Statistical test

[ChanceTGardener]

McNemar's test tests whether the discordant proportions are significantly different from each other. 

In the context of your problem, let:

P[UpVote] = sum of all students who upvoted

P[DownVote] = sum of all students who downvoted

Students whose scores do not change are not factored into the chi-square statistic. 

The null hypothesis is P[UpVote] = P[DownVote], meaning the total upvotes and downvotes are statistically equivalent

The alternative is P[UpVote] != P[DownVote].

McNemar's test is testing whether or not these values are significantly different from each other.

Your description " "did enough opinions change - whether up or down, doesn't matter - to be able to say that the new information changed opinions?", does not make a distinction between upvotes and downvotes. 

If you're treating upvotes and downvotes the same, then no, McNemar's test is not the right choice. 

[newtriks]

The null is "the votes did not change": every relative vote (before vs. after) = 0

Alternative is "the votes changed": every relative vote (or a significant enough amount of them) = 1

[newtriks]

The null is "the votes did not change": every relative vote (before vs. after) = 0

CORRECTION Alternative is "the votes changed": ABSOLUTE VALUE of every relative vote (or a significant enough amount of them) = 1

[ChanceTGardener]

For each student, let:

D = After - Before

Here, D=0 corresponds to no change in score. 

If D is normally distributed, use the t-test mentioned by others earlier in this thread. If it is not normally distributed, use the Wilcoxon Signed-Rank Test, which does not assume normality. Both tests assume the distribution is symmetric. 

This blog describes both in more detail and how to apply in SAS: https://blogs.sas.com/content/iml/2023/07/19/wilcoxon-signed-rank.html

[newtriks]

So there is no way to measure absolute change? Theoretically, by the t-test every score could change by 2 but as long as half of them are +2 and half are -2, the test will reflect no change at all. Is this correct, or am I missing something?