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When we make inferences about one population proportion, what assumptions do we need to make? Mark all that apply.
Well, I do assume simple random sample (A). And since data is categorical (yes/no), it's not normally distributed (so not B). The sample size (n) of 30 is a population mean/ sample mean assumption (so not C). But what about D or E? —Preceding unsigned comment added by 70.169.186.78 ( talk • contribs) 05:34, 24 July 2009
You need (a) or something like it. Let's say you want to estimate the proportion of voters who will vote Republican next week. If you take your sample from the group of Republicans who are meeting in the building next door, you're making a mistake.
It doesn't make sense to assume a normal distribution. Each person will either vote Republican or not, so you get either a 0 or a 1, and that's not normally distributed. But you might conclude that the total number who will vote Republican is approximated normally distributed—that depends in part on sample size and in part on how the sample was taken. But it's a logical inference, not an assumption.
For a binary response variable, the question of whether that sum is approximately normally distributed depends not only on sample size, but also on how close the proportion is to either of the two extremes–0 and 1. And there are ways of drawing inferences when it's not approximately normally distributed and the sample size is small.
One sometimes sees a rough rule of thumb that you shouldn't conclude approximate normality unless you've got at least five outcomes in each of the two categories. I would add that you should use a continuity correction unless the numbers in both categories are pretty big. Michael Hardy ( talk) 23:52, 24 July 2009 (UTC)
Mathematics desk | ||
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< July 23 | << Jun | July | Aug >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
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The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
When we make inferences about one population proportion, what assumptions do we need to make? Mark all that apply.
Well, I do assume simple random sample (A). And since data is categorical (yes/no), it's not normally distributed (so not B). The sample size (n) of 30 is a population mean/ sample mean assumption (so not C). But what about D or E? —Preceding unsigned comment added by 70.169.186.78 ( talk • contribs) 05:34, 24 July 2009
You need (a) or something like it. Let's say you want to estimate the proportion of voters who will vote Republican next week. If you take your sample from the group of Republicans who are meeting in the building next door, you're making a mistake.
It doesn't make sense to assume a normal distribution. Each person will either vote Republican or not, so you get either a 0 or a 1, and that's not normally distributed. But you might conclude that the total number who will vote Republican is approximated normally distributed—that depends in part on sample size and in part on how the sample was taken. But it's a logical inference, not an assumption.
For a binary response variable, the question of whether that sum is approximately normally distributed depends not only on sample size, but also on how close the proportion is to either of the two extremes–0 and 1. And there are ways of drawing inferences when it's not approximately normally distributed and the sample size is small.
One sometimes sees a rough rule of thumb that you shouldn't conclude approximate normality unless you've got at least five outcomes in each of the two categories. I would add that you should use a continuity correction unless the numbers in both categories are pretty big. Michael Hardy ( talk) 23:52, 24 July 2009 (UTC)