It is an attempt to correction for violations of sphericity that can occur with repeated-measure ANOVAs. The assumption in the ANOVA is that the covariance of any two-levels of the repeated factor is always the same.

 

A two-sample t-test is not an appropriate test to compare two con images from the same subject. It is statistically inappropriate. If you are using two con images from the same subject, then you need to use a paired t-test to properly account for the scans being repeated-measurements. Alternatively, you could subtract the two con images and use a one-sample t-test. In the case of two con images, there is no possible violation of sphericity and no correction for non-sphericity. This only occurs with factors with 3 or more levels.

 

Setting the independence to NO, means that the scans are repeated. This is required for repeated-measures. The setting of variance to equal or unequal will alter the correction for non-sphericity. Again, this requires more than 2 levels of the repeated factor.