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2 M.A.(Psy) Research Methods and Statistics-I Course Code: MAP 604 Semester: First e-Lesson: 7 SLM Unit: 9-11 https://images.app.goo.gl/ibaW7YhjJ7LmSLJV6 www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

RESEARCH METHODS 33 AND STATISTICS OBJECTIVES INTRODUCTION Understand the basic concept and importance of In this unit basic concept of inferential research, the basics of research design and statistics and correlation evaluate types of research designs The unit further discusses the topics of Understand and evaluate the process of regression and parametric and non- research and sampling. parametric statistics. Understand the concepts and explore the types of reliability and validity and evaluate the data analysis. Understand and explore Correlation and Regression and parametric and nonparametric test www.cuidol.in Unit-9-11(MMAAPP660044)) INASlTl ITriUgThEt OarFeDrIeSsTeArNvCeEd AwNitDh OCNUL-IIDNOE LLEARNING

TOPICS TO BE COVERED 4 >] INFERENTIAL STATISTICS > REGRESSION > PARAMETRIC AND NON-PARAMETRIC STATISTICS https://images.app.goo.gl/qhiaHBQmdQUHqGr8A www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

INFERENCIAL STATISTICS 5 It is about using data from sample and then making inferences about the larger population from which the sample is drawn. The goal of the inferential statistics is to draw conclusions from a sample and generalize them to the population. It determines the probability of the characteristics of the sample using probability theory. The most common methodologies used are hypothesis tests, Analysis of variance etc. https://a8h2w5y7.rocketcdn.me www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

INFERENCIAL STATISTICS 6 For example: Suppose we are interested in the exam marks of all the students in India. But it is not feasible to measure the exam marks of all the students in India. So now we will measure the marks of a smaller sample of students, for example 1000 students. This sample will now represent the large population of Indian students. We would consider this sample for our statistical study for studying the population from which it’s deduced. https://miro.medium.com/max www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

INFERENCIAL STATISTICS 7 So Inferential Statistics is : 1. Work with the large data set 2. Process in a more complex as we have to decide on the best sampling techniques. 3. Results obtained represent a portion of the Population, but can be used to deduce Information about the entire population With some amount of uncertainty. 4. Error involved is usually more. https://images.app.goo.gl/o45s7ihbFN2jTNVB6 www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

INFERENCIAL STATISTICS 8 There are two main areas of inferential statistics that are : • Estimating parameters. This means taking a statistic from your sample data (for example the sample mean) and using it to say something about a population parameter (i.e. the population mean). • Hypothesis tests. This is where we can use sample data to answer research questions. For example, you might be interested in knowing if a new cancer drug is effective. Or if breakfast helps children perform better in schools. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

9 www.cuidol.in https://correlation-160404081305/95/ All right are reserved with CU-IDOL Unit-9-11(MAP 604)

CORRELATION 10 The correlation is one of the most common and most useful statistics. A correlation is a single number that describes the degree of relationship between two variables. Correlation is used to denote the association between two quantitative variables. When assessing for correlation, certain assumptions have to be made; the association is linear in that one variable increases or decreases a fixed amount for a unit increase or decrease in the other. Correlation is described as the analysis which lets us know the association or the absence of the relationship between two variables 'x' and 'y', www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

CORRELATION 11 The scatter plot explains the correlation between the two attributes or variables. It represents how closely the two variables are connected. There can be three such situations to see the relation between the two variables – 1. Positive Correlation – when the value of one variable increases with respect to another. If the weight of an individual increases in proportion to increase in his height, the relation between this increase of height and weight is called as positive correlation. It ranges from 0 to + 1. If it is 0 then there is no relation at all. When it is + 1, then there is perfect positive Correlation. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

CORRELATION 12 2. Negative Correlation – when the value of one variable decreases with respect to another. It is just the opposite of positive correlation. If the weight of an individual does not increase in proportion to increase in his height or if the weight of an individual decreases with an increase in height, then it is said to be negative correlation, also ranges from 0 to -1. -1 is perfect negative correlation. 3. No Correlation – when there is no linear dependence or https://a8h2w5y7.rocketcdn.me/ no relation between the two variables. • Zero correlation is a correlation showing no relationship, or a correlation having a correlation coefficient of zero. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

CORRELATION 13 Importance of Correlation: 1. Correlation is very important in the field of Psychology and Education as a measure of relationship between test scores and other measures of performance. 2. With the help of correlation, it is possible to have a correct idea of the working capacity of a person 3. With the help of it, it is also possible to have a knowledge of the various qualities of an individual. After finding the correlation between the two qualities or different qualities of an individual, it is also possible to provide his vocational guidance. 4. In order to provide educational guidance to a student in selection of his subjects of study, correlation is also helpful and necessary. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

CORRELATION 14 Methods of calculation of Correlation: Various persons have suggested various methods for finding out correlation. Two methods that are prevalent and important are:- 1. Rank order method. 2. Product Moment method. 1. Rank order Method: Differences among individuals in many traits can often be expressed by ranking the subjects is 1 -2 – 3 order when such differences cannot be measured directly. For instance, individuals may be ranked in order of merit for obedience, industriousness, punctuality, honesty, salesmanship or social adjustment. Similarly various advertisements colour combinations, jokes and picture which are difficult to evaluate numerically may be put in order of merit for beauty, humour, artistic quality or some other quality. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

CORRELATION 15 The formula for calculating the correlation by Rank order method is as under: P (rho) stands for coefficient of correlation from rank differences. ∑D2 represents the sum of the squares of differences in rank. N represents number of pairs. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

CORRELATION 16 In order to illustrate this formula, we give below an example: www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

CORRELATION 17 2. Karl Pearson’s Coefficient of Correlation is widely used mathematical method wherein the numerical expression is used to calculate the degree and direction of the relationship between linear related variables. Pearson’s method, popularly known as a Pearsonian Coefficient of Correlation, is the most extensively used quantitative methods in practice. The coefficient of correlation is denoted by “r”. If the relationship between two variables X and Y is to be ascertained, then the following formula is used: www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

CORRELATION Add up all of the numbers in the columns and put the result at the bottom of the column. 18 The Greek letter sigma (Σ) is a short way of saying “sum of.” SUBJECT AGE X GLUCOSE LEVEL Y XY X2 Y2 1 43 99 4257 1849 9801 2 21 65 1365 441 4225 3 25 79 1975 625 6241 4 42 75 3150 1764 5625 5 57 87 4959 3249 7569 6 59 81 4779 3481 6561 Σ 247 486 20485 11409 40022 Use the following correlation coefficient formula. www.cuidol.in The answer is: 2868 / 5413.27 = 0.529809 All right are reserved with CU-IDOL Unit-9-11(MAP 604)

REGRESSION 19 • Father of regression analysis Carl F, Gauss (1777-1855). • Contribution to physics, Mathematics and Astronomy. • The term regression was first used in 1877 by Francis Galton. https://regression-150422012703-conversion-gate01 www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

REGRESSION 20 Regression is a statistical method used in finance, investing, and other disciplines that attempts to determine the strength and character of the relationship between one dependent variable (usually denoted by Y) and a series of other variables (known as independent variables). https://regressionanalysis-110723130213-phpapp02/95 www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

REGRESSION 21 The two basic types of regression are simple linear regression and multiple linear regression, Simple linear regression uses one independent variable to explain or predict the outcome of the dependent variable Y, while multiple linear regression uses two or more independent variables to predict the outcome. Regression can help finance and investment professionals as well as professionals in other businesses. Regression can also help predict sales for a company based on weather, previous sales, GDP growth, or other types of conditions. The capital asset pricing model (CAPM) is an often-used regression model in finance for pricing assets and discovering costs of capital. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

REGRESSION 22 The general form of each type of regression is: Simple linear regression: Y = a + bX + u Multiple linear regression: Y = a + b1X1 + b2X2 + b3X3 + ... + btXt + u Where: Y = the variable that you are trying to predict (dependent variable). X = the variable that you are using to predict Y (independent variable). a = the intercept. b = the slope. u = the regression residual. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

REGRESSION 23 Thus Regression or Regression analysis estimates the relationship between two or more variables. Let’s understand this with an easy example: Let’s say, you want to estimate growth in sales of a company based on current economic conditions. You have the recent company data which indicates that the growth in sales is around two and a half times the growth in the economy. Using this insight, we can predict future sales of the company based on current & past information. There are multiple benefits of using regression analysis. They are as follows: 1. It indicates the significant relationships between dependent variable and independent variable. 2. It indicates the strength of impact of multiple independent variables on a dependent variable. Regression analysis also allows us to compare the effects of variables measured on different scales, such as the effect of price changes and the number of promotional activities. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

PARAMETRIC AND 24 NON PARAMETRIC STATISTICS 1. PARAMETRIC STATSITICS A parametric test is a hypothesis testing procedure based on the assumption that observed data are distributed according to some distributions of well- known form (e.g., normal, Bernoulli, and so on)up to some unknown parameter(s) on which we want to make inference (say the mean, or the success probability). https://img-aws.ehowcdn.com/600x600p www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

PARAMETRIC AND 25 NON PARAMETRIC STATISTICS Parametric tests assume a normal distribution of values, or a “bell-shaped curve.” For example, height is roughly a normal distribution in that if you were to graph height from a group of people, one would see a typical bell-shaped curve. This distribution is also called a Gaussian distribution. Parametric tests are in general more powerful (require a smaller sample size) than nonparametric tests. 2. Nonparametric tests are used in cases where parametric tests are not appropriate. Most nonparametric tests use some way of ranking the measurements and testing for weirdness of the distribution. Typically, a parametric test is preferred because it has better ability to distinguish between the two arms. In other words, it is better at highlighting the weirdness of the distribution. Nonparametric tests are about 95% as powerful as parametric tests. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

PARAMETRIC AND 26 NON PARAMETRIC STATISTICS In statistics, parametric and nonparametric methodologies refer to those in which a set of data has a normal vs. a non-normal distribution, respectively. Parametric tests make certain assumptions about a data set; namely, that the data are drawn from a population with a specific (normal) distribution. Non-parametric tests make fewer assumptions about the data set. The majority of elementary statistical methods are parametric, and parametric tests generally have higher statistical power. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

PARAMETRIC AND 27 NON PARAMETRIC STATISTICS The main assumption s of Parametric and Non Parametric Statistics www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

PARAMETRIC AND 28 NON PARAMETRIC STATISTICS Classification of tests used in Parametric& Nonparametric Statistics www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

PARAMETRIC AND NON PARAMETRIC STATISTICS 29 Advantages of Parametric Tests 1: Parametric tests can provide trustworthy results with distributions that are skewed and non normal. 2: Parametric tests can provide trustworthy results when the groups have different amounts of variability. 3: Parametric tests have greater statistical power. Advantages of Nonparametric Tests 1: Nonparametric tests assess the median which can be better for some study areas 2: Nonparametric tests are valid when our sample size is small and your data are potentially nonnormal 3: Nonparametric tests can analyze ordinal data, ranked data, and outliers www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

SUMMARY 30 •Thus here we have discussed about the inferential statistics , correlation, regression and parametric statistics & non parametric statistics that are very important measures of Research methods and statistics. In which Inferential statistics is to draw conclusions from a sample and generalize them to the population. •Correlation is used to denote the association between two quantitative variables. •Parametric and nonparametric are two broad classifications of statistical procedures. Parametric tests are based on assumptions about the distribution of the underlying population from which the sample was taken. The most common parametric assumption is that data are approximately normally distributed. www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

MULTIPLE CHOICE QUESTIONS 31 1. The range of the correlation coefficient is? a. -1 to 0. b. 0 to 1. c. -1 to 1. d. None of the above. 2. Which one of the following statement is false? a. A nonparametric test is a hypothesis test. b. A nonparametric test requires a specific condition. c. Nonparametric tests are easier to perform than corresponding parametric tests. d. Nonparametric tests are less efficient than parametric tests. 3. Product moment method is given by_____________. Answers: 1. c) 2.c) 3. Karl pearson www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

MULTIPLE CHOICE QUESTIONS 32 4. A regression analysis should probably not be conducted unless a scatter plot of the data reveals a relationship that a. approximates a straight line. b. resembles a normal distribution. c. is scattered randomly throughout the range. d. is concave downward. 5. Rank the score of 5 in the following set of scores: 9, 3, 5, 10, 8, 5, 9, 7, 3, 4 6. Chi square test is a parametric test. True False Answers: 4. c) 5. a) 6.b) www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

FREQUENTLY ASKED QUESTIONS 33 1. What is Inferential Statistics? 2. What is the difference between correlation and regression? 3. Give an example of perfect positive correlation. 4. What are formula of rank order method and product moment method? 5. What are the difference between parametric and non parametric statistics? www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

REFERENCES 34 Kothari, C.R., (2004). Research Methodology: Methods and Techniques. 2nd ed. New Delhi: New age international Itd. Herson, M. & Barlow, D. H. (1980) Single – Case Experimental Designs New Delhi: Prentice – Hall of India Limited. Singh A.K. (2006). 5th ed. Tests, Measurement and Research Methods in Behavioral Sciences. Patna: Bharati Bhavan. http://www.psychologydiscussion.net/educational-psychology/statistics/correlation-definit..... https://www.investopedia.com/terms/n/nonparametric-statistics.asp www.cuidol.in Unit-9-11(MAP 604) All right are reserved with CU-IDOL

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