FORMULAS - CHAPTER 6
T-TEST WITH HETEROSCEDASTICITY
You can use the independent-samples t test formulas shown in Section 6.3.3 only when
data from the two categories of subjects have equal variances, or homoscedasticity. So,
before performing an independent-samples t test, you must compare the variances of your
data sets. If the variance differ significantly1, making them heteroscedastic, then you must
calculate t and the degrees of freedom using different formulas than those in Section 6.3.3.
The t test formula differs primarily because the pooled variance applies only to
homooscedastic samples. With heteroscedasticity, rather than computing SP, you must
compute standard error values (SE) for each category.
eq. 6.5.1
√
The standard error values for the two categories, notated as
formula as shown in Equation 6.6.1.
̅
̅
and
, fit into the t-test
eq. 6.6.1
√
The degrees of freedom formula also changes to accommodate unequal variances. Rather
than using Equation 6.7, you should use Equation 6.7.1. This formula requires you to
specify the individual variances.
1
You may not need to provide formal proof of homoscedasticity if variances or standard deviations that lie very
close together. However, you should be use as statistical test for homoscedasticity, such as Leven’s test, when
necessary. SPSS provides a p value for Levene’s test in its t-test output.
Equation 6.7 usually does not produce a whole number. You should round to the nearest
whole number to find the critical t-value in Appendix C.