Statistics and Research Methods in Psychology with Excel

Statistics and Research Methodsin Psychology with Excel

J. P. Verma

Statistics and ResearchMethods in Psychologywith Excel

123

J. P. VermaDepartment of Sport PsychologyLakshmibai National Institute of PhysicalEducationGwalior, India

ISBN 978-981-13-3428-3 ISBN 978-981-13-3429-0 (eBook)https://doi.org/10.1007/978-981-13-3429-0

© Springer Nature Singapore Pte Ltd. 2019This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd.The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721,Singapore

https://doi.org/10.1007/978-981-13-3429-0

Dedicated to my wonderful wife Haripriya

Preface

This new book on statistics and research methods in psychology with Excel hasbeen developed for the students in psychology at the graduate level. It can also beused by the students of humanities, social sciences and life sciences. It is written asa textbook and can be used for a 3-credit course. The exercises and examples thathave been discussed in this book are mainly related to the psychological aspects ofa human being. This should help students of psychology to understand statisticalconcepts effortlessly.

Measuring psychological characteristics is a challenging task; hence, a separatechapter has been developed on measurement and scaling techniques. This providesstudents with various tools to assess human behaviour and characteristics in anumerical form suitable for statistical analysis in drawing meaningful conclusions.

A prerequisite for this book is to have elementary knowledge in mathematics.The chapters have been framed in a manner by carefully selecting the topics rel-evant for the students to understand the concepts of statistics and research designsso that they are able to develop their research problems for their thesis work.

The most exciting feature of this book is the use of Excel in analysing the datausing different statistical techniques. At the end of each chapter, the procedure forsolving statistical techniques discussed in that chapter has been illustrated by meansof solved exercises. This will help the students to analyse their thesis data inde-pendently. By using guidelines provided in different chapters, the students canperform descriptive analysis, hypothesis testing (t, F and Z tests), correlation,regression analysis, one- and two-way ANOVA, completely randomized design,randomized block design and random sampling.

One of the main features of this book is that in each chapter exercises have beenarranged under different headings. The questions under the headings “Test yourstatistical concepts” and “Test your computing skill” have been provided afterdiscussing the major topics in each chapter to gauge the progress of the readers.Due to this, the student can enhance their learning skills. Lots of solved numericalexamples have been provided in each chapter to facilitate the students to understandthe procedure in solving these problems. In each chapter, multiple-choice questionswith their answers in addition to practice exercises have been provided for prac-tising different concepts.

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Initial chapters in this book shall help the students to understand the advancetopics discussed in the later chapters. Besides discussing widely used statisticaltechniques, a separate chapter has been framed on research designs, which preparesthe students to develop their own research proposal for their thesis. At the end ofeach chapter, all important definitions have been summarized for ready references.

This book consists of 14 chapters. The meaning and importance of statistics inpsychology have been discussed in Chap. 1. The measurement and scaling tech-niques generally used in psychology have been discussed in Chap. 2.

Since different kinds of descriptive and inferential statistics are used to describethe data, statistical concepts like measures of central tendency, measures of vari-ability, coefficient of variation and percentile rank have been discussed in Chap. 3.

The development of different types of graph that are commonly used by theresearcher in psychology has been discussed in Chap. 4. An emphasis has beengiven on reading and interpreting the graph. The probability and its concepts insolving different types of problem have been given in detail in Chap. 5. The conceptof set theory has been discussed for solving a variety of probability questions.Application of all the important theorems of probability has been discussed forsolving numerical problems based on it. The normal probability distribution and itsapplication have been discussed in Chap. 6. The emphasis has been given to solve avariety of problems using the normal probability curve.

The topics of correlation and regression have been discussed in Chap. 7. Dif-ferent types of correlations like product moment, partial and multiple correlationshave also been discussed. The concept of simple regression has been discussed bymeans of graphics. The concept of sampling has been covered in Chap. 8. Thereaders will come to know as to why the sample should be studied instead ofpopulation and what should be the optimum size of the sample. Different types ofprobability and non-probability sampling techniques have been discussed in thischapter. The design of experiments has been discussed in detail in Chap. 9. Varioustypes of design that are appropriate in different situations have been discussed here.Different methods of research like laboratory experiments, field experiments,observational study and case study have been given in detail.

The statistical inference has been discussed in Chap. 10. Theory of estimationand testing of hypothesis have been explained by means of examples. Importanttests like t, F and Z have been discussed by means of numerical examples. Theanalysis of variance which provides the mechanism to compare the means of morethan two groups has been covered in Chap. 11. Two-way analysis of variance alongwith interaction effect has also been discussed in this chapter to study the effect ofdifferent levels of two factors on the criterion variable.

The non-parametric techniques and correlations which are commonly used inpsychological research have been discussed in Chaps. 12 and 13. The factoranalysis has been discussed in detail in Chap. 14. This multivariate technique iswidely used by the researcher in psychological research.

Discussing Excel for computing at the end of each chapter has made this bookmore useful. The basic computation and formatting in Excel has been shown inChap. 1 by means of examples. Going through the contents, the readers can write

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the code for different formulas in Excel. The procedure for installing AnalysisToolPak has been given in Chap. 2. With the help of this module, a large number ofstatistical techniques can be applied by the readers in a simple manner. The com-putation of various descriptive statistics has been shown in Excel in Chap. 3.Constructing histogram using Excel has been discussed in Chap. 4, whereas thecomputation of probability has been discussed in Chap. 5. Computing skewnessand kurtosis with Excel has been shown in Chap. 6. These two parameters can beused to understand the distribution of data. Correlation and regression analysisusing Excel has been discussed in Chap. 7, whereas drawing a random sample hasbeen discussed in Chap. 8 . While discussing the design of the experiment in Chap.9, the solution in a completely randomized design has been shown by solving anexample using Excel. The solutions of different tests like z, two-sample t and pairedt have been shown in Chap. 10, by means of solving different examples usingExcel. This will provide an easy solution to the master’s degree students to com-plete their dissertation. The use of Excel in solving the analysis of variance has beenshown in Chap. 11, whereas the computation of chi-square and rank correlationusing Excel has been discussed in Chaps. 12 and 13, respectively.

While writing this book, I had three goals: first, this book must be compre-hensive; second, it should also be comprehensible; and third, it should be up to date.As far as the first goal of comprehensiveness is concerned, I have attempted toachieve this by means of covering all major topics which are traditionally part ofany introductory course. Turning to the comprehensibility, I decided at the outsetthat in selecting the materials for inclusion, I should devote careful attention to theirintelligibility and appeal to undergraduate and postgraduate students as well as theirscientific importance and value. Finally, for making this book up to date, I haveattempted to report the latest available information concerning each of the topicsexamined.

Any suggestion for further improvement in the text shall be highly appreciated.The feedback about this book may be sent directly to the author. More resourceson statistics and research can be seen at the author's website http://www.jpverma.org.You may reach the author at: [email protected].

Gwalior, India Prof. J. P. Verma, Ph.D.

Preface ix

http://www.jpverma.org

mailto:[email protected].

Acknowledgements

I would like to thank my students, especially the Ph.D. and M.Phil. scholars, whoconstantly hurled on me a barrage of queries during the numerous academic dis-cussions, which encouraged me to introduce many of the statistical concepts in themost simplified manner in this text. I am also thankful to my colleagues,Y. P. Gupta and R. Sekhar. My thanks are also due to my colleagues DeependerSingh and Pramod Raikwar, who provided technical support while preparing themanuscript. Lastly, I am delighted to share that my son Priyam did a wonderful jobin editing the text to its present form.

I must confess that during the preparation of this text, I got completely confinedto my work which resulted in our inability to spend enough time with my family.Hence, I would like to express my sincere gratitude to my family members. Last butnot least, I extend my thanks to all those who directly or indirectly helped me incompleting this text.

Prof. J. P. Verma, Ph.D.

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Contents

1 Importance of Statistics in Psychology . . . . . . . . . . . . . . . . . . . . . . 1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1What Is Statistics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Need for Understanding Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

To Understand Scientific Literature . . . . . . . . . . . . . . . . . . . . . . . . 4To Develop a Logical Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . 4To Develop a Good Research Problem . . . . . . . . . . . . . . . . . . . . . 5To Assess the Authenticity of Research Findings . . . . . . . . . . . . . . 5To Develop Measurement Scales . . . . . . . . . . . . . . . . . . . . . . . . . . 5To Develop Questionnaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6To Conduct Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Nature of Psychological Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Descriptive Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Relationship Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Inferential Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Predictive Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Application of Statistics in Psychology . . . . . . . . . . . . . . . . . . . . . . . 8Psychometrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Clinical Psychology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Abnormal Psychology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Developmental Psychology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Psychotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Scope of Statistics in Psychology . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Formatting Cell Entries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

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Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Long-Answer-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Check Your Statistical Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2 Measurement and Scaling Techniques . . . . . . . . . . . . . . . . . . . . . . 23Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23What Is Data? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Nature of Psychological Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Categorical Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Discrete Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Continuous Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Random Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Levels of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Non-metric Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Metric Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Concept Construct and Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Check Your Statistical Concepts-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Construction of a Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Steps in Test Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Uses and Implications of Psychological Tests . . . . . . . . . . . . . . . . . . . 33Scaling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Comparative Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Non-comparative Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Check Your Statistical Concepts-II . . . . . . . . . . . . . . . . . . . . . . . . . . 45Reliability of Measurement Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Meaning of Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Methods of Estimating Reliability . . . . . . . . . . . . . . . . . . . . . . . . . 47

Validity of Measurement Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Face Validity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Construct Validity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Content Validity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Criterion-Related Validity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Psychological Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Assessment of Personality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Assessment of Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Assessment of Aptitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Assessment of Achievement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Assessment of Attitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Neuropsychological Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Check Your Statistical Concepts-III . . . . . . . . . . . . . . . . . . . . . . . . . . 60Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

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Installing Analysis ToolPak in Excel . . . . . . . . . . . . . . . . . . . . . . . 61Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Construction of Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Scaling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Reliability and Validity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Psychological Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Long-Answer-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 68Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3 Descriptive Analysis of Psychological Data . . . . . . . . . . . . . . . . . . . 71Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Raw Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Frequency Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Assumptions in Computing Different Statistics from the GroupedData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

The Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Computation of Mean with Grouped Data . . . . . . . . . . . . . . . . . . . 77The Median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82The Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86When to use Mean, Median and Mode . . . . . . . . . . . . . . . . . . . . . 89

Check your Computing Skill-I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Check your Statistical Concepts-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Measures of Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

The Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Quartile Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Mean Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Data Types Suitable for Different Measures of Variability . . . . . . . . . . 106Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Standard Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Coefficient of Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108Percentile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Percentile Rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Check Your Computing Skills-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Check Your Statistical Concepts-II . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

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Measures of Central Tendency and Variability . . . . . . . . . . . . . . . . 126Measuring Variation and Identifying Positional Value . . . . . . . . . . 126


Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Check Your Computing Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 131Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Long-Answer-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

4 Graphical Presentation of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Basics of Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Deciding the Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136Detailing the Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136Locating a Point and its Coordinates on the Graph . . . . . . . . . . . . . 137Deciding the Scale Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137Points on the Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Features of a Good Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138Check Your Graphical Concepts-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 139Types of Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Bar Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Check Your Graphic Skill-I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141Frequency Polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142Frequency Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142Cumulative Frequency Polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Ogive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144Pie Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Check Your Graphical Skill-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Check Your Graphical Concepts-II . . . . . . . . . . . . . . . . . . . . . . . . . . 148Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Constructing Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Types of Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152


Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Check Your Graphical Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Check Your Graphical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 159Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159Long-Answer-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

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5 Probability and Its Application in Psychology . . . . . . . . . . . . . . . . 161Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161Understanding Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

Terminologies Used in Probability . . . . . . . . . . . . . . . . . . . . . . . . 162Classical Definition of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

Computation of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166Problems with Classical Approach of Probability . . . . . . . . . . . . . . . . 171Check Your Computing Skill-I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171Check Your Statistical Concepts-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 172Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Subset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Equal Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Proper Subset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Empty Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Complement of a Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174Union of Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174Intersection of Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174Disjoint Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Universal Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Some Laws of Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175De Morgan’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Axiomatic Definition of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . 175Addition Theorem of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176Multiplication Theorem of Probability . . . . . . . . . . . . . . . . . . . . . . . . 183Check Your Computing Skill-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186Check Your Statistical Concepts-II . . . . . . . . . . . . . . . . . . . . . . . . . . 186Bayes’ Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187Check Your Computing Skill-III . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Finding the Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

Classical Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192Axiomatic Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193


Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 198Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198Long-Answer-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

Contents xvii

6 Normal Distribution and Its Application . . . . . . . . . . . . . . . . . . . . . 201Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

Properties of Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 202Standard Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

Application of Standard Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204How to Test Normality of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

Skewness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204Kurtosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206Application of Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 207Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207Problems Based on Normal Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

Initial Steps in Solving Problems Based on Normal Curve . . . . . . . 208Problems Based on Locating Area in the Curve . . . . . . . . . . . . . . . 209Problems Based on Finding Limits When Area Is Known . . . . . . . 215Problems Based on Area Distribution . . . . . . . . . . . . . . . . . . . . . . 217Problems Based on Developing Grading Limits . . . . . . . . . . . . . . . 219General Problems Based on Areas . . . . . . . . . . . . . . . . . . . . . . . . . 221

Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

Computing Skewness and Kurtosis . . . . . . . . . . . . . . . . . . . . . . . . 225Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229Long-Answer Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 233Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234Long-Answer Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

7 Correlation and Regression Techniques . . . . . . . . . . . . . . . . . . . . . 237Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

The Scattergram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

Computation of Product Moment Correlation Coefficient . . . . . . . . 239Check Your Statistical Concepts-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 246Partial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

Assumptions of Partial Correlation . . . . . . . . . . . . . . . . . . . . . . . . 247Limitations of Partial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . 247Test of Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

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Multiple Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249Coefficient of Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249Characteristics of Multiple Correlation . . . . . . . . . . . . . . . . . . . . . . 249Limitations of Multiple Correlation . . . . . . . . . . . . . . . . . . . . . . . . 250Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

Check Your Computing Skill-I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252Check Your Statistical Concepts-II . . . . . . . . . . . . . . . . . . . . . . . . . . 253Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

Application of Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . 254Regression Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254Regression Equation in Standard Score Form . . . . . . . . . . . . . . . . . 255Conditions of Symmetrical Regression Equations . . . . . . . . . . . . . . 255Properties of Regression Coefficients . . . . . . . . . . . . . . . . . . . . . . . 256Regression Equation with Least Squares Method . . . . . . . . . . . . . . 257Computing Regression Coefficients by Least Squares Methods . . . . 258Assumptions in Simple Regression . . . . . . . . . . . . . . . . . . . . . . . . 259Standard Error of the Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

Multiple Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261Limitations of Multiple Regression . . . . . . . . . . . . . . . . . . . . . . . . 262

Check Your Computing Skill-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262Check Your Statistical Concepts-III . . . . . . . . . . . . . . . . . . . . . . . . . . 263Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

Computing Correlation Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 273Regression Analysis with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . 276

Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280Partial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280Multiple Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281


Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 287Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288Long-Answer-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

8 Sampling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291Principles of Sample Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

Representativeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

Contents xix

Sample Survey and Its Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . 292Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293Administrative Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293Better Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293Reliability of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293Less Non-response Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

Characteristics of a Good Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 294Important Terminologies in Sampling . . . . . . . . . . . . . . . . . . . . . . . . 294

Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295Parameter and Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295Sampling Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295Sampling Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296Sampling Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

Depositories of Scientific Information . . . . . . . . . . . . . . . . . . . . . . . . 296Primary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297Secondary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298Digital Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299Sharing of Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299Transparency and Honesty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

Methods of Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300Interview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300Questionnaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

Sampling Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301Standard Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301Sampling Distribution of Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . 301Sampling Distribution of Difference of Means . . . . . . . . . . . . . . . . 302Sampling Distribution of Proportion . . . . . . . . . . . . . . . . . . . . . . . 302Sampling Distribution of Difference of Two Proportions . . . . . . . . 302Standard Error of Different Statistics . . . . . . . . . . . . . . . . . . . . . . . 303

Check Your Statistical Concepts-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 303Types of Sampling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

Probability Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304Non-probability Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

Considerations in Choosing Probability Sampling . . . . . . . . . . . . . . . . 312Considerations in Choosing Non-probability Sampling . . . . . . . . . . . . 313

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Criteria in Selecting Sample Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313Sample Size on the Basis of Cost Factor . . . . . . . . . . . . . . . . . . . . 313Sample Size on the Basis of Accuracy Factor . . . . . . . . . . . . . . . . 314

Biases in Survey Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316Biases Due to Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316Biases Due to Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

Steps in Survey Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317Objectives of the Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317Defining the Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318Deciding the Sampling Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 318Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318Pilot Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319Compilation of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319Interpretation of Findings and Conclusions . . . . . . . . . . . . . . . . . . 320

Check Your Statistical Concepts-II . . . . . . . . . . . . . . . . . . . . . . . . . . 320Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

Finding Random Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

Sampling and Its Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325Sample and Population Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 326Method of Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326Sampling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327



9 Research Design in Psychology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333Experimental Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334Non-experimental Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334Design of Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

Independent Group Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335Repeated Measures Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

Principles of Design of Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 336Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336Replication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337Blocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

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Methods of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338Laboratory Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338Field Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340Field Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341Observational Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343Ex-Post Facto Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344

What Is Research Design? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345Experimental Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

Factorial Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

Solving Experimental Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352Completely Randomized Design with Excel(One-Way ANOVA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

Experimental and Non-experimental Research . . . . . . . . . . . . . . . . 357Methods of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357Research Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358


Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 363Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

10 Statistical Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365Theory of Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

Point Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367Interval Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368Factors Affecting the Confidence Interval . . . . . . . . . . . . . . . . . . . 369Confidence Intervals for Population Mean in Large Sample . . . . . . 370Confidence Intervals for Population Mean When r is Unknown . . . 372Confidence Interval for the Proportion in Large Sample . . . . . . . . . 375

Check Your Computing Skill-I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376Check Your Statistical Concepts-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 377Testing of Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377Important Terminologies in Hypothesis Testing . . . . . . . . . . . . . . . . . 378

Types of Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378Type I and Type II Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379Level of Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

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Power of the Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380Relation Between a and b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380One-Tailed and Two-Tailed Tests . . . . . . . . . . . . . . . . . . . . . . . . . 381Degree of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382Test Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382Rejection Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383The p-value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

Procedure of Testing Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384Criteria for Test Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

Large Sample Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385Critical Value of Z-statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385Z-test for One Sample (r Known) . . . . . . . . . . . . . . . . . . . . . . . . . 387Z-test for Two Independent Samples: Population Variances r21 andr22 Known . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

Test of Significance for Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . 392Testing the Significance for Single Proportion . . . . . . . . . . . . . . . . 393Assumptions in Testing the Significance of Proportion in a SingleGroup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393Testing the Significance of Difference BetweenTwo Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394Assumptions in Comparing the Proportions in Two Groups . . . . . . 395

Small Sample Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398Critical Values of t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399t-test for One Sample: Population Variance (r2) is Unknown . . . . . 399t-test for Independent Samples: Population Variances r21 and r22Are Unknown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403Computation of Mean and Pooled Standard Deviation . . . . . . . . . . 404Computation of Mean and Pooled Standard Deviation . . . . . . . . . . 406t-test for Paired Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407Computation of D and SD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411Testing of Hypothesis for Single Group Variance . . . . . . . . . . . . . 412Test of Significance for the Difference Between Two Variances . . . 414

Test of Significance for Correlation Coefficient . . . . . . . . . . . . . . . . . 416Check Your Computing Skill-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417Check Your Statistical Concepts-II . . . . . . . . . . . . . . . . . . . . . . . . . . 418Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

Comparing Group Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

Testing of Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430Large Sample and Small Sample Tests . . . . . . . . . . . . . . . . . . . . . 431


Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436

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Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 436Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437Long-Answer-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

11 Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439One-Way Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

One-Way ANOVA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440Procedure of Applying One-Way ANOVA . . . . . . . . . . . . . . . . . . 441Using Several t-tests Instead of ANOVA . . . . . . . . . . . . . . . . . . . . 444

Check Your Statistical Concepts-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 451Two-Way Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452

Two-Way ANOVA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454Procedure of Applying Two-Way ANOVA . . . . . . . . . . . . . . . . . . 454

Check Your Statistical Concepts-II . . . . . . . . . . . . . . . . . . . . . . . . . . 462Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464

Two-Way Analysis of Variance with Excel . . . . . . . . . . . . . . . . . . 464Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468One-Way Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 468Two-way Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

Excercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469Long-Answer Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471

Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 474Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475Long-Answer Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475

12 Non-parametric Tests for Psychological Data . . . . . . . . . . . . . . . . . 477Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477Non-parametric Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478Advantages of Non-parametric Tests . . . . . . . . . . . . . . . . . . . . . . . . . 478Disadvantages of Non-parametric Tests . . . . . . . . . . . . . . . . . . . . . . . 478Non-parametric Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479Chi-Square Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

Assumptions in Chi-Square Test . . . . . . . . . . . . . . . . . . . . . . . . . . 480Application of Chi-square Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 480Yates’ Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

Check Your Statistical Concepts-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

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Runs Test to Test the Randomness . . . . . . . . . . . . . . . . . . . . . . . . . . 486Runs Test in Small Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487Runs Test in Large Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

Sign Test for One Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490Sign Test for Paired Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493Median Test for Two Independent Samples . . . . . . . . . . . . . . . . . . . . 495Mann–Whitney U Test for Two Samples . . . . . . . . . . . . . . . . . . . . . . 498Kruskal–Wallis Test (One-Way ANOVA for Non-parametric Data) . . . 504The Friedman Test (One-Way Repeated Measure ANOVA forNon-parametric Data) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507Check Your Statistical Concepts-II . . . . . . . . . . . . . . . . . . . . . . . . . . 510Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512

Computing Chi-Square in Excel . . . . . . . . . . . . . . . . . . . . . . . . . . 512Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516


Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 520Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521Long-Answer-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

13 Non-parametric Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523Rank Order Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524

Limits of the Rank Order Correlation . . . . . . . . . . . . . . . . . . . . . . 525Advantages of Rank Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 525Limitations of Rank Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 525

Bi-Serial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527Steps in Computing Bi-serial Correlation . . . . . . . . . . . . . . . . . . . . 528Limits of Bi-serial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529Characteristics of Bi-serial Correlation . . . . . . . . . . . . . . . . . . . . . . 529Limitations of Bi-serial Correlation . . . . . . . . . . . . . . . . . . . . . . . . 529Testing the Significance of Bi-serial Correlation . . . . . . . . . . . . . . . 529

Point Bi-Serial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530Testing the Significance of Point Bi-serial Correlation . . . . . . . . . . 531

Check Your Statistical Concepts-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 536Tetrachoric Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537

Steps in Computing Tetrachoric Correlation . . . . . . . . . . . . . . . . . . 538Limits of Tetrachoric Correlation . . . . . . . . . . . . . . . . . . . . . . . . . 538Testing the Significance of Tetrachoric Correlation . . . . . . . . . . . . 539

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Phi Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545Steps in Computing Phi Coefficient . . . . . . . . . . . . . . . . . . . . . . . . 545Limits of Phi Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546Testing the Significance of Phi Coefficient . . . . . . . . . . . . . . . . . . . 546

Contingency Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550Check Your Statistical Concepts-II . . . . . . . . . . . . . . . . . . . . . . . . . . 552Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554

Computing Rank Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557


Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 563Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564Objective-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564Long-Answer-Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564

14 Application of Factor Analysis in Psychological Data . . . . . . . . . . . 567Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567History of Factor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

Assumptions in Factor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 569Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570

Important Terminologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 570Factor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571Factor Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572Communality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572Eigenvalue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572Kaiser Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573Percentage Variance Explained . . . . . . . . . . . . . . . . . . . . . . . . . . . 573Factor Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574

Steps Followed in Factor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 574Describing Procedure in Factor Analysis . . . . . . . . . . . . . . . . . . . . . . 575Check Your Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581Check Your Computing Skill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582Computing with Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583Important Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583

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Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584



Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611

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About the Author

Prof. J. P. Verma is currently working as Professor of statistics, Headof the Department of Sport Psychology and Dean Students Welfare at LakshmibaiNational Institute of Physical Education (LNIPE), Gwalior, India. He also workedas Director, Centre for Advanced Studies at the institute. Prof. Verma is a tripleMasters – in Statistics, Psychology and Computer Application, besides a PhD inMathematics, and has an experience of more than thirty seven years in teaching andresearch. He has published ten books with leading publishers like Wiley, Springer,McGraw Hills on research and statistics in the area of management, exercise sci-ence, health, sports and physical education. He has a patent to his credit on Fit-nessWatch (a fitness assessment and management system for school children andyouth). In 2018 he has completed a major research project on talent identification insports, funded by the Ministry of Youth Affairs and Sports, Govt. of India. Prof.Verma was a visiting fellow in the University of Sydney in 2002. He has under-taken academic visits to the universities in Bulgaria, Qatar, Australia, Poland andScotland, where he has conducted numerous workshops on research methodology,research designs, multivariate analysis, and data modeling in the area of manage-ment, social sciences, physical education, sports sciences, economics, and healthsciences.

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Statistics and Research Methods in Psychology with Excel

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