"That is, if there is a hundred point test and the norm is 95%, subnormal is 90%, and supernormal is 100%, is it meaningful to give the 95s a C, the 90s a D, and the 100 a B? Plus, there is no way to tell if some might have earned an A, because of the performance ceiling. And do we really want to say that 85% is failing?"
There is too much here to deal with so I am just going to pick a couple of points. I'm not a statistician btw so I hope we can move on to less math soon.
First whenever there is an academic test that a significant number of testees score above 90%, I question whether the instrument has adequately tested anything. When participants score above 95% you don't really know what the test accomplished. It could be that the testee just misread a question rather than not known the proper answer. 100% only tells us that we didn't test the limits of this participant's knowledge. I would say that the meaning for this test example, is that it is a poorly designed test. I see no point in even administering such tests unless you are trying to show how this population compares with the general population, which is a normative study.
Second: There are many ways to measure statistics when there is an anomoly in the population. The example you gave of comparing two groups might produce a double hump type of curve (one with two means). For every situation you can come up with there is a way to measure it using normative data. Is it meaningful to do so? In applied statistics you look for significance. If the outcome of the math work is significant, then research can apply meaning to it.
Third: You could take a group of 120 IQ and compare them with a group of 100 IQ on some performance measure. If the groups were large enough you would likely be able to find a meaningful corrolation on most academic studies.
Fourth: The only justifiable reason to administer a test (other than to determine a simple comparison to the norm)is to measure what the student knows as well as what they don't know so that you can better map out future learning experiences. If the learning experience leading up to the test was based on challenging academic goals then the potential for failure should be just as real as the potential for exellence and everything in between.
Fifth: If the requirements for a course are designed so that the completers will be compared with a larger sample (ie all third year microbiologists at Research One Universities) then the grades achieved should be normed against the larger population. It would then be fine if you had a particularly competitive and gifted group to see them all getting an "A" which represents their mastery of the subject. You are still doing normed comparisons (all microbiologists) but you are not grading on a intraclassroom curve. |
