On the AP Stats exam, when writing a significance test (free response section) , what support is needed for the test statistic and p-value? Do students need the equation? Do they need a labeled and shaded curve? If they use technology to find these values, what should they write on their paper to support these values? Thank you!

Here are some thoughts about using technology for inference questions on the AP exam:

Recent rubrics have been very consistent in requiring that students name the inference procedure OR provide the formula to get credit for identifying the inference procedure. After the procedure has been identified, simply stating the output from the calculator is sufficient for the calculations.

p-value is sufficient to earn credit for the calculation step. For example, saying “The two-sample t test gives t = 1.28, df = 11.7,p-value = 0.11” would get credit for identifying the procedure and doing the calculations (assuming the values are correct, of course).But, being this brief comes with a risk: mis-typing an entry into the calculator will give wrong calculations and no partial credit can be given for the calculations without any work shown. However, if the student showed the formula with the correct numbers substituted in but got incorrect endpoints due to a typo, credit would be awarded for the procedure and most likely the calculations as well, provided that the calculations aren’t unreasonable in the context of the question. So, this seems like the safer option.

…until you get to two sample procedures. I don't know how typical my students are, but they have a lot of trouble keeping track of all the details involved in tests and intervals for differences of means and proportions. For many of my students, reporting the endpoints of a two-sample t interval from their calculator is much less risky than trying to get all the details of the formula correct. Not only that, it helps them keep their eyes on the big picture--what information the interval/test provides, rather than all the messy calculations.

A few more thoughts:

On recent questions I have graded, many students have lost points by providing the correct endpoints for an interval (or test stat and p-value for a test) from their calculator and then mess up when trying to supplement their calculator work with the formula. On the AP exam, when students attempt to answer a question two different ways, they always get graded on the worse of the two responses. So, correct calculator work with wrong supplemental work gets graded as if the correct calculator work wasn't there. If your students attempt to do the calculations both ways, tell them to make sure that their responses match. Otherwise, pick one and cross out the other.

Also, if students choose to show the formula, I would suggest that they start with the numbers substituted into the formula. That is, don’t include the formula with symbols only. Many times students incorrectly write sigma when they mean s (or write p when they mean p-hat). This could also result in a loss of points, even if the numbers substituted in the formula are correct.

As for sketching the z or t distribution, it isn’t necessary and has the same risks/benefits of using the formula. Done well it can help a student think through a problem and communicate their method. But done incorrectly it can take away points from an otherwise fine answer. For inference questions, I don’t have my students draw the curve. But I do on probability questions!

All of these comments apply only to the free-response questions. It is certainly possible that a MC question might ask for a CI for a difference in proportions and then provide choices that include only formulas. So, I think it would be a bad idea to completely skip the formulas entirely. Also, these are suggestions for success on the AP exam—what you choose to require in your classroom (and what you deduct points for) is certainly up to you.

The strategy that you choose to use with your students regarding calculators and showing work will depend on several things, including the amount of time you have to develop the ideas and the abilities of your students. I don't have a perfect solution to this issue, but I hope that these thoughts are helpful!

Thanks,

Josh Tabor