![]() ![]() Now we can use the Standard Error scale to determine 95% intervals. Again, decreases in Standard Error correspond to narrowing of the sampling distribution. Since n is in the denominator of the Standard Error formula, as n increases Standard Error decreases. Larger sample sizes have narrower sampling distributions. ![]() The p * (1 – p) term in the numerator is called the proportion variance. 1 rather than 10% and 1 rather than 100%). The variable p is the proportion rather than percentage. The Standard Error formula, which I’ll explain a piece at a time, is as follows: And it’s labelled “Error” because we don’t expect our sample statistic values to be exactly equal to the population parameter there will be some amount of error. It’s labeled “Standard” because it serves as a standard unit. The unit to be used is called Standard Error. And the rescaling to that unit must account for the effects of the population percent-in-favor value (number 1above) and sample size (number 2 above). It would be useful to convert them all to one standard scale. The various sampling distributions have different locations on the horizontal axis and they have different widths. Larger sample sizes have narrower sampling distributions.Sampling from populations with percent-in-favor close to 50% have wider sampling distributions than populations with percentages closer to 0% or 100%.With random sampling of binomial values (in-favor vs. ![]()
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