Cover
Preface
Acknowledgments
About the Companion Website
1 Importance of Assumptions in Using Statistical Techniques
1. 1.1 Introduction
2. 1.2 Data Types
3. 1.3 Assumptions About Type of Data
4. 1.4 Statistical Decisions in Hypothesis Testing Experiments
5. 1.5 Sample Size in Research Studies
6. 1.6 Effect of Violating Assumptions
7. Exercises
8. Answers
2 Introduction of SPSS and Segregation of Data
1. 2.1 Introduction
2. 2.2 Introduction to SPSS
3. 2.3 Data Cleaning
4. 2.4 Data Management
5. Exercises
6. Answers
3 Assumptions in Survey Studies
1. 3.1 Introduction
2. 3.2 Assumptions in Survey Research
3. 3.3 Questionnaire's Reliability
4. Exercise
5. Answers
4 Assumptions in Parametric Tests
1. 4.1 Introduction
2. 4.2 Common Assumptions in Parametric Tests
3. 4.3 Assumptions in Hypothesis Testing Experiments
4. 4.4 F‐test For Comparing Variability
5. 4.5 Correlation Analysis
6. 4.6 Regression Analysis
7. Exercises
8. Answers
5 Assumptions in Nonparametric Tests
1. 5.1 Introduction
2. 5.2 Common Assumptions in Nonparametric Tests
3. 5.3 Chi‐square Tests
4. 5.4 Mann‐Whitney U Test
5. 5.5 Kruskal‐Wallis Test
6. 5.6 Wilcoxon Signed‐Rank Test
7. Exercises
8. Answers
6 Assumptions in Nonparametric Correlations
1. 6.1 Introduction
2. 6.2 Spearman Rank‐Order Correlation
3. 6.3 Biserial Correlation
4. 6.4 Tetrachoric Correlation
5. 6.5 Phi Coefficient (Φ)
6. 6.6 Assumptions About Data
7. 6.7 What if the Assumptions Are Violated?
8. Exercises
9. Answers
Appendix Statistical Tables
Bibliography
Index
End User License Agreement

List of Tables

Chapter 1
1. Table 1.1 Assumptions about data in computing measures of central tendency.
2. Table 1.2 Marks for the students in an examination.
3. Table 1.3 Statistical errors in hypothesis testing experiment.
4. Table 1.4 Implication of errors in hypothesis testing experiment.
5. Table 1.5 Sample size for different precision.
Chapter 2
1. Table 2.1 Response of the subjects and their demographic data on the issue “Shou...
2. Table 2.2 Descriptive statistics.
3. Table 2.3 Frequencies of “Response” variable.
4. Table 2.4 Commands for selecting cases with different conditions in SPSS.
Chapter 3
1. Table 3.1 A typical scoring of the subject's response in a lifestyle assessment ...
2. Table 3.2 Scores of the subjects in each group of statements.
3. Table 3.3 English test with possible answers.
4. Table 3.4 Computation in Kuder–Richardson test for testing reliability.
5. Table 3.5 Sample questions on a lifestyle assessment test.
6. Table 3.6 Response of the subjects on different items of the questionnaire.
7. Table 3.7 Reliability statistics.
8. Table 3.8 Output of the reliability analysis.
9. Table 3.9 Guidelines for internal consistency benchmark.
Chapter 4
1. Table 4.1 Performance of the students.
2. Table 4.2 Tests of normality for the data on students' performance.
3. Table 4.3 Marks of the students.
4. Table 4.4 Tests of normality for the data on students' marks.
5. Table 4.5 Transformed data.
6. Table 4.6 Tests of normality for the transformed data on students' marks.
7. Table 4.7 Runs test for the data on weight.
8. Table 4.8 Data showing the effect of outlier.
9. Table 4.9 Data file for Levene's test.
10. Table 4.10 Results of Levene's test for equality of variances.
11. Table 4.11 Anxiety scores.
12. Table 4.13 Tests of normality for the data on students' marks.
13. Table 4.12 Students marks in mathematics.
14. Table 4.14 Descriptive statistics.
15. Table 4.15 T‐table for the data on marks in mathematics.
16. Table 4.17 Tests of normality for the data on hemoglobin.
17. Table 4.18 Pairedt‐test for the data on hemoglobin.
18. Table 4.16 Hemoglobin contents of the participants before and after the exercise...
19. Table 4.19 Data on hemoglobin and computation in sign test.
20. Table 4.20 Memory scores.
21. Table 4.21 Tests of normality for the data on memory.
22. Table 4.22 Data file in SPSS for independent‐samplet‐test.
23. Table 4.23 Independent‐samplest‐test for the data on memory.
24. Table 4.24 Test statistics for Mann–Whitney test.
25. Table 4.25 IQ scores of students.
26. Table 4.26 Descriptive statistics for IQ scores.
27. Table 4.27 Tests for normality.
28. Table 4.28 Levene's test of equality of error variances.
29. Table 4.29 The analysis of variance (ANOVA) table.
30. Table 4.30 Multiple comparisons post‐hoc test.
31. Table 4.31 Learning scores of the subjects in different treatment groups.
32. Table 4.32 Data format in SPSS for one‐way ANOVA.
33. Table 4.33 Test of homogeneity of variances.
34. Table 4.34 ANOVA table for the scores in Maths.
35. Table 4.35 Tests of normality.
36. Table 4.36 Mean ranks of different groups.
37. Table 4.37 Output of Kruskal‐Wallis test.
38. Table 4.38 Child data.
39. Table 4.39 Pearson's correlation coefficient.
40. Table 4.40 Spearman's correlation coefficient.
41. Table 4.41 Testing for multicollinearity.
42. Table 4.42 Testing for autocorrelation.
43. Table 4.43 The ANOVA table: testing for overall model fitness.^a
44. Table 4.44 Model summary.^b
45. Table 4.45 Regression coefficients.^a
Chapter 5
1. Table 5.1 Runs test for the Gender and Age of respondents.
2. Table 5.2 Frequencies for the chi‐square goodness‐of‐fit test.
3. Table 5.3 Chi‐square goodness‐of‐fit test results.
4. Table 5.4 Chi‐square test for independence: crosstabs results.
5. Table 5.5 Chi‐square test of independence results.
6. Table 5.6 Chi‐square test for homogeneity: crosstabs results.
7. Table 5.7 Chi‐square test for homogeneity: test statistic andp‐value.
8. Table 5.8 Ranks for the variable Gender.
9. Table 5.9 Test statistics: Mann‐Whitney U test.
10. Table 5.10 Hypothesis test summary for Mann‐Whitney U test.
11. Table 5.11 Ranks for the variable Happiness of marriage.
12. Table 5.12 Kruskal‐Wallis test results.
13. Table 5.13 Hypothesis test summary for Kruskal‐Wallis H test.
14. Table 5.14 Independent samples test view.
15. Table 5.15 Sample average rank of Race of respondents.
16. Table 5.16 Migraine score before and after treatment.
17. Table 5.17 Ranks for the before and after treatment scores.
18. Table 5.18 Results for the Wilcoxon Signed‐Rank test.
Chapter 6
1. Table 6.1 Heart rate and number of visits.
2. Table 6.2 Correlations.
3. Table 6.3 Test score and handedness data.
4. Table 6.4 Correlations.
5. Table 6.5 Responses of the raters to classify subjects having neurosis.
6. Table 6.6 Clinical findings of psychotherapists on depression.
7. Table 6.7 Results: crosstabulation (Rater A × Rater B) and Phi coefficient.

List of Illustrations

Chapter 1
1. Figure 1.1 Showing the distribution of data.
2. Figure 1.2 Distribution of mean under null and alternative hypotheses.
3. Figure 1.3 Showing comparison of power in (b) one‐ and (a) two‐tailed tests at ...
Chapter 2
1. Figure 2.1 Screen for creating/opening data file.
2. Figure 2.2 Screen for defining variables and their characteristics.
3. Figure 2.3 Defining code of nominal variable.
4. Figure 2.4 Screen after defining all the variables and their properties.
5. Figure 2.5 Screen after entering the data in SPSS file.
6. Figure 2.6 Data importing.
7. Figure 2.7 Data import options.
8. Figure 2.8 Screen showing command sequence for descriptive statistics.
9. Figure 2.9 Screen showing selection of variables in the analysis.
10. Figure 2.10 Screen for selecting different statistics for computation.
11. Figure 2.11 Screen for selecting chart type.
12. Figure 2.12 Graph for checking normality of “Response” variable.
13. Figure 2.13 Screen showing commands for sorting cases.
14. Figure 2.14 Screen for selecting variable(s) for sorting cases.
15. Figure 2.15 Data file with sorted cases on response and district variables.
16. Figure 2.16 Screen showing commands for sorting variables.
17. Figure 2.17 Screening showing option for sorting criterion.
18. Figure 2.18 Screening showing sorted data column wise based on variable's name.
19. Figure 2.19 Command for switching data from coding to categories and vice versa...
20. Figure 2.20 Data file showing nominal variables as per their categories.
21. Figure 2.21 Screen showing commands for selecting cases.
22. Figure 2.22 Screen for selecting cases.
23. Figure 2.23 Screen showing condition for selecting cases with Male responding A...
24. Figure 2.24 Screen showing selected cases with Male having response Agree.
25. Figure 2.25 Screen showing option for selecting specified number of cases rando...
26. Figure 2.26 Screen showing randomly selected cases.
27. Figure 2.27 Screen showing commands for splitting the file.
28. Figure 2.28 Screen showing option for defining the split variable.
29. Figure 2.29 SPSS data file.
30. Figure 2.30 Screen for defining formula for computing variable.
31. Figure 2.31 Screen showing data file with newly created BMI variable.
Chapter 3
1. Figure 3.1 Screen showing commands for reliability analysis.
2. Figure 3.2 Screen showing selection of items for reliability analysis.
3. Figure 3.3 Screen showing options for reliability outputs.
Chapter 4
1. Figure 4.1 Commands for testing normality.
2. Figure 4.2 Screen showing options for computing Shapiro–Wilk test.
3. Figure 4.3 Normal we Q–Q plot for the data on student's performance.
4. Figure 4.4 Distribution of data on weight by means of histogram.
5. Figure 4.5 Histogram showing distribution of X (Maths scores).
6. Figure 4.6 Histogram showing distribution of X (Science scores).
7. Figure 4.7 Screen showing options for Runs Test.
8. Figure 4.8 Screen showing option for selecting variables and identifying outlie...
9. Figure 4.9 Box plot for all three groups of scores.
10. Figure 4.10 Screen showing commands for Levene's test in SPSS.
11. Figure 4.11 Screen showing commands for inputs in Levene's test.
12. Figure 4.12 Screen showing steps for inputs in one‐sample t test.
13. Figure 4.13 Screen showing option for paired t test.
14. Figure 4.14 Screen showing options for independent‐samples t‐test.
15. Figure 4.15 Screen showing options for Mann–Whitney test. Source:
16. Figure 4.16 Three different groups/treatments with their means.
17. Figure 4.17 Three different groups/treatments with their means and overall mean...
18. Figure 4.18 Data file in SPSS for testing ANOVA assumptions. Source:
19. Figure 4.19 Path for testing Skewness and Kurtosis.
20. Figure 4.20 Procedure for testing Skewness and Kurtosis.
21. Figure 4.21 Path for testing normality.
22. Figure 4.22 Procedure for testing normality.
23. Figure 4.23 Normal Q–Q plots for IQ scores.
24. Figure 4.24 Procedure for Levene's test.
25. Figure 4.25 Path for One‐Way ANOVA.
26. Figure 4.26 Procedure for One‐Way ANOVA.
27. Figure 4.27 Means plot.
28. Figure 4.28 Procedure for Tukey's Post‐Hoc test.
29. Figure 4.29 Data file in SPSS for one‐way ANOVA.
30. Figure 4.30 Screen showing selection of variables in one‐way ANOVA.
31. Figure 4.31 Screen showing option for Post Hoc test in one‐way ANOVA.
32. Figure 4.32 Screen showing option for homogeneity test and means plot.
33. Figure 4.33 Screen showing sequence of commands in Kruskal‐Wallis test.
34. Figure 4.34 Screen showing selection of variables defining coding.
35. Figure 4.35 Data file in SPSS for correlation and regression analysis.
36. Figure 4.36 Procedure for creating a scatter plot.
37. Figure 4.37 Scatter plots for linearity.
38. Figure 4.38 Path for bivariate correlations.
39. Figure 4.39 Procedure for bivariate correlations.
40. Figure 4.40 Path for linear regression analysis.
41. Figure 4.41 Procedure for Linear Regression analysis.
42. Figure 4.42 Procedure for testing autocorrelation and multicollinearity.
43. Figure 4.43 Procedure for testing the normality of errors assumption.
44. Figure 4.44 The histogram (a) and P–P plot (b).
45. Figure 4.45 Scatter plot for the standardized residual.
Chapter 5
1. Figure 5.1 Path for the Runs test.
2. Figure 5.2 Choosing options for Runs test.
3. Figure 5.3 Path for chi‐square goodness‐of‐fit test.
4. Figure 5.4 Choosing options for chi‐square goodness‐of‐fit test.
5. Figure 5.5 Path for the chi‐square test of independence.
6. Figure 5.6 Choosing options for the chi‐square test of independence – 1.
7. Figure 5.7 Choosing options for the chi‐square test of independence – 2 and 3.
8. Figure 5.8 Clustered bar chart: Happiness of marriage vs. General happiness.
9. Figure 5.9 Weight cases procedure for testing homogeneity.
10. Figure 5.10 Clustered bar chart: testing for homogeneity based on gender.
11. Figure 5.11 Path for transforming variables.
12. Figure 5.12 Path 2 for Mann‐Whitney U test.
13. Figure 5.13 Choosing options for Mann‐Whitney U test (path 1).
14. Figure 5.14 Path 2 for Mann‐Whitney U test.
15. Figure 5.15 Mann‐Whitney U test: option 1, path 2.
16. Figure 5.16 Mann‐Whitney U test: option 2, path 2.
17. Figure 5.17 Mann‐Whitney U test: option 3, path 2.
18. Figure 5.18 Mean ranks distribution graph for Mann‐Whitney U test.
19. Figure 5.19 Path for Kruskal‐Wallis H test (path 1).
20. Figure 5.20 Options for Kruskal‐Wallis H test (path 1).
21. Figure 5.21 Path for Kruskal‐Wallis H test (path 2).
22. Figure 5.22 Options for Kruskal‐Wallis H test (path 2).
23. Figure 5.23 Kruskal‐Wallis test: option 1, path 2.
24. Figure 5.24 Kruskal‐Wallis test: option 2, path 2.
25. Figure 5.25 Pairwise comparisons of Race of respondents.
26. Figure 5.26 Data file in SPSS for Wilcoxon Signed‐Rank test.
27. Figure 5.27 Path for Wilcoxon Signed‐Rank test.
28. Figure 5.28 Options for Wilcoxon Signed‐Rank test.
Chapter 6
1. Figure 6.1 Data file in SPSS for computing Spearman rank‐order correlation.
2. Figure 6.2 Path for bivariate correlations.
3. Figure 6.3 Window for defining option for Spearman correlation.
4. Figure 6.4 Data file in SPSS for biserial correlation.
5. Figure 6.5 Options for bivariate correlations.
6. Figure 6.6 Path for crosstabs: Phi coefficient.
7. Figure 6.7 Screen showing option for selecting rows and columns in crosstabs.
8. Figure 6.8 Options for the Phi coefficient.

Copyright

This edition first published 2019

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Preface

The book titled Testing Statistical Assumptions in Research is a collaborative work of J. P. Verma and Abdel‐Salam G. Abdel‐Salam. While conducting research workshops and dealing with research scholars, we felt that most of the scholars do not bother much about the assumptions involved in using different statistical techniques in their research. Due to this reason, the results of the study become less reliable, and in certain cases, if the assumptions are severely violated, the results get completely reversed. In other words, in detecting the effect in hypothesis testing experiment, although the effect exists, it is not visible due to the extreme violation of assumptions. Since lots of resources and time are involved in conducting any survey or empirical research, one must test the related assumptions of statistical tests used in his or her analysis for making his or her findings more reliable.

The bringing out of this text has two specific purposes: first, we wish to educate the researchers about assumptions that are required to be fulfilled in different commonly used statistical tests and show the procedure of testing them using IBM SPSS®¹ Statistics software (SPSS) via illustrations. Second, we endeavor to motivate them to check assumptions by showing them the adverse effects of severely violating assumptions using specific examples. We have also suggested the remedial measures in using different statistical tests if assumptions are violated.

This book is meant for research scholars of different disciplines. Since most of the graduate students also write dissertations, this text is equally useful for them as well.

The book contains six chapters. Chapter 1 discusses the importance of assumptions in analyzing research data. The concept of hypothesis testing and statistical errors has been discussed in detail. We have also discussed the concept of power, sample size, and effect size and relationship among themselves in order to provide the foundation of hypothesis to the readers.

In Chapter 2, we have introduced SPSS functionality to the readers. We have also shown how to segregate data, draw random samples, file split, and create variables automatically. These operations are extremely useful for the researchers in analyzing the survey data. Further, acquaintance with SPSS in this chapter shall facilitate the readers to understand the procedure involved in testing assumptions in different chapters.

In Chapter 3, we have discussed different assumptions required in survey studies. We have deliberated upon the importance of designing surveys in reporting the efficient findings.

Chapter 4 gives various parametric tests and the related assumptions. We have shown the procedures for testing these assumptions using the SPSS software. In order to motivate the readers to use assumptions, we have shown many situations where violation of assumptions affects the findings. In this chapter, we have discussed assumptions in all those statistical tests that are commonly used by researchers such as z, t, and F tests, ANOVA, correlation, and regression analysis.

In Chapter 5, we have discussed assumptions required for different nonparametric tests such as Chi‐square, Mann‐Whitney, Kruskal‐Wallis, and Wilcoxon Signed‐Rank test. We have shown the procedures of testing these assumptions as well.

Finally, in Chapter 6, assumptions in nonparametric correlations such as bi‐serial correlation, tetrachoric correlation, and phi coefficient have been discussed. These types of analyses are often used by researchers in survey studies.

Hope this book will serve the purpose for which it has been written. The readers are requested to send their feedback about the book or about the problems that they encounter to the authors for further improvement in the text. You may contact the authors at their emails: Prof. J. P. Verma (email: vermajprakash@gmail.com, web: www.jpverma.org) and Dr. Abdel‐Salam G. Abdel‐Salam (email: abdelsalam811@gmail.com or abdo@vt.edu, web: https://www.abdo.website) for any help in relation to the text.

J. P. Verma

Abdel‐Salam G. Abdel‐Salam

Note