2. What is Nonparametric Test
• Techniques that do not rely on data belonging
to any particular distribution
• Non-parametric statistics do not assume any
underlying distribution of parameter.
• Non-parametric does not meant that model
lack parameters but that the number and
nature of the parameters are flexible.
3. Why Nonparametric Test
• Sample distribution is unknown.
• When the population distribution is abnormal
i.e. too many variables involved.
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. Parametric v Non-parametric
• Parametric tests => have info about population, or
can make certain assumptions
– Assume normal distribution of population.
– Data is distributed normally.
– population variances are the same.
• Non-parametric tests are used when there are no
assumptions made about population distribution
– Also known as distribution free tests.
– But info is known about sampling distribution.
6. Types of Non-parametric test
1. One sample test
• Chi-square test
• One sample sign test
2. Two samples test
• Median test
• Two samples sign test
3. K-samples test
• Median tets
• Kruskal Wallis test
7. 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.
8. • 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
