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I have 10 people working together. They work in groups for 6 days: Three days in week 1, three days in week 2. In each day I don't have the full set of people, but a subset of them. In each day I measure the individual performances.

I have to say if the general performance was higher in week 1 or 2.
So I was planning to do a t-test on two groups like this, for instance:

Group 1 – Week 1 Performances

Day 1: Paul, Mary, John Day 2: Paul, Sara Day 3: Jessica, Sara

Group 2 – Week 2 Performances

Day 4: Paul, Rita Day 5: John, Paul, Sara Day 6: Jessica, Rita

Questions:

  • Can I consider the two groups as independent and do an independent t-test?
  • Could you suggest me the best way to say if general performance was better in week 1 or 2?

My concern is about the different people in each day and the different sizes of workgroups for each day. I'm also concerned because I have the same people in different days and in both groups. So it looks like the samples are overlapping.

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  • $\begingroup$ I suspect performance is measured as some sort of score and not on a metric scale (e.g. kg/day). Then you can't do t-tests or ANOVA anyway. $\endgroup$ – Horst Grünbusch Mar 16 '15 at 14:48
  • $\begingroup$ Would you mind if the difference between both weeks is only caused by the different participants? Or do you want to conclude something about the conditions of the weeks themselves (e.g. "performance on the first week was best due to sunshine, no matter who participated")? $\endgroup$ – Horst Grünbusch Mar 16 '15 at 14:58
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You can try to use regression. Let $Y$, the response, be the performance measurtement. Then you make dummys for the persons and for the weeks. Now, this might get you more $x$-variables than observations, but maybe it can be salvaged, you can try to treat the person variable as a random effect, and week as a fixed effect.

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You measure the performance for each person multiple times on different days and compare the two groups with the same people in each group. Therefore you should treat the two groups as non-independent, because it is very likely that the performance of one person will correlate on different days.

There are several options to test your hypothesis. Some ideas (assuming the requirements are met):

  • A simple method would be to calculate the average performance for each person, separated for week 1 and week 2. Then you compare the two means using a paired t-test. However, this will ignore some information like the size or composition of the workgroup.
  • Another approach is a repeated-measure ANOVA, where you could include the performance of each day, as well as covariates like the group size. Then you test your hypothesis using contrasts. The composition of the workgroup is still ignored.
  • If you have reason to believe the performance is dependent on the composition of the workgroup, you could do a multilevel/mixed-design model and add the day as a random effect.
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