Effect of Outlier on Analysis of Variance

Abstract

This article discusses the effect of outliers on the analysis of variance. It is observed that outliers significantly increase the variation within groups, which leads to a significant change to F-statistic and resulting in a Type II error, where the null hypothesis is accepted incorrectly. Outliers significantly affect the P-values derived from ANOVA, potentially leading to misleading significance levels. Outliers violate the basic assumptions of ANOVA that the residuals are normally and independently distributed with mean 0 and constant variance, making the ANOVA results unreliable. One practical example is given.