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
1

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
Sample Size
Types of data
No of
groups/ data
sets
Distribution
of data
Data Group
design
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. Normal
Non-Normal
Dichotomous
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
Numerical/
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
One group (Two or > Two Data sets)
Two groups (Two data sets)
> Two groups/ > 2 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. UNPAIRED /
INDEPENDANT
PAIRED /
MATCHED
•2 GROUPS OR > 2
GROUPS OF TOTALLY
DIFFERENT SET OF
SUBJECTS
INDEPENDENT OF
EACH OTHER
• ONE GROUP
BEFORE OR AFTER
INTERVENTION
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:
1. Aim: To evaluate anti-asthmatic effect of new drug
2. Hypothesis: (Null) The new drug is NOT effective anti-asthmatic.
3. No of groups/data: 2 groups
4. Data Group design: Unpaired/Independant
5. Distribution: Non-normal (Small sample size)
6. 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 U1 and U2, defined below.
Ucalculated=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. Decision rule is to
reject H0 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:
1. Aim: To evaluate anti-autistic effect of new drug
2. Hypothesis: (Null) The new drug is NOT effective in treating autism
3. No of groups/data: one group but two data sets
4. Group Data design: Paired
5. Distribution: Non-normal (Small sample size)
6. 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

24. 24

25. Example 3
Does the number of symptoms in a patient predict their willingness to take
medication?
Steps:
1. Aim: To evaluate co-relation between number of symptoms the patients have to
their willingness to take medicine
2. Hypothesis: (Null) There is NO correlation between the two variable
3. No of groups/data: one groups
4. Group Data design: NA
5. Distribution: Non-normal (ordinal data)
6. 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

28. 28

29. 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

30. 31

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

32. 33

33. 34
Some Perks in Statistical Concepts:
• Uniform Distribution
• Degree of Freedom
• Kurtosis
• Normality testing

34. 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.

35. 36
Thank you for your Attention