Having a significant p-value after checking for equality of variances which actually tested the assumption of the independent samples t test that your samples have the same variance may mean that The summary plot shows p-values and confidence intervals for the equal variances tests. The types of tests and intervals that Minitab displays depend on whether you selected Use test based on normal distribution in the Options dialog box and on the number of groups in your data. If you did not select Use test based on normal distribution, the \(F\)-Tests for Equality of Two Variances. In Chapter 9 we saw how to test hypotheses about the difference between two population means \(μ_1\) and \(μ_2\). In some practical situations the difference between the population standard deviations \(σ_1\) and \(σ_2\) is also of interest. Standard deviation measures the variability of a random Test for Equal Variance/Homogeneity Tests The table produces tests of the homogeneity of variance for each dependent variable across all level combinations of the between-subjects factors. If the assumption is not satisfied, there are several options to consider including elimination of outliers and data transformation. It is recommended that you test for unequal variances before performing a hypothesis test. As a new Stata user it is recommended that you start by using the Stata menus to perform your analysis. Each analysis, such as a t-test or variance test, will show up in your Review pane (on the left side of the Stata screen) as the equivalent Stata command. Step 2: Determine Equal or Unequal Variance. Next, we can calculate the ratio of the sample variances: Here are the formulas we typed into each cell: Cell E1: =VAR.S (A2:A21) Cell E2: =VAR.S (B2:B21) Cell E3: =E1/E2. We can see that the ratio of the larger sample variance to the smaller sample variance is 4.533755. A paired t-test is designed to compare the means of the same group or item under two separate scenarios. An unpaired t-test compares the means of two independent or unrelated groups. In an unpaired t-test, the variance between groups is assumed to be equal. In a paired t-test, the variance is not assumed to be equal. Test for Equality of the Variances. To determine which of the two formulas to use, we first test the null hypothesis that the population variances of the two groups are equal. First, test H 0: σ 1 2 = σ 2 2. The test for equality of variances is based on the distribution of the ratio of the variances and uses the F statistic, F = s 1 2 /s 2 2 .

how to test for equal variance