How should this test be scored?

Wiz and others...

My wife and I are at odds about how to score a recent test we took and we would like to hear ideas for the best way to score the test. We both agree that the goal should be to determine which test taker is (generally, for lack of a better term) most knowledgeable. I will make up a list of specifics that I feel should be considered in determining the best way to score the test.

The test contains 10 questions. Some of the questions require only a single answer and others require multiple answers. For the sake of the problem, let's assume that the first six questions are "single answer". The last four are as follows: question #7 has two parts, question #8 has three parts, question #9 has four parts, and question #10 has five parts. There is no penalty for guessing. Partial credit can and will be given in the event all answers in multiple part questions are not correct.

One of us (either my wife or me) feels that the best way to score the test will be to add up the total number of answers. In this example, there would be a total of 20 answers. Then, the way to calculate the score would be to take the percentage of total correct answers out a possible 20. A perfect score for the test would be 20/20.

The other person (either my wife or me) wants to "weigh" each answer so that a perfect score for the test would be 10/10.

An example test has the first six answers correct. In the last four questions. ONE (and only ONE) of the parts is INCORRECT. i.e. the scores on the last four questions are as follows: #7 - 1/2; #8 - 2/3; #9 - 3/4, and #10 - 4/5.

Using the FIRST method to score the test, four out of a possible 20 answers were missed so the score is 16/20 or 80%. Using the SECOND method is a bit more complicated and results in the following score. 8.71/10 or 87.1%. 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; question #8 is 40/60; question #9 is 45/60; and #10 is 48/60. Therefore, the "total" for the last four questions is 163/60 which is equal to 2-43/60. Adding this to the six points for the first six questions, gives a final (numerical) score of 8-43/60 out of a possible ten points. THAT percentage is (approximately) 87.1%.

Lastly, if a second test was scored and question #1 was NOW incorrect, but question #7 had BOTH parts correct, the final test score would be: Method 1... still 16/20 for 80% and Method 2... gives us 8-13/60 for (approximately) 82.1% As one can see, using the first method the scores on the two tests are the same, but using the second method, the scores are much different.

So, (ASSuming that my math is correct) which is the better way to score the test? Yes, all tests will be scored the same so (I suppose) it is all relative, but intuitively it seems to me that the score and subsequent rankings will vary depending on which of the specific 20 answers are incorrect.

Any and all comments and suggestions would be greatly appreciated.
Thank you.

You have neglected to provide some information. Why is question #10 a five-part question rather than five questions? Similarly, why are questions #1 through #6 separate questions rather than one six-part question? Is there any reason to consider any question or part of a question of greater value than another?

Without knowing more about those things, I don't know any way to even attempt to answer your question. If everything that is being asked is equally important, my feeling is that there are really 20 questions that should be graded as 5% each.

Given only those two options, I would do a 10 point scale with partial-credit for partially-correct multi-part answers. It's generally better to under-weight rather than over-weight related answers (for example, knowing 5 of snow white's 7 dwarfs is worth closer to 5/7 of 1 point than it is to 5 points). Another option, which is similar to how you're doing the 10-point weighting, is to pick a middle point between 11 and 19 for the possible total score. Make the weights yield a perfect score of 15 (any number from 11-19), and you give some added weight to the multi-part answers without giving them so much value that one correct string of related answers on #10 makes up for 5 misses on 1-5.

I feel like it really depends on the type of test and the difficulty/involvement on each question. So offhand I can't give a very good answer. The multi-part questions probably should be weighted more unless the 1-part question is just as involved.

See I took engineering in college, so an hour exam to me is 3 or 4 questions each worth in the 25 to 30 point range. And even though I would hate it to grade, I would be very liberal with partial credit (i.e. a dumb math mistake that gives you a wrong final answer is 27/30 assuming everything else is correct).

I don't think there is an answer to your question, because there is no question asked.

Do you really ask whether or not a given test should be evaluated with fixed or weighted points per question ?
This obviously depends on the test itself. The evaluation procedure of should be part of the test specification itself. Then the test result gives you an "index", meaning there is (or should be) a certain degree of statistical correlation between your index and the performance you want to test.

This is a clear example of needing to define parameters before an event, not after it. "Most" tests, if listing 'questions' 1 - 10, will count each 'question' as 10%, even if any or all of the 'questions' have more than one answer. But if a teacher said, there are ten questions, but some have multiple answers, totalling 20, so each answer is worth 5%, that would be ok, too, if DEFINED IN ADVANCE.

But you really already know the correct answer, and had no need to ask the forum this question...

Whichever way you score it so your wife comes out ahead is the correct way to score it, so you have a better chance to score......