A study of the effect of outliers on regression inference and the performance of the t-test statistic using the standard deviation method

One of the essential requirements for smooth regression analysis based on ordinary least squares (OLS) method is normality of the data. When the dataset passes the normality test, it is virtually free from unusual observations, OLS method can then be applied effectively to obtain the required estimate of the regression parameters and make inference. It is quite obvious that presence of outlier distorts regression inference when non-robust methods are used. This article highlighted on the consequences of including outlier in the analysis of regression models based on the t test statistics. Standard deviation (SD) method was employed in measuring the effect of outlier on t test statistics taking into account the sample sizes and the number of independent variables at different intensity of outlier both using real examples and simulation study. It was discovered that outlier affect the estimate of regression coefficient negatively which in return render the classical regression estimators inefficient. In addition, it can alter the odds of making both type I and type II error as well as influence the estimate of regression that are of essential interest.