The NIH is funding a trial for a new antidepressant drug. A sample of 1000 people with severe depression are recruited and, at baseline, are given a questionnaire asking about their demographic...

The NIH is funding a trial for a new antidepressant drug. A sample of 1000 people with severe depression are recruited and, at baseline, are given a questionnaire asking about their demographic characteristics
and their mental health. They are then randomly assigned to one of two groups. The treatment group receives the new antidepressant, a pill that must be taken twice a day. The control group receives a placebo pill containing nothing medically active, which must also be taken twice a day. After 10 weeks, researchers locate the individuals and ask them to fill out a questionnaire again assessing their mental health. At the end of the study, researchers find no statistically significant difference in the mental health

of the treatment and control groups.

Q: Should we be concerned about unbalanced groups here? Is it possible to empirically explore whether this is a problem for this study?