**Calculate a Statistical Sample Size – Attribute**

Sampling

Sampling

This calculator allows you to estimate the random sample size required to achieve a specified level of statistical precision in making a sample inference about a population. All inputs must be greater than zero.

#### How to Use:

- Enter the (estimated) Population Count for the period. *
- Enter the Estimated Incidence Rate (of that population). For a population of funded loans, the incidence rate may refer to the incidence of defective loans in the population. **
- Enter your Desired Precision Level and select a Confidence Level, either one-sided or two-sided. The industry standard is 2% precision at 95% confidence.
- Click on the Calculate button. The System will calculate the sample size required to achieve the desired precision level.

* In loan quality control, some investors or GSE’s require lenders to achieve the stated statistical precision within 6 months (i.e., a “statistical statement” of 6 months). Others accept 12 months. The shorter the statistical statement period, the more loans must be reviewed.

### Learn the 21 Key Statistical Concepts for Loan Quality Control

**To calculate a 6-month statement:**

- Enter the TOTAL estimated population for the 6 months (by multiplying your average monthly origination volume by 6)
- Enter your average incidence/defect rate
- Enter your required precision and confidence levels
- Calculate a result. This is the number of loans to be sampled for the ENTIRE 6 months.
- DIVIDE the calculated Sample Size by 6 to derive a sample size for a single month.

## Example: Sample Size Estimation (6-month statement)

This illustration assumes 1,000 loans originated per month, 5% average defect rate, 2% precision and 95% confidence (one-sided).

Thus, for a 6-month statement, if 1,000 loans are originated per month, then the estimated random sample size is 51 loans per month.

** Since we cannot know the actual defect rate of the population beforehand, this number must be an estimate. Ideally your estimate is based on prior history with similar populations. If unavailable, consider a pilot study on a portion of the population to derive an estimate.