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education/statistics/Sampling.md
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@ -6,7 +6,7 @@
| Quantitative | A numerical value (7, 8, 9) | | Quantitative | A numerical value (7, 8, 9) |
| Population | The entire set of existing units that investigators wish to study | | Population | The entire set of existing units that investigators wish to study |
| Sample | A portion or subset of the population | | Sample | A portion or subset of the population |
| Parameter | A number that describes a characteristic of a *population* (*10%* of US senators voted for something) | | Parameter | A number that describes a characteristic of an entire *population* (*10%* of US senators voted for something) |
| Statistic | A number that describes a *sample* characteristic (*71%* of Americans feel that ...) | | Statistic | A number that describes a *sample* characteristic (*71%* of Americans feel that ...) |
> A global consumer survey reported that 6% of US taxpayers used or owned cryptocurrency in 2020. The US government is interested in knowing if this percentage has increased. The University of Chicago surveys 1,004 taxpayers and finds that 13% have used or owned crypto in the past year (2021) > A global consumer survey reported that 6% of US taxpayers used or owned cryptocurrency in 2020. The US government is interested in knowing if this percentage has increased. The University of Chicago surveys 1,004 taxpayers and finds that 13% have used or owned crypto in the past year (2021)
@ -38,11 +38,12 @@ An ideal sample will represent the whole population.
## Percentages ## Percentages
(Ch 20, stat 1040) (Ch 20, stat 1040)
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 sample size, the standard error changes 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 $\frac{1}{\sqrt{n}}$.
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.
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`).
$$ \sqrt{\frac{(\%\space of\space 1s)(\%\space of\space 0s)}{num_{draws}}} $$(Ch 21, stat 1040) $$ \sqrt{\frac{(\%\space of\space 1s)(\%\space of\space 0s)}{num_{draws}}} $$
If asked