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I'm really struggling to select the correct statistical test.

Basically, I have 2 groups and each group contains 10 people. People in group 1 are treated with a drug and people in group 2 are given a placebo. Both groups are trained on a memory test across 10 days. As both groups are trained in the memory test, their scores increase across days. I notice that for both groups, their averaged score increases to 85% and hovers around that level (the asymptote of learning). However, group 1 reaches this asymptote on day 6 , whilst group 2 reaches the asymptote at day 9.

Could any of you point me in the direction of how I could go about testing whether or not there is a significant difference in the time it takes for one group to reach the asymptote compared to another?

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One way is to do alpha-corrected t tests sequentially backwards from day 9. When you reach significance, you know they have diverged.

A better way would be to fit an exponential approach to a limit and test the rate parameters. I think there's work by Brian McElree on that.

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