I taught many subjects to 5th graders, undergraduates and graduate students. I taught statistics on Wisconsin Public Television but you may have missed the lessons since they aired at 6 AM on Sunday mornings. It seems to me that having taught many lessons, there should be some that are ok to be on this blog.
We don't apply statistical methods unless we have some numbers to apply them to. A book that me and the others in my program studied from is Harold Gulliksen's "Theory of Mental Tests" and it shows many mathematical concepts and formulas but teachers know that math and people don't always mix so well. I am not thinking of the well-known and widespread dislike of math and calculation. I am referring to the strictness and rigidity of math compared to the slipperiness and flexibility of human minds and personalities.
You may have heard some of the history of intelligence tests, attempts to see who is smart and who isn't. t.ly/5C8z (short link to a Duckduckgo search) When I hear about school tests, I naturally put on my doubting cap. In rough generalites, most of the time, in ordinary circumstances -whatever they are- when a student takes a test honestly without bribery or secret use of a smartphone, doing well on the test usually means the student does indeed know what he is supposed to know. In contrast, when a student does not do well, that student may not know the subject but intervening variables may have distorted the performance or the test score.
Harold Gulliksen and many others used the concepts of 'reliability' and 'validity' to discuss good scores and poor ones, not good for the student but more basically good. Reliability is often compared to stability. If a test says the student knows but, on repeat, says he doesn't, but on repeat says he does, we may feel that is a poor test. That sort of yes and no result in any measurement, height, weight, intelligence, blood pressure, whatever isn't appreciated. Of course, some phenomena do change steadily or erratically and up and down scores may be trying to tell us that.
The other property, validity, is often said to be about whether the test "measures" what we think it does. This is usually trickier and more difficult.
You can download Gulliksen's book in eKindle format for $59.95.
