Non parametric statistics

1. NON PARAMETRIC
STATISTICS
APPLICATION NUMBER/ STUDENT ID: EE8A5F4AEC4611E9A6408DE3F212CAF4
SHUBHAM PANDEY
BANARAS HINDU UNIVERSITY

2. 1.Does not specify any condition about the parameter of population
2. Also known as distribution free statistics
3. Does not specify any rigid conditions although certain assumptions are
associated with it and are as;
A. The variables under study should be continuous
B. Observations should be independent
Non parametric test should be used only in the following cases;
1. Distribution of population sample is not normal one
2. The variables have been quantified on the basis of
a. Nominal Measures (Frequency counts) &
b. Ordinal Measures (Ranking)
Note: Because non-parametric statistical tests are based upon frequency
counts or rankings rather than on the measured values they are less precise
and our list likely to reject a null hypothesis when it is false i.e., possibility of
committing Type 2 error.
And that is why a non parametric statistical test is used only when the
parametric assumptions can not be met.

3. Some statistician however argue that nonparametric statistical tests are
more powerful and have more merits than parametric test because
their validity is not based upon the assumptions about the population
distribution.
For some population distributions NPST are superior in power to PST
(Whitney, 1948).
Non parametric methods:
There is at least one non parametric test equivalent to a parametric test
and these tests fall into several categories and are as;
1. Tests of differences between groups for independent samples
2. Tests of differences between variables for dependent samples
3. Tests of relationship between variables

4. A. DIFFERENCES B/W INDEPENDENT GROUPS
1.TWO SAMPLES COMPARE MEAN VALUE FOR SOME
VARIABLE OF INTEREST
Parametric Non Parametric
T test for independent samples Wald Wolfowitz runs test
Mann Whitney U test
Kolmogrove-Smirnov two sample test

5. 2.MULTIPLE GROUPS
Parametric Non Parametric
Analysis of variance ANOVA/MANOVA Kruskal-Wallis analysis of ranks
Median test

6. B.DIFFERENCE B/W DEPENDENT GROUPS
1.COMPARE TWO VARIABLES MEASURED IN THE SAME
SAMPLE
Parametric Non Parametric
T test for dependent samples Sign Test
Wilcoxon’s matched pairs tests

7. 2. IF MORE THAN TWO VARIABLES ARE MEASURED IN
SAME SAMPLE
Parametric Non Parametric
Repeated measures ANOVA Friedman’s two way analysis of variance
Cochran Q

8. C. RELATIONSHIP B/W VARIABLES
TWO VARIABLES OF INTEREST ARE CATEGORICAL
Parametric Non Parametric
Correlation coefficient Spearman R
Kendall Tau
Coefficient Gamma
Chi Square
Phi Coefficient
Fisher exact test
Kendall coefficient of
concordance

9. Difference between Parametric and
Non Parametric test
•Parametric tests need many assumptions but Non Parametric
tests do not need assumptions about the nature and shape of
population involved.
•Parametric test and non parametric test both assume that the
observations are independent but non parametric test does not
require that the population of values be normally distributed.
•Non Parametric tests are used on Ordinal and Nominal data
parametric tests are used on Ratio and interval data.
•Parametric tests are statistically more powerful than non-
parametric tests i.e. they are more likely to detect a difference
truly exists.

10. References
A. K. Singh, “Tests, Measurements and Research Methods in Behavioral Sciences”, Revised 4thEdition,
Bharati Bhawan, 2009

11. Acknowledgement
I’m highly obliged to convey my gratitude towards the “Academic Writing” faculty for creating
this insightful course. As a budding learner with a quest to do research, I find this course to be
very exhaustive that covers every essential domain in the field of research with academic
writing as its quintessential prospect. I feel fortunate to be a part of this process of learning
and I will be looking forward for more of such lectures.
SWAYAM