# Statistical Test in Pattern Recognition

## Abstract

Given the few experimental sample observations, we are interested in testing whether they are the outcomes of the random variable *X* that follows the typical distribution function. For instance, if we observe the percentage of success obtained by the typical constructed classifier by performing repeated experiments. We would like to know whether they are the outcomes of the random variable *X* (Gaussian distributed) with mean (average mark) greater than the typical value *μ* (say). This is needed to conclude the statement “The average POS obtained using the constructed classifier exceeds *μ* with the identified confident level.” The confident level is obtained using statistical mean test. Similarly, the statistical mean tests are needed to show the statistical evidence to claim the better performance of the proposed classifier. Statistical variance tests are also used to test the consistence of the performance of the typical classifier. The performance of the *k* classifiers is tested with multiple data sets. We need to check whether the performance of the classifier depends upon the data set chosen. Suppose we collect the features from the data and are subjected to classification. We would like to know which feature is more responsible for classification. This is done using ANOVA test (analysis of variance test). These are known as feature selection technique. In place of mean test, median test is performed using signed rank values. This chapter gives the introduction about how to perform the basic statistical test like mean test, variance test, Proportion test, ANOVA, Wilcoxon/Mann–Whitney test, and Kruskal–Wallis test.