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20 subjects Day 1. Shooting test - Basketball free throw shooting accuracy (number of successful shots out of 10)

Day 2. Given coaching and can practice technique.

Day 3. Shooting test again (as above)

Want to see if the coaching has positively or negatively impacted number of successful shots?

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    $\begingroup$ This experimental design will not be capable of telling you much about coaching. You need to include a control group if you want to do that, so that you can compare two groups whose treatments differ solely in terms of coaching. $\endgroup$
    – whuber ♦
    Apr 6, 2016 at 20:35
  • $\begingroup$ To expand on whuber's comment, you can't tell your results from what would happen if everything was as above but just the coaching part was absent; it's possible a simple learning effect from the first test to the second (caused by testing the first time and any practice on day 2) accounts for all the improvement seen, for example. Or maybe coaching makes things worse, compared to that learning effect, but is small so the overall effect is still an increase -- in that case you could end up concluding coaching helps when it does the opposite. $\endgroup$
    – Glen_b
    Apr 6, 2016 at 23:58
  • $\begingroup$ Thanks for responding. Please ignore the study design and inferences that can or cannot be made about coaching etc, this is part of a bigger study etc The question is really - when the same people are tested on a task that has a binomial outcome (i.e. hit/miss, 0/1, yes/no) before and after some kind of intervention, how should you treat the data when choosing a statistical test. Thanks! $\endgroup$
    – James Fern
    Apr 7, 2016 at 17:44

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In this situation, when you have data like frequency, you should use a non-parametric test Wilcoxon Signed Rank Test.

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    $\begingroup$ please consider expanding upon your answer. As it stands now, it's really more of a comment. For example, why is this test appropriate? What makes other tests inappropriate? $\endgroup$
    – Sycorax ♦
    Apr 6, 2016 at 20:46
  • $\begingroup$ I'm not this is appropriate here? There is no ranking to the data? The question is really - when the same people are tested on a task that has a binomial outcome (i.e. hit/miss, 0/1, yes/no) before and after some kind of intervention, how should you treat the data when choosing a statistical test. $\endgroup$
    – James Fern
    Apr 7, 2016 at 17:48
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For this simple design you can use a Fisher-exact test. Say in day 1, x1 shoots were successful and y2 were missed; in day 3, x2 shoots were successful and y2 were missed.

Run the following R command:

fisher.test(matrix(c(x1,y1,x2,y2), nrow=2))

will tell you the odds ratio and the p-value (or google to find an online fisher exact test site).

If you have more than 2 outcomes then you can still do a chi-square test or Fisher-exact test. But if the outcomes are ordered, I would suggest a trend test, which would be more powerful than chi-square test.

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  • $\begingroup$ Welcome to our site! I've edited your answer by including some spaces in front of your code snippet, so it is formatted as such. Have a look at our editing help to see some other options for how to format code, and some other neat features when writing questions and answers here! $\endgroup$
    – Silverfish
    Apr 6, 2016 at 22:27
  • $\begingroup$ Thanks for the response and i can see why you would suggest this. But im not sure... for example how would the test choice change if rather than 2 possible outcome (miss/hit) there was a 3rd option (i.e. miss completely, hit the ring, score)? $\endgroup$
    – James Fern
    Apr 7, 2016 at 17:47
  • $\begingroup$ I have edited my answer to address the situation of more than two outcomes. $\endgroup$
    – Hao Hu
    Apr 8, 2016 at 20:56

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