notes/education/statistics/Sampling.md

(Ch 19, stat 1040)

| Term | Definition |
| ---- | ---- |
| Qualitative | A descriptive value (red, blue, high, low) |
| Quantitative | A numerical value (7, 8, 9) |
| Population | The entire set of existing units that investigators wish to study |
| 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) |
| 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)

In the above example:
- The *population* was *US taxpayers*
- The *parameter* was *6%*
- The *sample* was *1004 taxpayers*
- The *statistic* was *13%*

An ideal sample will represent the whole population.
## Sampling
| Sample Type | Description |
| ---- | ---- |
| Simple random | Advantages:<br>- Procedure is impartial<br>- Law of Averages<br>Disadvantages<br>- Not always possible<br>- Can be very expensive |
| Quota Sampling | Attempts to get certain proportions based on key characteristics. Quota sampling doesn't guarantee that the selection is an accurate representation. |
| Cluster Sampling | Divide population into subgroups, randomly select a subgroup, and sample all of the subjects in that group |
| Convenience | Sampling done near to the researcher because it's easier. |
## Simple Random Samples

## Bias
| Bias Type | Description |
| ---- | ---- |
| Selection | When the procedure that selects the sample is biased |
| Non-Response | Those that don't respond to a survey may have different characteristics than those that do respond |
| Response | When the question is worded in a leading way to elicit a certain response. |
| Volunteer response | Self selecting, individuals volunteer to answer |
| Measurement | Interviewing method influences the response, uses loaded words or ambiguities. |

## Percentages
(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%`

To determine by how much the standard error is affected, if `n` is the sample size, the standard error changes by $\frac{1}{\sqrt{n}}$

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`).
$$ \sqrt{\frac{(\%\space of\space 1s)(\%\space of\space 0s)}{num_{draws}}} $$(Ch 21, stat 1040)