Abstract: Background and Objectives: Assumptions in statistics are mostly violated when testing hypotheses, hence, the use of inappropriate statistical tests results to invalid research conclusions. Most real life data are void of these assumptions resulting to difficulty in analysis using either parametric or non-parametric tests. The objective of the study is to examine the probability of type I error rate and the power of the parametric tests. Materials and Methods: To find out probability of type I error and power of some parametric tests such as; Bartlett’s, Cochran’s, Hartley’s and O’Brien test were taken under three conditions; normal and non-normal distributions, equal and unequal sample variances and equal sample size. Results: Results showed that all tests were very robust when normality assumption was achieved. But when normality assumption was violated, Hartley’s and Cochran tests could not control the type I error applying chi-square and Gamma distribution. For power, Bartlett’s, Hartley’s and O’Brien tests were most powerful than Cochran test irrespective of the normality assumption and equality of variance. However, Cochran test is more robust than Hartley’s test when the distribution is chi-square while, the Hartley test is more robust when the distribution is gamma. Conclusion: It is concluded that care should be taken in the choice of an appropriate statistical test when assumption of normality is violated.