1. Home
2. MLC Tools
3. InfStat Calculators
4. \(\sigma_\bar{p}\) calculator

Sampling Distribution

\(\sigma_\bar{x}\) calculator \(\sigma_\bar{x}\) finite population \(\sigma_{\bar{x_1} - \bar{x_2}}\) calculator

\(\sigma_\bar{p}\) calculator \(\sigma_\bar{p}\) Finite Population \(\sigma_{\bar{p_1} - \bar{p_2}}\) calculator

Standard Error of Proportion

Is your population proportion known? Yes No

Sample Size

Proportion

Sample Proportion

Result

Please enter all values.

Tips about Hypothesis testing for Mean when σ known:

---

Definations

• The standard error of the proportion (\(\sigma_\bar{p}\)) is a measure of the variability or precision of a sample proportion estimate compared to the true population proportion. It quantifies how much the sample proportion \(\bar{p}\) is expected to fluctuate from the actual population proportion 𝑝 due to sampling variability.
• The formula for the standard error of the proportion is: \[ \sigma_{p} = \sqrt{\frac{{p}(1 - {p})}{n}} \]
• Often the popoulation proportion is unknown. In this case the satndard error for proportion is computed as follows: \[ \sigma_{\hat{p}} = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \]
Where:
\(p\) is Population Proportion
\(\hat{p}\) is sample proportion
\(n\) is a sample size.

Common Errors:

1. Misinterpreting Standard error and Standard Deviation:
   • Standard error measures the precision of the sample proportion estimate, while the standard deviation measures the variability within the data set itself. Confusing the two can lead to incorrect conclusions.
2. Using Standard error for Small Samples:
   • The Standard error formula assumes a large sample size. For small samples, the standard error might not be accurate, and adjustments or different methods might be necessary.
3. Ignoring Sample Size:
   • The sample size greatly affects the standard error. Smaller sample sizes result in larger standard error, indicating less precise estimates. Ignoring this relationship can lead to overconfidence in results.
4. Assuming Normality:
   • Ensure that your sample size is large enough for the normal approximation to be valid. A common rule of thumb is that both \(n{\bar{p}}\) ≥ 5 and \(n(1-{\bar{p}})\) ≥ 5.

Additional Tips

1. Consider Finite Population Correction:
   • If sampling without replacement from a finite population, apply the finite population correction factor to adjust the standard error: \[\sigma_{\hat{p}} = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \times \sqrt{\frac{N - n}{N - 1}}\]
2. Report Standard error with Sample Proportion:
   • Always report the standard error alongside the sample proportion to provide context for the estimate's precision. This practice enhances transparency and accuracy in data interpretation.