1. By MURAD KHAN &
MUHAMMAD SALEEM
M.Phil Statistics
1st Semester
Department of statistics Abdul
Wali Khan Unicersity Mardan
KPK
NONPARAMETRIC TESTS
Presentation

2. Parametric or nonparametric – Determination
2
Type of
Data
Categorical
Metric
Are the data
approximatel
y normally
distributed?
Yes
No
Are the
variances of
populations
equal?
Nonparametric Tests
Parametric Tests
Nonparametric Tests
No Nonparametric Tests
Yes

3. What is Nonparametric Test?
 A method commonly used in statistics to test and
analyze ordinal or nominal data with small sample
sizes. Unlike parametric tests, nonparametric tests do
not require the researcher to make any assumptions
about the distribution of the population, and so are
sometimes referred to as a distribution-free method.
 Typically, this method will be used when the data has
an unknown distribution, is non-normal, or has a
sample size is so small that the central limit theorem
can't be applied to assume the distribution.

4. USAGE
 Decision making/ forecasting.
 Studying populations that take on a ranked order
(such as movie reviews receiving one to four
stars)
 Simple analysis.

5. Types of Non-parametric test
 Chi-square test (χ2):
 Used to compare between observed and expected data.
1. Test of goodness of fit
2. Test of independence
3. Test of homogeneity
 Kruskal-Wallis test-
 for testing whether samples originate from the same
distribution.
 used for comparing more than two samples that are
independent, or not related
 Alternative to ANOVA.
 Wilcoxon signed-rank-
 used when comparing two related samples or repeated
measurements on a single sample to assess whether their
population mean ranks differ.

6.  Median test-
 Use to test the null hypothesis that the medians of the
populations from which two samples are drawn are
identical.
 The data in sample is assigned to two groups, one
consisting of data whose values are higher than the
median value in the two groups combined, and the
other consisting of data whose values are at the
median or below
 Sign test:
 can be used to test the hypothesis that there is "no
difference in medians" between the continuous
distributions of two random variables X and Y,
 Fisher's exact test:
 test used in the analysis of contingency where sample
sizes are small

7. Situation
To use
Parametric
To use Non
parametric
1.Data type Ratio or Interval Ordinal or Nominal
2. Usual central measure Mean Median
3.Correlation test Pearson spearman
4.Independent measure
two groups
Independent measure t-
test
Mann whitny-test
5.Independent measure
more than two groups
6.Repeated Measure two
conditions
7.Repeated measure
more than two conditions
One way independent
measure ANOVA
Matched Pair t-test
One way repeated
measure
ANOVA
Kruskal –wallis test
Wilcoxon test
Friedman’s test

8. SPSS EXAMPLES
Binomial Test
 Say we wish to test whether the proportion of
females from the variable “gender” differs
significantly from 50%, i.e., from 0.5. We will
use the exact statement to produce the exact
p-values.
 Get the data. Follow the steps as shown below

9. Continue…..

10. Continue…..
 Get the variable gender in the test variable list.

11. Result
Since p value is 0.690 it is insignificant and we
fail to reject null hypothesis and conclude that
the proportion of females from the variable
“gender” does not differ significantly from 50%.

12. Run Test for Randomness
 Let’s see whether the variable “AGE” in the dataset below is
random or not.
 Follow the following steps.

13. Continue…..

14. Continue…..
 Select “AGE” in the test variables list.

15. Result
Now p value is 0.450. So it is not significant and
we can say that AGE is randomly selected.

16. One-Sample Kolmogorov-Smirnov
Test
 is used to test the null hypothesis that a
sample comes from a particular distribution.
 If we want to compare the distributions of two
variables, use the two-sample Kolmogorov-
Smirnov test in the Two-Independent-Samples
Tests procedure.

17. Continue…..
 Follow the following steps.

18. Continue…..
Click OK

19. Result
The p value is 0.993 which is insignificant and
therefore we can say that “AGE” have an
approximate normal distribution.

20. Two-Independent-Samples Tests
 The nonparametric tests for two independent samples
are useful for determining whether or not the values of
a particular variable differ between two groups.
 Open the dataset

21. Continue…..
 Let’s compare between design 1 and 2.

22. Continue…..
 Enter variable sales in test variable list and design in grouping variable.
Define
Group 2 and
1

23. Result
Now two p values are displayed, asymptotic which is appropriate
for large sample and exact which is independent of sample size.
Therefore we will take the exact p value i. e. 0.548 which is not
significant and we conclude that there is no significant difference
in sales between the design group 1 and group 2.

24. Multiple Independent Samples Tests
 We can test more than two Independent samples

25. Continue…..
Minimum: 1
and
Maximum: 4

26. Continue…..
P value is 0.004 which is significant. Therefore we conclude that there
is significant difference between the groups (meaning- at least two
groups are different)