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COOLSerdash
COOLSerdash
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Why is the standard error of a proportion, for a given n$n$, largest for 0$p=0.55$?

The standard error of a proportion will be the largest it can be for a given N$N$ when the proportion in question is 0.5$p=0.5$, and gets smaller the further the proportion is from 0.5$0.5$. I can see why this is so when I look at the equation for the standard error of a proportion, but I can't explain this any further.

Is there an explanation beyond the mathematical properties of the formula? If so, why is there less uncertainty around estimated proportions (for a given N$N$) as they get closer to 0$0$ or 1$1$?

Why is the standard error of a proportion, for a given n, largest for 0.5?

The standard error of a proportion will be the largest it can be for a given N when the proportion in question is 0.5, and gets smaller the further the proportion is from 0.5. I can see why this is so when I look at the equation for the standard error of a proportion, but I can't explain this any further.

Is there an explanation beyond the mathematical properties of the formula? If so, why is there less uncertainty around estimated proportions (for a given N) as they get closer to 0 or 1?

Why is the standard error of a proportion, for a given $n$, largest for $p=0.5$?

The standard error of a proportion will be the largest it can be for a given $N$ when the proportion in question is $p=0.5$, and gets smaller the further the proportion is from $0.5$. I can see why this is so when I look at the equation for the standard error of a proportion, but I can't explain this any further.

Is there an explanation beyond the mathematical properties of the formula? If so, why is there less uncertainty around estimated proportions (for a given $N$) as they get closer to $0$ or $1$?

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GeoMatt22
GeoMatt22
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edstatsuser
edstatsuser
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Why is the standard error of a proportion, for a given n, largest for 0.5?

The standard error of a proportion will be the largest it can be for a given N when the proportion in question is 0.5, and gets smaller the further the proportion is from 0.5. I can see why this is so when I look at the equation for the standard error of a proportion, but I can't explain this any further.

Is there an explanation beyond the mathematical properties of the formula? If so, why is there less uncertainty around estimated proportions (for a given N) as they get closer to 0 or 1?