I have two separate groups of students. A control (n=23) and intervention (n=19) group. Both groups took a pre test measure (score of 0-100). I have done an independent t-test on the Post_minus_Pre test scores and found the following:

Independent T-Test on Differences of Test Scores

Tests for normality using Shapiro-Wilk showed normally distributed data. Levene's test shows non-equal variances, so I'll need to interpret the alternative scores.

My question(s):

  1. How can I properly interpret this table, given that I'm testing the differences of differences (i.e., differences from pre-post scores)? I'm having a heck of a time finding guidance on this kind of test (lots of guidance on other independent t-tests). What I think is correct is: "The intervention group showed a significant decrease of 16.95 (SD=20.16) of test scores compared to the control group." But this interpretation does not seem to take into account the control group score.
  2. What are the best practices for presenting this in a table form, specifically with APA?

The mean score has decreased in the intervention group while it has remained roughly unchanged in the control group. Indeed, the first table indicates that the mean change score (post minus pre) is equal to $-16.95$ ($\text{sd} = 20.159$) in the intervention group, and to $0.562$ ($\text{sd} = 5.566$) in the control group. The difference between the mean change score in the intervention group and the mean change score in the control group is estimated as $-16.95 - 0.562 = -17.513$ with standard error $\text{se} = \sqrt{\frac{20.159^2}{19} + \frac{5.566^2}{23}} = 4.768$, as indicated in the second table (unequal variance). The last two columns of that table indicates that the two-sided 95% confidence interval for that difference of mean change scores is $[-27.450, -7.575]$. Values outside the confidence interval are rejected as plausible values for the true difference of mean change scores.

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