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Ask Marilyn: How Should This Test Be Scored?
Dave Aring of Overland Park, Kansas, writes:
Marilyn: My wife and I are at odds about how to score a test we took. We agree that the goal should be to determine which test-taker is more knowledgeable. Specifics follow:
The test contains ten questions. Some of the questions require a single answer; others require multiple answers. For the sake of illustration, let's assume questions #1 through #6 are single-answer questions. The last four are as follows: Question #7 has two parts, #8 has three parts, #9 has four parts, and #10 has five parts. There is no penalty for guessing. Partial credit is given if all answers in multiple part questions are not correct.
One of us feels that the best way to score the test is to add up the total number of answers. With this method, there is a total of 20 answers. One would take the percentage of total correct answers out a possible 20. A perfect score would be 20/20.
The other person wants to weigh each answer so that a perfect score for the test would be 10/10. As an example, say the test has the first six answers correct. But in the last four questions, one (and only one) of the parts is incorrect. So the scores on the last four questions are as follows: question #7 -1/2; #8 - 2/3; #9 - 3/4, and #10 - 4/5.
Using the first method of scoring, four out 20 answers were missed, so the score is 16/20 or 80 percent. Using the second method results in 8.71/10 or 87.1 percent. (That score was determined by getting the lowest common denominator for each question. That number is 60, so the score for the first six questions is 60/60. Question #7 is 30/60; #8 is 40/60; #9 is 45/60; #10 is 48/60. So the total for the last four questions is 163/60 or 2-43/60. Adding this to the six points for the first six questions gives a final score of 8-43/60 out of a possible ten points. That percentage is about 87.1 percent).
If a second test was scored, and question #1 is incorrect, but question #7 had both parts correct, the score with method #1 would still be 16/20 or 80 percent. With method #2, the score would be 8-13/60 or about 82.1 percent. So, as one can see, with the first method, the scores on the two tests are the same, but with the second method, the scores are quite different.
Which is the better way to score the test?
I would score the test with method #1, which gives all answers equal weight. After all, each one was a response to a separate question, even though the last 14 questions were grouped in various ways. You wrote that the test contains ten questions. If that's the case, what are they? In other words, I see this test as having ten parts with a total of 20 questions.
Method #2 gives only the first six answers equal weight. The remaining fourteen answers get less and less credit, depending on how many answers were grouped. I see no reason for this difference. Questions are sometimes labeled "extra credit" if they're considered to be more difficult, but I never see questions labeled "less credit," do you?!