Parametric &
Non-parametric
Parametric
 A parameter to compare
Mean, S.D.
Normal Distribution & Homogeneity
Non-Parametric
 No parameter is compared
Significant numbers in a category plays the role
 No need of Normal Distribution & Homogeneity
 Used when parametric is not applicable.
Parametric &
Non-parametric
Parametric
Vs
Non-parametric
Which is good ?
If parametric is not applicable, then only we go for a non-parametric
Both are applicable, we prefer parametric. Why?
In parametric there is an estimation of values.
Null hypothesis is based on that estimation.
In non-parametric we are just testing a Null Hypothesis.
Normality ?
How do you check Normality ?
 The mean and median are approximately same.
 Construct a Histogram and trace a normal curve.
Example
? Level of Significance / p-value / Type I error / α
? Degree of Freedom
Types of variables
Independent variable
Dependent variable
Data representation
1. Continuous or Scale variable
2. Discrete variable
(Categorical)
Nominal
Ordinal
Decide your test
Decide your test
Paired t-test
Areas of application
>> When there is one group pre & post scores to compare.
>> In two group studies, if there is pre & post assessment, paired t is applied
to test whether there is significant change in individual group.
S=
S.E. =
Example
t=
S.E.
Unpaired/independent
t-test
Areas of application
>> When there is two group scores to compare.
(One time assessment of dependent variable).
>> In two group studies, if there is pre & post assessment, paired t is applied
to test whether there is significant change in individual group.
After this, the pre-post differences in the two groups are taken for testing.
Example
ANOVA
Areas of application
>> When there is more than two group scores to compare.
Group A x Group B x Group C
Post-HOC procedures after ANOVA
helps to compare the in-between groups
AxB , AxC , BxC
Similar to doing 3 unpaired t tests
Example
Wilcoxon Matched
Pairs
A Non-parametric procedure
>> This is the parallel test to the parametric paired t-test
 Before after differences are calculated with direction + ve or –ve
 0 differences neglected.
 Absolute differences are ranked from smallest to largest
 Identical marks are scored the average rank
 T is calculated from the sum of ranks associated with least frequent sign
 If all are in same direction T = 0
Example
Mann Whitney U
A Non-parametric procedure
>> This is the parallel test to the parametric unpaired t-test
 Data in both groups are combined and ranked
 Identical marks are scored the average rank
Sum of ranks in separate groups are calculated
 Sum of ranks in either group can be considered for U.
 n1 is associated with ∑R1i , n2 is associated with ∑R2j
Example
Median Test
A Non-parametric procedure
Similar to the cases of Mann Whitney
>> This is the parallel test to the parametric unpaired t-test
 Data in both groups are combined and median is calculated
 Contingency table is prepared as follows
Kruskal Walis
A Non-parametric procedure
>> This is the parallel test to the parametric ANOVA
>> ANOVA was an extension of 2-group t-test
>> Kruskal Walis is an extension of Mann Whitney U
 Data in all groups are combined and ranked
 Identical marks are scored the average rank
Sum of ranks in separate groups are calculated
Areas of application
Example
>> Areas similar to ANOVA
>> Comparison of dependent variable between categories in a
demographic variable
Mc Nemar’s Test
Areas of application
>> Similar to the parametric paired t-test, but the dependent variable
is discrete, qualitative.
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