Non Parametric Tests

v When to Choose a Statistical Tests OR When NOT to Choose? v Parametric vs. Non-Parametric Tests (Comparison)
v Parameters to check when Choosing a Statistical Test:
- Distribution of Data
- Type of data/Variable
- Types of Analysis (What’s the hypothesis)
- No of groups or data-sets
- Data Group Design
v Snapshot of all statistical test and “How” to Choose using above parameters v Explanation using Examples:
- Mann Whitney U Test
- Wilcoxon Sign Rank Test
- Spearman’s co-relation
- Chi-Square Test
v Conclusion

1. Dr. Zarrin Ansari Second Year Resident Pharmacology Dept. LTMMC & GH, Sion June 28, 2021 Non-Parametric Tests 1 Statistics For Non-Statisticians

2. 2 Table of Content When to Choose a Statistical Tests OR When NOT to Choose? Types of Statistical Tests (Parametric vs. Non-Parametric Tests) Parameters to check when Choosing a Statistical Test: Distribution of Data Type of data/Variable Types of Analysis (What’s the hypothesis) No of groups or data-sets Data Group Design Snapshot of all statistical test and “How” to Choose using above parameters Explanation using Examples: Mann Whitney U Test Wilcoxon Sign Rank Test Spearman’s co-relation Chi-Square Test

3. 3 When to Choose a Statistical Tests? Or When NOT to Choose a Statistical Tests?

4. Parametric Test Non-Parametric test Normal Distribution Skewed Distribution Based on assumptions Less rigid & fewer assumptions Quantitative Data Qualitative Data More Statistical power Less Statistical Power No outliers Outliers present Mainly compares means +/- SDs Mainly compares % and proportions Jain V . (2019) Review of preventive & social medicine: Including biostatistics. 11th ed. 4 Types of Statistical Test

5. 5 How to Choose a Statistical Test? Parameters to Check R Raveendran et al. (2014) A Practical Approach to PG Dissertation … ..a handbook of research methodology for postgraduate students. Second Edition. Chapter 8

6. Distribution of Data All bodily parameters follow Normal Distribution exception; Ab titers Measure of ranks/scores viz. Apgar, Scoring of liver fibrosis, Pain in visual analogue scale follow Non-normal Distribution Variables measured as counts e.g. no of people having headache etc. are binomial measurements. These for Non-normal distribution If Mean < 2 times SD then the distribution is Non-Normal Distribution Mean=Median=Mode Normal Distribution 6

7. Left sided Skewing Mean < Median < Mode Right sided Skewing Mean > Median > Mode Non-Normal Distribution Normal Distribution No Skewing Mean = Median = Mode Dakhale GN, Hiware SK, Shinde AT, Mahatme MS. Basic biostatistics for post-graduate students. Indian journal of pharmacology. 2012 Jul;44(4):435. 7

8. Types of Data/Variable Categorical/Non-numerical/ Qualitative N umerical/ Quantitative Ordinal (Order/Hierarchy) E.g. Tumor Staging Nominal (any Order/Hierarchy) E.g. Gender/Race etc. Discrete (Whole numbers) E.g. No of patients Continuous (Can take Decimals) E.g. Weight 8 R Raveendran et al. (2014) A Practical Approach to PG Dissertation … ..a handbook of research methodology for postgraduate students. Second Edition. Chapter 8

9. Types of Analysis ( What we want to do ?) (What’s the Hypothesis) Comparison Between Mean, Median & Proportions of one or > one group Co-relation Analysis Find relationship between two variable Regression Analysis: Predicting one variable with another R Raveendran et al. (2014) A Practical Approach to PG Dissertation … ..a handbook of research methodology for postgraduate students. Second Edition. Chapter 8 9

10. No of Groups & Data sets 10 R Raveendran et al. (2014) A Practical Approach to PG Dissertation … ..a handbook of research methodology for postgraduate students. Second Edition. Chapter 8

11. Data Group Design 11 R Raveendran et al. (2014) A Practical Approach to PG Dissertation … ..a handbook of research methodology for postgraduate students. Second Edition. Chapter 8

12. C1 C2 C3 Comparison Association of two variables Regression analysis of two variables Of 2 data sets Of > 2 data sets Paired Unpaired Paired Unpaired C1a C1b C1c C1d R1 Normally distributed continuous data (Summarized as means) Paired t test Unpaired t test Repeated Measures ANOVA (Two way ANOVA) One-way ANOVA Pearson correlation Linear regression R2 Scores, ranks & non-normally distributed continuous data (Summarized as Median) Wilcoxon singed rank test Mann Whitney U Test Friedman test Kruskal -Wallis test Spearman’s rank correlation Non-parametric regression R3 Dischotomous Data (Summarized as proportions) Mc Nemar’s test Fischer’s test or Chi square test Cochrane Q test Chi square test Contingency coefficient Logistic regression How to Choose a Statistical Test? 12 R Raveendran et al. (2014) A Practical Approach to PG Dissertation … ..a handbook of research methodology for postgraduate students. Second Edition. Chapter 8

13. Example 1 Drug X (New anti-asthmatic) given in one group of patients (n=5). Placebo given in second group (n=5). Measure number of asthma attack/weak Steps: Aim: To evaluate anti-asthmatic effect of new drug Hypothesis: (Null) The new drug is NOT effective anti-asthmatic. No of groups/data: 2 groups Data Group design: Unpaired/ I ndependant Distribution: Non-normal (Small sample size) Type of analysis: Comparison Table: Mann Whitney U Test 13

14. C1 C2 C3 Comparison Association of two variables Regression analysis of two variables Of 2 data sets Of > 2 data sets Paired Unpaired Paired Unpaired C1a C1b C1c C1d R1 Normally distributed continuous data (Summarized as means) Paired t test Unpaired t test Repeated Measures ANOVA (Two way ANOVA) One-way ANOVA Pearson correlation Linear regression R2 Scores, ranks & non-normally distributed continuous data (Summarized as Median) Wilcoxon singed rank test Mann Whitney U Test Friedman test Kruskal -Wallis test Spearman’s rank correlation Non-parametric regression R3 Dischotomous Data (Summarized as proportions) Mc Nemar’s test Fischer’s test or Chi square test Cochrane Q test Chi square test Contingency coefficient Logistic regression How to Choose a Statistical Test? 14 R Raveendran et al. (2014) A Practical Approach to PG Dissertation … ..a handbook of research methodology for postgraduate students. Second Edition. Chapter 8

15. Consider a Phase II clinical trial designed to investigate the effectiveness of a new drug to reduce symptoms of asthma in children. A total of n=10 participants are randomized to receive either the new drug or a placebo. Participants are asked to record the number of episodes of shortness of breath over a 1 week period following receipt of the assigned treatment. https:// sphweb.bumc.bu.edu / otlt /mph-modules/ bs /bs704_nonparametric/bs704_nonparametric4.html#:~:text=The%20test%20statistic%20for%20the,our%20example%2C%20U%3D3. 15

16. https:// sphweb.bumc.bu.edu / otlt /mph-modules/ bs /bs704_nonparametric/bs704_nonparametric4.html#:~:text=The%20test%20statistic%20for%20the,our%20example%2C%20U%3D3. The first step is to assign ranks and to do so we order the data from smallest to largest. This is done on the combined or total sample (i.e., pooling the data from the two treatment groups (n=10)), and assigning ranks from 1 to 10 . R1= 37 R2= 18 16

17. The test statistic for the Mann Whitney U Test is denoted  U  and is the  smaller  of U 1  and U 2 , defined below. U calculated =3 Smaller values of U support the research hypothesis, and larger values of U support the null hypothesis . U tabular = 2 https:// sphweb.bumc.bu.edu / otlt /mph-modules/ bs /bs704_nonparametric/bs704_nonparametric4.html#:~:text=The%20test%20statistic%20for%20the,our%20example%2C%20U%3D3. 17

18. D ecision rule is to reject H  if Ucalc   <   U tab Ucalc = 3 > Utab =2 H0 is NOT rejected The difference between the two arms is not statistically different https:// sphweb.bumc.bu.edu / otlt /mph-modules/ bs /bs704_nonparametric/bs704_nonparametric4.html#:~:text=The%20test%20statistic%20for%20the,our%20example%2C%20U%3D3. 18

19. Descriptive Statistics 19

20. Example 2 Drug X given in one group of autistic children (n=8). The number of repetitive behavior was observed over period of three hours before and after the administration of the new drug for a period of one weak Steps: Aim: To evaluate anti-autistic effect of new drug Hypothesis: (Null) The new drug is NOT effective in treating autism No of groups/data: one group but two data sets Group Data design: P aired Distribution: Non-normal (Small sample size) Type of analysis: Comparison Table : Wilcoxon singed rank test 20

21. C1 C2 C3 Comparison Association of two variables Regression analysis of two variables Of 2 data sets Of > 2 data sets Paired Unpaired Paired Unpaired C1a C1b C1c C1d R1 Normally distributed continuous data (Summarized as means) Paired t test Unpaired t test Repeated Measures ANOVA (Two way ANOVA) One-way ANOVA Pearson correlation Linear regression R2 Scores, ranks & non-normally distributed continuous data (Summarized as Median) Wilcoxon singed rank test Mann Whitney U Test Friedman test Kruskal -Wallis test Spearman’s rank correlation Non-parametric regression R3 Dischotomous Data (Summarized as proportions) Mc Nemar’s test Fischer’s test or Chi square test Cochrane Q test Chi square test Contingency coefficient Logistic regression How to Choose a Statistical Test? 21 R Raveendran et al. (2014) A Practical Approach to PG Dissertation … ..a handbook of research methodology for postgraduate students. Second Edition. Chapter 8

22. W+ (sum of the positive ranks ) =32 W- (sum of the negative ranks ) =4 The test statistic is W ( cal ) = 4. https:// sphweb.bumc.bu.edu / otlt /mph-modules/ bs /bs704_nonparametric/BS704_Nonparametric6.html 22

23. If W (calculated) =/< W (tabulated), then reject H0 If W (calculated) > W (tabulated), then DO NOT reject H0 W (calculated) = 4 W (tabulated) = 6 Thus, null hypothesis is rejected … .. https:// sphweb.bumc.bu.edu / otlt /mph-modules/ bs /bs704_nonparametric/BS704_Nonparametric6.html 23

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25. Example 3 Does the number of symptoms in a patient predict their willingness to take medication? Steps: Aim: To evaluate co-relation between number of symptoms the patients have to their willingness to take medicine Hypothesis: (Null) There is NO correlation between the two variable No of groups/data: one groups Group Data design: NA Distribution: Non-normal (ordinal data) Type of analysis: Correlation Table : Spearman rank correlation analysis 25

26. C1 C2 C3 Comparison Association of two variables Regression analysis of two variables Of 2 data sets Of > 2 data sets Paired Unpaired Paired Unpaired C1a C1b C1c C1d R1 Normally distributed continuous data (Summarized as means) Paired t test Unpaired t test Repeated Measures ANOVA (Two way ANOVA) One-way ANOVA Pearson correlation Linear regression R2 Scores, ranks & non-normally distributed continuous data (Summarized as Median) Wilcoxon singed rank test Mann Whitney U Test Friedman test Kruskal -Wallis test Spearman’s rank correlation Non-parametric regression R3 Dischotomous Data (Summarized as proportions) Mc Nemar’s test Fischer’s test or Chi square test Cochrane Q test Chi square test Contingency coefficient Logistic regression How to Choose a Statistical Test? 26 R Raveendran et al. (2014) A Practical Approach to PG Dissertation … ..a handbook of research methodology for postgraduate students. Second Edition. Chapter 8

27. 27 Spearman’s Correlation co-efficient ( Rs )= 0.8

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29. Example 2 Is smoking associated with cancer? Steps: Aim: To evaluate of smoking and cancer Hypothesis: (Null) The new drug is NOT effective in treating autism No of groups/data: one groups Study design: P aired Distribution: Non-normal (Small sample size) Type of analysis: Comparison Table : Wilcoxon singed rank test 29

30. Chi-Square Test Used to test significance of association between 2 or more qualitative characteristics It checks for patterns and relationships in categorical variable Is used to compare proportions in 2 or more groups Is used for Non-normal distribution Applications of Chi-square test - Test of Independence - Test of Goodness of Fit Jain V. Review of preventive & social medicine: Including biostatistics. 11th ed. New Delhi, India: Jaypee Brothers Medical; 2019. 30

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32. To see relationship between Smoking and Cancer H0 = There is NO relationship between Smoking and Cancer H1 = Smoking is associated with Cancer 32

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34. 34 Some Perks in Statistical Concepts: Uniform Distribution Degree of Freedom Kurtosis Normality testing

35. 35 Methods to Check for Normality of Data Visual Methods: Histogram, Box-plots, Q-Q plots Normality Tests Kolmogorov-Smirnov (K-S) test Lilliefors corrected K-S test Shapiro- Wilk test Anderson-Darling test Cramer-von Mises test Kurtosis Skweness Ghasemi et al. Normality Tests for Statistical Analysis: A Guide for Non-Statisticians. Int J Endocrinol Metab. 2012;10(2):486-489.