Hello Mariyana,

I'm not quite clear on what you have. Is it: (a) two groups, one of which received an intervention and one of which did not, and each group was subsequently measured on some relevant variable; or (b) two groups, each measured pre-intervention and post-intervention on some relevant measure? (or something else?)

If (a), then assuming groups were in fact comparable prior to the intervention, the fact that the intervention group has a slightly higher SD than the non-intervention group simply means the impact of the intervention wasn't equal for all participants in the intervention condition. Of course, if groups weren't comparable at the outset, then you simply can't be sure this wasn't merely an a priori difference between groups/batches.

If (b), pretty much the same thing: post-intervention scores are more variable than pre-intervention scores, which implies some persons benefited more from the intervention than did others.

It's not apparent why this might be a study limitation, unless you're worried about a homogeneity of variance assumption for a significance test (as in option "a", above). If that's the case, then you can:

1. Opt for bootstrap/resampling methods to estimate group differences (and the CI for same);

2. Apply an exact/permutation test;

3. Use robust regression model;

4. If it makes sense to do so, try transforming scores on the measure of interest so as to stabilize variances;

5. Use one of the common methods for adjusting/penalizing t-test/anova models for violation of homogeneity, such as: Welch method; Brown-Forsythe method.

Good luck with your work.

Just an additional aspect:

distributions of variables like intensities, concentrations and alike are very typically modelled best by right-skewed distributions like the log-normal or gamma distribution. Such variables very typically show a relationship between mean and variance (tha larger the mean, the larger the variance). When the mean of such a variable is large compared to the variance, the distribution looks very symmetric and seems to be described quite well by a normal distribution. However, when the mean of the variable increases, its variance will increase, too. So this is an indication that the normal distribution assumption may not be the best choice. But, as I said: if the variance is small compared to the means and the means are not very different (their ratio is close to 1), it does not make much of a difference if you fit a normal model (additive on the original scale) or log-normal model (which would be multiplicative on the original scale).

@Jochen Wilhelm, thank you for your answer too. This is also very useful