A New View of Statistics
It's hard to put a figure on what are considered small, medium and large differences between the frequencies of something in two groups, because it depends on the frequencies. If one group has about 50% with a characteristic, a frequency of 60% or 40% in the other group can be considered small. That difference corresponds to a relative risk of about 1.2 (or 0.8, depending which way around the frequencies are). Once the frequencies get low (e.g. 1% in one group), relative risks have to be 2 or more before people get excited.
Notice that the two groups differ in exposure to something that might cause the disease. A somewhat different statistic, the odds ratio, is used when the basis of the grouping is whether subjects already have the disease: in other words, when the groups are cases and controls. In the example shown, the odds of being a smoker in the heart-disease group are 75/25 = 3. Similarly, the odds of being a smoker in the healthy group are 30/70 = 0.43. The odds ratio is therefore 3/0.43 = 7. Interpret this statistic as "seven people with heart disease smoke for every healthy person who smokes". Or, if you had two people in front of you, a healthy person who smokes and a person with heart disease, you would break even in the long run by betting at odds of 7:1 that the person with heart disease is a smoker. Fine, but I still have trouble getting my brain around this statistic. Are those odds good or bad, in terms of the effect of smoking on heart disease? I don't know. I guess I don't work with this statistic enough to have a feel for it. (I used to have here "seven smokers have heart disease for every one smoker who doesn't" or "if you are a smoker, odds are 7 to 1 that you have heart disease", but these interpretations are wrong. Thanks, Chris Rhoads!).
Coming up next is the important question of how
big is big in effect statistics.
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Last updated 16 March 02