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?