evansp@byu.edu,

The source code has an example page that explains the quiz statistics that are available for each question type. It does not explain what they mean, those explanations are found in statistics textbooks and on websites. Another page in the source code documents that it is constructed for single pre-defined answers in a multiple-choice or true/false question.

If you Google point biserial correlation, you'll find more documentation about it than Canvas has. What I'm writing here is based off of what I Googled and what I got from the Canvas source.

I don't do much with quiz statistics, but the calculations are in the item_analysis/item.rb file. I don't speak fluent Ruby, either, so this is my interpretation of what's going on, but you should defer to statistics sites if my explanations disagree. I tried to compute the point biserial correlation based on the calculations in Canvas, but I got 0.705 when using a sample standard deviation and 0.730 when using the population standard deviation (which is what it looks like Canvas is doing), while they got 0.70065 for the point biserial correlation. When I run the same data through Minitab, I get 0.730 for the correlation between points for the question and the score on the exam.

Without a lot of investigation, I imagine the reason for the difference in the calculations is that my Student Analysis included all attempts of the students who took the quiz, while the Item Analysis only included the kept version of the quiz. For the question I was looking at, I had 15 attempts in the Student Analysis but only 6 students in the Item Analysis. In other words, if you allow multiple attempts like I do, your hand calculations from the Student Analysis may not match the supplied values from the Item Analysis because you're using different data sets.

As far as the calculations go, an item is each answer (response) that is possible for a multiple choice or true false question. Only those students who were administered the question are used in the calculations.

- It calculates the mean score for people who gave that answer and the mean score for people who gave a different answer.
- It finds the ratio of people who gave that answer to the question
- If finds the standard deviation in the score for all people who answered the question
- It calculates the mean score for those who gave that answer minus the mean score of those who gave a different answer. It divides this by the standard deviation of all scores. It multiplies this by the square root of the the product of the ratio who gave this answer and the ratio of people who gave a different answer.

The interpretation of the point biserial correlation is similar to that of the Pearson product moment correlation coefficient. Values close to 0 indicate that this answer is not a good predictor of overall score. Positive values indicate that people who gave that particular answer did better overall, while a negative value indicates that people who gave that particular answer did worse overall. The closer the magnitude (absolute value) of the number is to 1, the more convinced you are that there is a relationship.

For a multiple choice question with more than 2 choices / options / levels / answers / responses, this process is repeated for each answer. If there are 4 possible responses, there would be 4 point biserial correlations. For each of them, the breakdown is between those who gave that response and those who gave some other response. One of the point biserial correlations is between the correct response and all of the incorrect responses. The others (three in this case) are between each of the incorrect responses and the other responses.

Alpha is Cronbach's Alpha. There is a single value of alpha for the entire quiz, but because of the way that the data is delivered, Canvas repeats it for each student. Based on the source code that computes Alpha, each item appears to be a question (the key for the item is the question id).