let's exaggerate the problem:
Month 1: 1 person, 0 redhead (0%)
Month 2: 99 people, 99 redhead (100%)
method 1:
(0% + 100%)/2 = 50%
method 2:
(0+99)
1+99) = 99%
the first method gives an equal weighting to each month, regardless of the number of people in it's measurement.
the second number gives equal weighting to each person, regardless of the month he was observed in.
now, as Tom said, it really depends on what exactly is the question you are trying to answer.
That's an interesting way to put it. I'm not even actually sure which of those would be the correct way to look at the situation. The actual issue at hand (which I have cleverly disguised as a study of redheads but which I can't actually discuss because it's part of internal work at my department) isn't laid out neatly with specific phrasing such as a math problem on a test. Those test problems were so much easier than real life.
Also there is some real Red-Headed League shit going down in that second month of your example.
My instinct is still to believe that 99% (the second method) is the best way to look at it, because saying that the average percentage of redheads per month is 50% in that scenario just strikes me as a misrepresentation of the reality, despite its statistical truth. Sareitha and Tom (my thanks for your answers, by the way) gave me reason to doubt, but I haven't been convinced. The term "average percentage" lends itself better to the first method, as Sareitha and Tom mentioned -- it's an average of the percentages. But I can't shake the feeling that for what I need, each person should be weighted individually across the study period. If you add up the total number of people and divide, you get the average number of people in the room per month. And if you add up all the redheads and divide, you get the average number of redheads in the room per month. Divide that by the average number of people and it seems as if you should have the average monthly redhead percentage. But I haven't convinced myself of that either.
In the real situation I'm working with, the numbers are large enough to mostly swallow the differences, and the two methods come out very similar (if you round to the nearest tenth of a percentage point, they're the same). So it might be a moot question. But what I've read here will help me out when it comes to making a final call (or rather in laying out the difference and recommending a final call to someone with the authority to make it).
Thanks again, everyone! Except for math. No thanks there. It's confused me too much to earn my thanks.
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- 03/04/2014 08:26:20 AM
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