I have a math question for people. I'm not getting standard deviations when there's an odd distribution. For example, I have this survey where it was not possible to be even 1 standard deviation above average, because the average scores were 4.4/5 with a standard deviation of .88.
So, what does that mean? Are these stats valueless?
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Pretty much. Someone had to slam a square peg into a round hole to get that SD. In systems where there is an artificial upper limit instead of an unbounded test then you should be expressing scores as percentiles. Then you could use a z test for SD.
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This thread is evil.
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I have a math question for people. I'm not getting standard deviations when there's an odd distribution. For example, I have this survey where it was not possible to be even 1 standard deviation above average, because the average scores were 4.4/5 with a standard deviation of .88.
So, what does that mean? Are these stats valueless?
The stats aren't valueless. You've (obviously) got a very strong ceiling effect there, which means you can't really tell if someone/something is better than average, but the converse of that is that your data allows you to make very fine-grained and powerful distinctions about the low end of the distribution. If for some reason you need to determine the worst-of-the-worst, this could be a good data set.
A real-world example of this kind of test (albeit reversed) would be the Putnam exam, or the various intelligence tests used by the super-high-IQ organizations like such as the Triple Nine Society or the Prometheus society. Conventional IQ tests tend not to give useful numbers above about IQ 13o, so how do you tell the difference between someone with a "mere" 160 (which doesn't qualify for Prometheus) and 170 (which does)?
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~cries as I realize that I am below average~
I doubt that I would qualify for either the Triple Nine Society or the Prometheus society.
I doubt that I would qualify for either the Triple Nine Society or the Prometheus society.
That's a fairly safe bet for the vast majority of us. I'd not worry too much about it. I'm more bothered by the fact that I'll (probably) never be an Olympic gold medalist.
Oh, I am not upset about it. Just being honest.