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The test-re/post/test methodology entails establishing a baseline, introducing a condition and measuring the effect size. The condition is known. But whether or not it yielded some changes, is what needs to be established. HO no difference H1 there is a difference

What if the treatment condition is unknown? But one assumes that there is something must have influenced the results. How does one go about proving that the data is distributed the way it is, not due to chance, but by the divine will? In this task, I'm trying to reverse engineer the test/retest method to show presence of a condition, as opposed to introduce it and measure the outcome.

HO no condition H1 there is a condition.

Example: 100 athletes are asked to make 10 x 100m laps. Individual time x 10 is measured and recorded. We know min and max time for each runner. How do I show that difference in their running abilities (across athletes) is due to extranous variables, such as age, access to performance enhancers, dehydration, whatever. I need to show that the difference is not random (or is it?), otherwise everyone would have finished at the same time.

What do you compare the data to? There is no pre-test. There is intra-athelete performance data and inter-athlete performance data and the normal distribution, which is not helpful due to central tendency and large numbers.

What statistical test can I run here?

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  • $\begingroup$ I am not aware of your level of knowlede in statistics. If you have basic understanding of ANOVA, it may be useful to apply repeated measures Anova. Try ! $\endgroup$ – Subhash C. Davar May 18 '16 at 22:00
  • $\begingroup$ Thanx! That actually might work. it is all about the variance. $\endgroup$ – lrn2code May 18 '16 at 22:16
  • $\begingroup$ Have you tried ? $\endgroup$ – Subhash C. Davar May 19 '16 at 3:58
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Unfortunately, I think that what you want is ultimately not possible. If you didn't measure a given variable, such as age, you have no way of distinguishing its effects from random variation. Statistics does have methods to characterize random distributions, such as distinguishing a normal distribution from a Cauchy distribution, or attempting to separate a mixture distribution into its components. And it has methods to impute missing values in a variable for which not all values are missing. But it can't summon entire variables from the void.

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  • $\begingroup$ Thanx. I'm afraid you are right. can't prove the influence without a baseline, but is there a way to infer that each athlete is affected differently by looking at variance? $\endgroup$ – lrn2code May 18 '16 at 22:37
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    $\begingroup$ To be clear, your problem (having no measurements of a variable of interest) is a deeper problem than lacking a baseline measurement. I don't think I understand your question: infer that each athlete is affected differently by what? In any case, there are all sorts of unsupervised-learning methods that can group random variation, such as cluster analysis (which can group subjects) and factor analysis (which can group variables), but these can't help you find predictors or causes of the variation that you could've measured but didn't. $\endgroup$ – Kodiologist May 18 '16 at 23:53
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    $\begingroup$ Maybe just something can be salvaged. If you have some data variables which can be used that somebody have a similar age, you can make such groups and use as a blocking variable. That will not help to learn about the effect of age, but it can make the inferences about the other variables a little better, maybe. $\endgroup$ – kjetil b halvorsen Feb 16 '18 at 12:13

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