When is equal variance assumed in a t test

Use the Paired t-Test to determine if the average score of the 2nd test has improved over the average score of the 1st test. Free Trial. Search form X. Contact Us Login. Live Chat Help Desk. Enter A2:A11 for Variable 1 Range. This is our first set of values, the values recorded at the beginning of the school year. Enter B2:B11 for Variable 2 Range.

This is our second set of values, the values recorded at the end of the school year. Enter "0" for Hypothesized Mean Difference. If the significance is. In this example, since the significance is.

Both the top and bottom row provide the same information, they just use different tests to calculate the test statistic, which results in slightly different calculations.

This table provides the test statistic or t value, the degrees of freedom and other values helpful for determining confidence intervals. If your p-value is greater than. If your p-value is less than. In this case, you can reject the null hypothesis because the significance is. By robustness, we mean the ability of the test to not falsely detect unequal variances when the underlying data are not normally distributed and the variables are in fact equal. By power, we mean the ability of the test to detect unequal variances when the variances are in fact unequal.

Levene's original paper only proposed using the mean. Brown and Forsythe extended Levene's test to use either the median or the trimmed mean in addition to the mean. They performed Monte Carlo studies that indicated that using the trimmed mean performed best when the underlying data followed a Cauchy distribution i.

Using the mean provided the best power for symmetric, moderate-tailed, distributions. Although the optimal choice depends on the underlying distribution, the definition based on the median is recommended as the choice that provides good robustness against many types of non-normal data while retaining good power.

If you have knowledge of the underlying distribution of the data, this may indicate using one of the other choices. Note that this is the opposite of some texts and software programs. Levene's test, based on the median, was performed for the GEAR.