This is a one sample test design where proficiency for was assessed pre and post, with the sample size being over 1000. There are 4 categories that were used to score them: unsatisfactory, developing, proficient, and exemplary. These categories are dependent of each other. What statistical test should be used here?
I think you can use Shapiro-Wilk test, test the normality of scores (pretest and post test). If scores are normally distributed use Paired samples t-test, (this test enable to see you changes over time)
If your data is not normally distributed (pretest and post test scores) use Wilkinson signed rank test. This test enables you to see your changes over time.
Compare pre-test and post test scores using independent sample t-tests or manN- Whitney if normality assumption is violated. This demonstrates your intervention effectiveness. If there were no difference in pre-test scores between groups but experimental group scores are significantly higher than control group. If pre-test scores significantly differ across groups, use ANCOVA and add co-variate as pre-test scores. Set group as fixed factor ( experimental and control) and post-test score as dependent variable.
Pre and Post test or Before and After test, you can use the Paired sample t test, if you data set satisfies the assumption of normality, However, if it does not then you can use the wilcoxon sign rank test if you data satisfies the assumption of symmetrically-shaped distribution of difference), if you are not sure of this you can use the Sign Test. AND If the nature of data are of 0 and 1 (dichotomous) you are advised to use the McNema test
In my opinion, you should be consider for statistic method that probably try to use regression analysis. It can yield the magnitude of effect between pre-post score (namely-mean difference ; using coefficient and 95%CI ). However, I'm not skilled enough , so please get further advice for another experts.
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