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I am writing a paper on the impact of a PLC (a specific type of education reform effort) on student performance outcomes. The IV is the PLC and the DV are the performance outcomes (AIMS Test Scores).

My IV has two levels, experimental and control. The experimental group are schools that have implemented a PLC, and the control schools are the ones that have not. Each school is my study are similar in nature and in the same school district. The Experimental group consists of scores from two subjects, Math and Science, with an n = 72 each, a total of n = 144 for the experimental group. The control school is identical (with an n = 72 each, a total of n = 144)

The scores are both ordinal (as they can be ordered) and interval (because the distance between each score and the Pass/Fail criteria are important).

My design is a pre-test/post-test control group design comparing scores before and after implementation of a PLC in the experimental group and cross-comparing to the control group using a two-tailed t-test.

I need to check for normality first and was struggling to find the right test. The Sharpio Wilks test seems to be the most fitting but I was worried as my sample size is larger than n=50.

Any advice on selecting the correct parametric test for normality?

gung - Reinstate Monica
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Amanda
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    If your sample size is large enough, the t-statistic will have (approximately) the correct distribution even with non-normal data. Is testing for normality a de-facto requirement for publication in your field? – jbowman Jan 02 '19 at 00:04
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    A normal random variable is continuous by definition, not discrete. Could you please provide more detail on the data? - it may even be that a t-test isn't appropriate. – Scortchi - Reinstate Monica Jan 02 '19 at 00:12
  • "Sharpio Wilks" -> Shapiro-Wilk. – Nick Cox Jan 06 '19 at 01:49
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    You do not need to test for normality. You can use methods that do not assume normality. Also, it's not clear why you want a t-test or how you will use it. You could, I think, do it on the change score, but analysis of change scores is problematic when there is error in the measurements (as there surely is with any test of education). – Peter Flom Jan 06 '19 at 10:45
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    Hi Peter, Thanks for answering. I do have to test for normality, this is for a dissertation and it is required. I have landed on Shapiro-Wilk (yes, Nick...it was a typo) and will see what my committee says. Dissertation research is a bit different than the normal stats I deal with at work, and it can be confusing at times (at least to me). – Amanda Jan 06 '19 at 20:14
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    I agree with @PeterFlom , it seems to me you could simply perform analyses that do not require the normality assumption, and therefore, would obviate the need to perform any type of testing for normality. For example, you could simply perform a contingency table analysis and perform chi-squared tests, or you could consider performing ordinal regression. You shouldn't be performing normality tests just for normality sake. It seems to me you have this false impression that you must test for normality any time you carry out any analysis. This just isn't the case. – StatsStudent Apr 30 '19 at 16:14
  • See also https://stats.stackexchange.com/questions/3466/best-practice-when-analysing-pre-post-treatment-control-designs – kjetil b halvorsen Oct 10 '21 at 17:21

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