Pooled Two-sample t Statistic Suppose now that the two populations have the same standard deviation. Therefore has a standard normal distribution. Replacing the unknown by its estimator gives the pooled two-sample t statististic which has a t distribution with degrees of freedom. Status and honking . The conclusions are the same as before.
Summary Use the two-sample t test to compare the means of two groups.
SPSS gives two t statistics one assuming equal variances and one not. Use the pooled t test when the two sample standard deviations are not too different, say neither or is twice the other. For the pooled test, the df for the two groups add up. For the non-pooled test, the df are between the minimum and the sum of two individual df.