# why doesn't percent change of mean equal mean percent change?

I'm trying to analyze data between 2 timed trials and come up with an average percent change between Trial A and Trial B. The mean time of trial A is 12.87 seconds, and the mean time of trial B is 18.49 seconds. The percent change of those means is 43.67 seconds (using B-A/A *100). However, when I figure the individual %change for each participant in the two trials, add those percentages, and divide by the number of participants, I get a completely different answer-- 64.1%. Why is this so, and what is the best way to analyze such data?

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Try calculating the percent change between A and B using ${|A-B| \over avg(A,B)}*100$. –  Ben Oct 30 '12 at 0:48
The best way is to not use averages at all. If they are the same two participants in both trials, you should use a paired T test. If they are different participants, use the 2 sample T test. –  Daryl Oct 30 '12 at 0:55
Here's an "intuition pump". Suppose the times in Trial A are $(99, 1)$, and in Trial B are $(98, 2)$. The mean times of both trials are $50$, so the relative change in the mean is zero. But the relative individual changes are $-1\%$ and $100\%$, and the mean of those is far from zero... –  Rahul Oct 30 '12 at 1:01