Good test questions

[Jill VanderStoep]

Writing a good test with good questions can be challenging. Maybe if we all share a couple of our favorite questions, we could write a better test. 

I am sharing two questions. The first is a short multiple choice question:

Which of the following allows us to make causal conclusions for a statistically significant result?

a. random sampling

b. random chance

c. random assignment

d. random process

The second one I am attaching, and it is my favorite question to put on my final exam. The students need to go through the same steps they have gone through many, many times throughout the semester to find a p-value and state a conclusion based on the p-value. The twist is that they must use a novel statistic. 

I confess that I borrowed it from Allan Rossman. I have found Allan Rossman's blog on asking good questions to be very useful; not only for finding good questions, but also for thinking about student engagement in different ways.

Please share a good question (or two) with the group. It doesn't have to be long & fancy. It can be a multiple choice, true/false, fill in the blank, or matching type of question.

Happy test writing!

Jill

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Department of Mathematics & Statistics

Hope College
Holland, MI 49423

Retired June 2025
vander...@hope.edu

[allanj...@gmail.com]

Hi folks,

 

Many thanks to Jill for mentioning my blog in her message about exam questions.  Here are links to some of my blog posts that specifically provide and discuss exam and quiz questions:

https://askgoodquestions.blog/2019/11/25/21-twenty-exam-questions/

https://askgoodquestions.blog/2019/12/02/22-four-more-exam-questions/

https://askgoodquestions.blog/2019/12/23/25-group-quizzes-part-1/

https://askgoodquestions.blog/2019/12/30/26-group-quizzes-part-2/

 

In case you’d prefer not to follow links (but are continuing to read this message), I’ll describe one of my favorite questions here …

 

I once attended a conference presentation in which the presenter said that he had asked his students this question: Which is larger – the average weight of 10 people or the average weight of 1000 cats (ordinary domestic housecats)?  The presenter said that his students struggled somewhat with this question, because they struggled with proportional reasoning, so they thought that 1000 of something would weigh more than 10 of something else.  I suspected that my students would have no trouble at all with this question, so I asked it on a final exam.  Sure enough, I was right: My students aced this question. 

 

But lest you think that I’m becoming too full of myself, I must admit that I also asked a follow-up question, on which my students performed terribly: Which is larger – the standard deviation of the weights of 1000 people, or the standard deviation of the weights of 10 cats (ordinary domestic housecats)?  More than half of my students mistakenly answered that the weights of the 10 cats would have the larger standard deviation.  I believe that they mistakenly believed that I had told them that a larger sample size produces a smaller standard deviation.  Of course, I told them no such thing!  What I told them, and what I tried to help them to see for themselves with simulations, is that a larger sample size produces a smaller standard deviation of a sample statistic such as a sample mean or a sample proportion.  But my exam question had asked about variability of the weights themselves, not about average weights in a sample.  I think this reinforces that the concept of sampling variability is a very challenging one for students (and everyone else too!) to really wrap their minds around.  And before you object, I don’t think this is a trick question.  In fact, I would argue that the concept of variability is the most fundamental one in statistics.

 

Anyway, if you’re still reading this somewhat long message, and if you enjoy these kinds of ramblings, you’ll find lots of this in my blog.  I suggest that you start with the list of posts (see link below) to look for titles or topics that appeal to you.  If you can tolerate one more piece of advice, I suggest starting with post #1 (at the bottom of the list) and reading them in order:

https://askgoodquestions.blog/posts/

 

Thanks for reading,

 

Allan Rossman

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