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education/statistics/Sampling.md
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@ -42,15 +42,18 @@ Throughout this chapter, percentages are often represented by referencing a box
The expected value for a sample percentage equals the population percentage. The standard error for that percentage = `(SE_sum/sample_size) * 100%`. The expected value for a sample percentage equals the population percentage. The standard error for that percentage = `(SE_sum/sample_size) * 100%`.
To determine by how much the standard error is affected, if $n$ is the proportion that the population changed by, the standard error will change by $\frac{1}{\sqrt{n}}$. To determine by how much the standard error is affected, if $n$ is the proportion that the population changed by, the standard error will change by $\frac{1}{\sqrt{n}}$. For example, if a population changed from 20 to 40, that change was by a proportion of 2, and so you would say the standard error decreased by $\frac{1}{\sqrt{2}}$.
Accuracy in statistics refers to how small the standard error is. A smaller standard error means your data is more accurate. Accuracy in statistics refers to how small the standard error is. A smaller standard error means your data is more accurate. As the sample size increases, the percentage standard error decreases.
You can use the below equation to find the percentage standard error of a box model that has ones and zeros. the % of ones and zeros should be represented as a proportion (EG: `60% = 0.6`). You can use the below equation to find the percentage standard error of a box model that has ones and zeros. the % of ones and zeros should be represented as a proportion (EG: `60% = 0.6`).
$$ \sqrt{\frac{(\%\space of\space 1s)(\%\space of\space 0s)}{num_{draws}}} $$
$$ SE_\% = \sqrt{\frac{(\%\space of\space 1s)(\%\space of\space 0s)}{num_{draws}}} $$
If asked if an observed % is reasonable, you can calculate the z score, and if the z score is more than 2-3 standard deviations away. If asked if an observed % is reasonable, you can calculate the z score, and if the z score is more than 2-3 standard deviations away.
## Sampling Distributions
(Ch 23, stat 1040) (Ch 23, stat 1040)
Take a sample, find the average, plot it and repeat. After many many samples, the empirical probability histogram for sample averages
looks like the theoretical probability
histogram.