Explain why the homogeneity of variance assumption must be satisfied before you

Question

Explain why the homogeneity of variance assumption must be satisfied before you can interpret the results of an independent-measures t test. A biopsychologist studies the role of a new pain medication on pain tolerance. They have people put their hands in super cold water and measure the time in seconds that they can keep their hands in the water. One group is given the pain medication and the other group is given a placebo. State the null and alternative hypotheses in symbols and words. Perform the F-max test. Decide what to do regarding H_0 and state your conclusion in APA format. Also, calculate the effect size. Use an alpha level of 05, two tails.

Explanation / Answer

28) The assumption of homogeneity of variance is an assumption of the independent samples t-test and ANOVA stating that all comparison groups have the same variance. The independent samples t-test and ANOVA utilize the t and F statistics respectively, which are generally robust to violations of the assumption as long as group sizes are equal. Equal group sizes may be defined by the ratio of the largest to smallest group being less than 1.5. If group sizes are vastly unequal and homogeneity of variance is violated, then the F statistic will be biased when large sample variances are associated with small group sizes. When this occurs, the significance level will be underestimated, which can cause the null hypothesis to be falsely rejected. On the other hand, the F statistic will be biased in the opposite direction if large variances are associated with large group sizes. This would mean that the significance level will be overestimated. This does not cause the same problems as falsely rejecting the null hypothesis, however, it can cause a decrease in the power of the test.

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