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I've collected data comparing the relative success of two different groups of participants on finding the answer to a difficult question. The problem is that not all the participants in the control group managed to reach the answer within the allotted time (30mins for both groups). However, all the participants in the experimental group managed to reach the answer in less than 30mins. The difference between the two groups is just shy of significant using a regular t-test with time as the dependent variable. However, this test excludes the data for the 3 participants in the control condition that didn't managed to solve the problem in the allotted time despite the fact that we know it would have taken them more than 30mins to solve the problem (seeing as they had yet to solve the problem before the 30 min time limit ended).

Curious, I set each of these censored values to 30mins, performed a t-test, and my p-value dropped to 0.049, barely significant. However, this is under the presumption that each of these individuals in the control group would have reached the answer the instant the time limit was reached, which is obviously unlikely.

So I started checking out how to analyze censored data, but I hit a snag when I started looking into the assumptions behind the kaplan-meier survival analysis (which seemed like the most reasonable method for analyzing my data). It appears you're only allowed to use the kaplan-meier if there is an even degree of censoring between each of your groups, which is certainly not true for my group as the experimental group had no censoring at all. When I ran a log rank test anyways in SPSS I was even more stumped, the significance value for the was worse than my original t-test.

Am I using the right test? If not which kind of test should I use? I haven't really gotten deep into the mathematics behind survival analysis but I'd be happy to learn a bit. Any help would be appreciated.

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Since in the last 3 years nobody seems to have come with an specific tool, I suggest a couple of strategies:

  • The mean can't be computed or tested with censored data. However, as explained in the question, it's possible to get a lower bound for the mean and and upper bound for p-value.
  • However, Kaplan-Meier and other survival models do yield estimates and confidence intervals for the median. If doing a test for the median instead of the mean is fine for you, you can do it with censored data, although you should keep in mind that inference on the median is usually less powerful than inference on the mean, so it's possible to get a larger p-value for the median than the upper bound of the p-value for the mean.
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