1. By MURAD KHAN &
Department of statistics Abdul
Wali Khan Unicersity Mardan
2. Parametric or nonparametric – Determination
Are the data
No Nonparametric Tests
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.
Decision making/ forecasting.
Studying populations that take on a ranked order
(such as movie reviews receiving one to four
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
for testing whether samples originate from the same
used for comparing more than two samples that are
independent, or not related
Alternative to ANOVA.
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
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
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
To use Non
1.Data type Ratio or Interval Ordinal or Nominal
2. Usual central measure Mean Median
3.Correlation test Pearson spearman
Independent measure t-
more than two groups
6.Repeated Measure two
more than two conditions
One way independent
Matched Pair t-test
One way repeated
Kruskal –wallis test
8. SPSS EXAMPLES
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
Get the data. Follow the steps as shown below
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.
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
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
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
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.