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.
Why Nonparametric Test• Sample distribution is unknown.• When the population distribution is abnormal i.e. too many variables involved.
USAGE• Decision making/ forecasting.• Studying populations that take on a ranked order (such as movie reviews receiving one to four stars)• Simple analysis.
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.
Types of Non-parametric test1. One sample test • Chi-square test • One sample sign test2. Two samples test • Median test • Two samples sign test3. K-samples test • Median tets • Kruskal Wallis test
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.
• 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,• Fishers exact test: – test used in the analysis of contingency where sample sizes are small