Is there any way to compare the changes in the averages between two groups who are not entirely equal at the start? RQ: analyzing the effect of completing a strenuous vs. more relaxing warm-up on reaction speed.
Methodology:

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*Randomly assigned the population to two conditions: complete a strenuous warm-up or a more relaxing one

*All participants took the reaction time test 3 times before being exposed to their condition to establish a benchmark.

*participants took the reaction time test 3 times again after being exposed to their condition

My problem is that the group that completed the more strenuous warm-up has a faster reaction speed for the benchmark so my groups aren't equal at the beginning. Is there any test I can do to test the statistical significance of the change in the mean reaction speeds? Would ANOVA work?

I'll provide a computational response and a conceptual response. Computationally, I agree with the Yashaswi that findings account for baseline measures when those baseline measures are included in the analytic model. If a direct analysis of the difference between the post-minus-pre averages of the two groups is desired, a difference test (e.g., t-test) could be performed. However, conceptually, because there was not sampling (i.e., it sounds like there was random assignment to treatment but not random sampling of individuals from the population to participate in the study), there is not a need for inferential statistics. That is, the population values are known and so do not need to be estimated. Similarly, differences among groups can be calculated through basic arithmetic and do not need to be inferred using standard errors (which is a sampling statistic). Findings can be reported in terms of average change in strenuous versus relaxed groups; the impact of the groups not being equivalent prior to treatment is not known. Replications and alternative designs could provide insight into unanswered questions.
Re: @num_39's assertion that this response is incorrect: I disagree but would agree that industry standard would be to attempt to generalize from the individuals in the study by making strong assumptions that either the specific individuals are representative of all possible individuals who could have been selected for the study or the specific combination of individuals assigned to treatment and control conditions are representative of all possible combinations. In this study, my bet would be that neither of those assumptions hold. So I would recommend describing the actual findings, rather than speculating about what would happen with different individuals or combinations of individuals. See the replication crisis literature in any field for the problems with relying on strong assumptions and the rampant over-generalization of findings.
