We are conducting research on coaches and athletes with a hugely disparate number of sample sizes. If I have an identified connection between coaches and athletes can I use the mean scores to their respective athletes to provide an equal sample size comparison? -jd
What you do with the data depends on your purpose and research question. If I follow, you have a multi-level data set with athletes nested in coaches. If you merely want to find out if there are differences among coaches on data assessed from athletes, you could do a simple one-way analysis of variance to test for mean differences among coaches (teams). If you want to directly relate coaches to their athletes on some variables, then yes you could take the mean score across athletes within teams. The issue is not about sample size, but about mixing levels (athlete level vs. team level), so you would want to aggregate the athletes to the team mean. You can certainly compute a correlation between coaches and the mean of their teams. Keep in mind that your inference remains at the team level, i.e., a coach characteristic relates to a team rather than individual athlete characteristic. I suspect that if you go to publish it, reviewers will complain that you should use multi-level modeling approaches that can deal with the two-level structure of the data.
This is helpful and the multi-level perspective will have to be clarified but the questions to the coach will be at the team level (how would you describe your coaching toward your team) and the athletes individually to the coach. I am stretching the limits of good will of the convenience sample as it is with each doing a single eval rather than the coach doing an indiv. eval. with all team members. Since the question does relate coaches to their athletes then it looks like I can certainly do that but will have to address the lack of multi-level in limitations. Thanks, this was helpful.
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