Problem with unequal variance

#1
Greetings,

I’ve collected some data on an office wellness program and have found mixed results between the treatment (wellness activities) and control group. One item that we did not explore was adherence to the wellness program. I’m thinking this could cause an increase in the within-group variance resulting in the unequal variance. In my reading on unequal variance, it seems it could increase the risk of both Type I and Type II errors. Also, the increased within-group variance could reduce effect size due to a larger pooled standard deviation. Does this sound like I’ve read the literature appropriately, or am I off the mark. Also, could the unequal variance be of a concern to anything else. Note the sample sizes were the same. I really appreciate any comments.