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I am a professor of statistics and political science at Columbia University and author of Bayesian Data Analysis (with John Carlin, Hal Stern, and Donald Rubin), Teaching Statistics: A Bag of Tricks (with Deborah Nolan), Data Analysis Using Regression and Multilevel/Hierarchical Models (with Jennifer Hill), and, most recently, Red State, Blue State, Rich State, Poor State: Why Americans Vote the Way They Do (with David Park, Boris Shor, Joe Bafumi, and Jeronimo Cortina).

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« The can, the clink, the pen, the slammer, the big house, up the river | Main | Valentine's Day statistical love poems »

Some thoughts on final exams

Posted on: February 10, 2010 9:08 AM, by Andrew Gelman

I just finished grading my final exams--see here for the problems and the solutions--and it got me thinking about a few things.

#1 is that I really really really should be writing the exams before the course begins. Here's the plan (as it should be):
- Write the exam
- Write a practice exam
- Give the students the practice exam on day 1, so they know what they're expected to be able to do, once the semester is over.
- If necessary, write two practice exams so that you have more flexibility in what should be on the final.

The students didn't do so well on my exam, and I totally blame myself, that they didn't have a sense of what to expect. I'd given them weekly homework, but these were a bit different than the exam questions.

My other thought on exams is that I like to follow the principles of psychometrics and have many short questions testing different concepts, rather than a few long, multipart essay questions. When a question has several parts, the scores on these parts will be positively correlated, thus increasing the variance of the total.

More generally, I think there's a tradeoff in effort. Multi-part essay questions are easier to write but harder to grade. We tend to find ourselves in a hurry when it's time to write an exam, but we end up increasing our total workload by writing these essay questions. Better, I think, to put in the effort early to write short-answer questions that are easier to grade and, I believe, provide a better evaluation of what the students can do. (Not that I've evaluated that last claim; it's my impression based on personal experience and my casual reading of the education research literature. I hope to do more systematic work in this area in the future.)

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Comments

1

I have taught large sections with multiple guess tests. I would make up questions covering the lecture before giving the lecture. After the lecture, I would get notes from my student assistant, so I would know what I actually lectured about, then revise the questions as needed, and incorporate them into the test file. I found it instructive to record one of my lectures and listen to it after a day or two had passed. I had forgotten a great deal of what I had lectured about.

Posted by: Jim Thomerson | February 11, 2010 8:42 PM

2

most of principles of psychometrics that I know try to achieve higher internal consistency among individual items (so high correlation between items), since these questions are designed to measure a single concept, which is different from an exam.

and one way to increase cronbach's alpha is to increase the number of questions.

Posted by: wei | February 23, 2010 11:15 AM

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