF LEARNING MATERIAL (SLM)

REFERENCES  Donald, R. Cooper & Pamela S. Schindler (2014).  Business Research Methods. New Delhi: Tata McGraw-Hill Publishing Co. Ltd.  Gupta, S.C. (2010). Fundamentals of Statistics. 6th Ed. Mumbai: HPH.  Gupta, S. P. (2002). Statistical Methods. New Delhi: Sultan Chand & Sons.  Beri, G. C. (2012). Business Statistics. New Delhi: Tata McGraw-Hill Publishing Co. Ltd.  Zikmund. (2015). Business Research Methods. New Delhi: Cengage Learning  Churchill, Gilbert A (1983) Marketing Research: Methodological Foundations, The Dryden Press, New York.  Kothari C.R. (1990) Research Methodology: Methods and Technique. Wishwa Prakashan, New Delhi.  Mahalotra N.K. (2002) Marketing Research: An Applied Orientation. Pearson Education Asia.  Mustafi, C.K. 1981. Statistical Methods in Managerial Decisions, Macmillan: New Delhi.  Raj, D. (1968), “Sampling Theory,” McGraw-Hill Book Company, New York.  Singh, D. and F.S. Chaudhary, 1986. Theory and Analysis of Sample Survey Designs, Wiley Eastern: New Delhi.  Yates, E (1960), “Sampling Methods for Censuses and Surveys,” Charles Griffin & Company, Ltd., London 133 CU IDOL SELF LEARNING MATERIAL (SLM)

UNIT-11 HYPOTHESIS TEST Structure Learning Objectives Introduction Parametric and Non Parametric Tests: Definition and use T Test Z Test Chi Square Test F Test Summary Keywords Learning Activity Unit End Questions (Mcq And Descriptive) References LEARNING OBJECTIVES After studying this Unit, you will be able to:  Explain various parametric tests  Discuss about various non-parametric tests INTRODUCTION When you conduct a piece of quantitative research, you are inevitably attempting to answer a research question or hypothesis that you have set. One method of evaluating this research question is via a process called hypothesis testing, which is sometimes also referred to as significance testing. Hypothesis testing or significance testing is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method, we test some hypothesis by determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true. A hypothesis is an educated guess about something in the world around you. It should be testable, either by experiment or observation. PARAMETRIC AND NON PARAMETRIC TESTS: DEFINITION AND USE 134 CU IDOL SELF LEARNING MATERIAL (SLM)

Parametric tests assume underlying statistical distributions in the data. Therefore, several conditions of validity must be met so that the result of a parametric test is reliable. For example, Student’s t-test for two independent samples is reliable only if each sample follows a normal distribution and if sample variances are homogeneous. Nonparametric tests do not rely on any distribution. They can thus be applied even if parametric conditions of validity are not met. Parametric tests often have nonparametric equivalents. You will find different parametric tests with their equivalents when they exist in this grid. T Test The t test tells you how significant the differences between groups are; In other words it lets you know if those differences (measured in means) could have happened by chance. A very simple example: Let’s say you have a cold and you try a naturopathic remedy. Your cold lasts a couple of days. The next time you have a cold, you buy an over-the-counter pharmaceutical and the cold lasts a week. You survey your friends and they all tell you that their colds were of a shorter duration (an average of 3 days) when they took the homeopathic remedy. What you really want to know is, are these results repeatable? A t test can tell you by comparing the means of the two groups and letting you know the probability of those results happening by chance. Another example: Student’s T-tests can be used in real life to compare averages. For example, a drug company may want to test a new cancer drug to find out if it improves life expectancy. In an experiment, there’s always a control group (a group who are given a placebo, or “sugar pill”). The control group may show an average life expectancy of +5 years, while the group taking the new drug might have a life expectancy of +6 years. It would seem that the drug might work. But it could be due to a fluke. To test this, researchers would use a Student’s t-test to find out if the results are repeatable for an entire population. The T Score The t score is a ratio between the difference between two groups and the difference within the groups. The larger the t score, the more difference there is between groups. The smaller the t score, the more similarity there is between groups. A t score of 3 means that the groups are three times as different from each other as they are within each other. When you run a t test, the bigger the t-value, the more likely it is that the results are repeatable.  A large t-score tells you that the groups are different.  A small t-score tells you that the groups are similar. T-Values and P-values 135 CU IDOL SELF LEARNING MATERIAL (SLM)

How big is “big enough”? Every t-value has a p-value to go with it. A p-value is the probability that the results from your sample data occurred by chance. P-values are from 0% to 100%. They are usually written as a decimal. For example, a p value of 5% is 0.05. Low p-values are good; They indicate your data did not occur by chance. For example, a p-value of .01 means there is only a 1% probability that the results from an experiment happened by chance. In most cases, a p-value of 0.05 (5%) is accepted to mean the data is valid. Calculating the Statistic / Test Types There are three main types of t-test:  An Independent Samples t-test compares the means for two groups.  A Paired sample t-test compares means from the same group at different times (say, one year apart).  A One sample t-test tests the mean of a single group against a known mean. You probably don’t want to calculate the test by hand (the math can get very messy, but if you insist you can find the steps for an independent samples t test here. Use the following tools to calculate the t test:  How to do a T test in Excel.  Ttest in SPSS.  Tdistribution on the TI 89.  Tdistribution on the TI 83. What is a Paired T Test (Paired Samples T Test / Dependent Samples T Test)? A paired t test (also called a correlated pairs t-test, a paired samples t test or dependent samples t test) is where you run a t test on dependent samples. Dependent samples are essentially connected — they are tests on the same person or thing. For example:  Knee MRI costs at two different hospitals,  Two tests on the same person before and after training,  Two blood pressure measurements on the same person using different equipment. When to Choose a Paired T Test / Paired Samples T Test / Dependent Samples T Test Choose the paired t-test if you have two measurements on the same item, person or thing. You 136 CU IDOL SELF LEARNING MATERIAL (SLM)

should also choose this test if you have two items that are being measured with a unique condition. For example, you might be measuring car safety performance in Vehicle Research and Testing and subject the cars to a series of crash tests. Although the manufacturers are different, you might be subjecting them to the same conditions. With a “regular” two sample t test, you’re comparing the means for two different samples. For example, you might test two different groups of customer service associates on a business-related test or testing students from two universities on their English skills. If you take a random sample each group separately and they have different conditions, your samples are independent and you should run an independent samples t test (also called between-samples and unpaired-samples). The null hypothesis for the for the independent samples t-test is μ1 = μ2. In other words, it assumes the means are equal. With the paired t test, the null hypothesis is that the pairwise difference between the two tests is equal (H0: µd = 0). The difference between the two tests is very subtle; which one you choose is based on your data collection method. Benefits of T-Test and Hypothesis Testing T-test and hypothesis testing presents a lot of benefits, both statistically and in business. In statistics, this method is particularly important for post-testing analysis to validate data findings between two different groups and demonstrate the extent of the compared differences. For businesses, it estimates the potential that these differences are purely chance.  Practical for business users: In many cases, a typical business user without statistical training can perform a simple t-test using the general formula.  Minimal data required: The t-test requires limited data for accurate testing; only the subject values regarding the variables from each individual group are needed.  Adapt marketing strategies: Create better marketing strategies based on the statistical difference between purchase quantities for two separate demographics.  Cost efficiency: Rather than performing expensive stress or quality testing, t-tests can accurately calculate the population variables from small test samples. Z Test A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. The test statistic is assumed to have a normal distribution, and nuisance parameters such as standard deviation should be known in order for an accurate z-test to be performed. A z-statistic, or z-score, is a number representing how many standard deviations above or below the mean population a score derived from a z-test is. 137 CU IDOL SELF LEARNING MATERIAL (SLM)

How Z-Tests Work Examples of tests that can be conducted as z-tests include a one-sample location test, a two-sample location test, a paired difference test, and a maximum likelihood estimate. Z-tests are closely related to t-tests, but t-tests are best performed when an experiment has a small sample size. Also, t-tests assume the standard deviation is unknown, while z-tests assume it is known. If the standard deviation of the population is unknown, the assumption of the sample variance equaling the population variance is made. Hypothesis Test The z-test is also a hypothesis test in which the z-statistic follows a normal distribution. The z-test is best used for greater-than-30 samples because, under the central limit theorem, as the number of samples gets larger, the samples are considered to be approximately normally distributed. When conducting a z-test, the null and alternative hypotheses, alpha and z-score should be stated. Next, the test statistic should be calculated, and the results and conclusion stated. One-Sample Z-Test Example Assume an investor wishes to test whether the average daily return of a stock is greater than 1%. A simple random sample of 50 returns is calculated and has an average of 2%. Assume the standard deviation of the returns is 2.5%. Therefore, the null hypothesis is when the average, or mean, is equal to 3%. Conversely, the alternative hypothesis is whether the mean return is greater or less than 3%. Assume an alpha of 0.05% is selected with a two-tailed test. Consequently, there is 0.025% of the samples in each tail, and the alpha has a critical value of 1.96 or -1.96. If the value of z is greater than 1.96 or less than -1.96, the null hypothesis is rejected. The value for z is calculated by subtracting the value of the average daily return selected for the test, or 1% in this case, from the observed average of the samples. Next, divide the resulting value by the standard deviation divided by the square root of the number of observed values. Therefore, the test statistic is calculated to be 2.83, or (0.02 - 0.01) / (0.025 / (50) ^ (1/2)). The investor rejects the null hypothesis since z is greater than 1.96 and concludes that the average daily return is greater than 1%. Chi Square Test The Chi-Square test is a statistical procedure used by researchers to examine the differences between categorical variables in the same population. For example, imagine that a research group is interested in whether or not education level and marital status are related for all people in the U.S. 138 CU IDOL SELF LEARNING MATERIAL (SLM)

After collecting a simple random sample of 500 U.S. citizens, and administering a survey to this sample, the researchers could first manually observe the frequency distribution of marital status and education category within their sample. The researchers could then perform a Chi-Square test to validate or provide additional context for these observed frequencies. Chi-Square calculation formula is as follows: When is the Chi-Square Test Used in Market Research? Market researchers use the Chi-Square test when they find themselves in one of the following situations:  They need to estimate how closely an observed distribution matches an expected distribution. This is referred to as a “goodness-of-fit” test.  They need to estimate whether two random variables are independent.  When to Use the Chi-Square Test on Survey Results  The Chi-Square test is most useful when analyzing cross tabulations of survey response data. Because cross tabulations reveal the frequency and percentage of responses to questions by various segments or categories of respondents (gender, profession, education level, etc.), the Chi-Square test informs researchers about whether or not there is a statistically significant difference between how the various segments or categories answered a given question. Important things to note when considering using the Chi-Square test First, Chi-Square only tests whether two individual variables are independent in a binary, “yes” or “no” format. Chi-Square testing does not provide any insight into the degree of difference between the respondent categories, meaning that researchers are not able to tell which statistic (result of the Chi-Square test) is greater or less than the other. Second, Chi-Square requires researchers to use numerical values, also known as frequency counts, 139 CU IDOL SELF LEARNING MATERIAL (SLM)