Last August, I wrote about the differing outcomes of the two Intensive Elementary French sections I taught: one remote synchronous, the other remote asynchronous. My write-up included some descriptive statistics, and ultimately concluded that learners in the synchronous course achieved higher scores than those in the asynchronous course. At the time I wrote the post, my statistical literacy was less than it is now, so the purpose of the present post is to determine whether these findings were statistically significant.

## I. Do final course grades differ between the two modalities?

I took the two sections, asynchronous (n = 19) and synchronous (n = 10), and conducted a two-sample t-test to determine whether there is a meaningful, measurable difference in the average final course grade for each modality. The data from each section were normally distributed according to visual testing and the Shapiro-Wilk test (asynchronous p = 0.12, synchronous p = 0.26). An F-test revealed that the data were not of equal variance (F = 13.66, p < 0.001, 95% CI [3.69, 40.01]). The Welch two-sample t-test revealed a statistically significant, large difference between the asynchronous and synchronous sections (t(22.49) = 3.87, p < 0.001, d = 1.29, 95% CI [-2.04, -0.53]). The observed difference in means was -26.46, with a 95% CI [-40.63, -12.29]. A post-hoc test revealed an actual power of 0.80.

As you can see from the visualization, the learners in the asynchronous course had a much wider spread of final grades, compared to the learners in the synchronous course. The huge, statistically significant difference between the modalities can be seen most glaringly: nearly 75% of the synchronous scores fall within just the fourth quartile of asynchronous scores.

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