statistics
I have around 100 students who have all sat 3 exams and are about to sit another. Since their last exam I have made changes to my instruction and I want to determine if any changes in student scores is statistically significant.
I took one statistics class in university, but I can't remember exactly how to calculate the p values, assuming that's the best way to determine statistical significance.
Thank you in advance.
In Chemistry, she was $\frac{102-90}{64}$ standard deviation units above the mean.
In Statistics, she was $\frac{77-70}{16}$ standard deviation units above the mean. Note that $\frac{7}{16}$ is quite a bit larger than $\frac{12}{64}$, so the performance in Statistics is (comparatively) better than in Chemistry.
Measuring in standard deviation units takes above (or below) the mean takes account of the different means and different amounts of variability in the class scores in the two subjects.
"Mound-shaped" presumably means more or less normally distributed. The probability that a normal random variable with mean $90$ and standard deviation $64$ is $\ge 102$ is equal to the probability that a standard normal is $\ge \frac{112-90}{64}$. If we look at a table of the standard normal, this is approximately $0.43$. The corresponding result for Statistics is about $0.33$. Informally, that means that about $43\%$ of the students were above her in Chemistry, and only about $33\%$ were above her in Statistics.
Remark: In my experience, unmanipulated marks from Mathematics exams have a very far from normal distribution. They are often consistent with being drawn from $2$ or more populations with radically different means.
I could be mistaken, but I think that in general, whenever you see something that is too far against the norm, it raises red flags, which may be what he is talking about. Here is a glaring example from standardized testing, where the minimum score to pass this test was 30%: 
Here is the original reddit post: https://www.reddit.com/r/dataisbeautiful/comments/27dx4q/distribution_of_results_of_the_matura_high_school/
Best Answer
Any test that simply looks at just the students who underwent the change in instruction isn't really valid. It would need to be compared with a before and after test of a similar number of students who didn't receive a change in instruction (a control group). Otherwise, how do you know the test wasn't simply easier? There are also other criteria for a valid test like randomly assigning treatment and control groups, double blind testing where the students and the graders don't know which group is which.
You could then run a test comparing a difference in means between the two groups. Take the mean and standard deviation of each groups' difference in scores and run a $2$ sample t-test.
$$t = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}$$
Where $\bar x$ is the mean of the difference in scores from before and after modified instruction tests, $s$ is the standard deviation of the differences and $n$ is the sample size.
Then look at a t-table to determine a p-value and compare it with an appropriate level of significance $(.05)$. A p-value less than $.05$ would be statistically significant.