Calculator Form
Example Data Table
| Case | Test Type | Null Value | Observed Value | Sample Size | Spread | Alternative | Alpha |
|---|---|---|---|---|---|---|---|
| Average delivery time | Mean | 100 | 104 | 50 | 12 | 106 | 0.05 |
| Defect rate audit | Proportion | 0.08 | 0.11 | 240 | Not used | 0.13 | 0.05 |
| Pass rate review | Proportion | 0.70 | 0.76 | 180 | Not used | 0.80 | 0.01 |
Formula Used
Mean Test Statistic
z = (x̄ - μ₀) / (σ / √n)
Proportion Test Statistic
z = (p̂ - p₀) / √(p₀(1 - p₀) / n)
P Value
Right tailed: P(Z ≥ z). Left tailed: P(Z ≤ z). Two tailed: 2 × P(Z ≥ |z|).
Power Approximation
Power is the probability of falling inside the rejection region when the chosen alternative value is true.
Beta
β = 1 - power
Sample Size Estimate
For a mean test, n = ((zα + zpower)σ / effect)². Two tailed tests use zα/2.
How To Use This Calculator
- Select whether your study tests a mean or a proportion.
- Choose the tail direction for the hypothesis test.
- Enter alpha, sample size, null value, and observed value.
- Enter the standard deviation when testing a mean.
- Enter the alternative value used for power estimation.
- Set the target power for sample size planning.
- Press calculate and read the result above the form.
- Export the report with the CSV or PDF buttons.
Article
About This Population Power Calculator
Population testing connects sample evidence with a claimed population value. This calculator helps you examine that link before or after a study. It handles a one population mean or a one population proportion. You can choose a left tailed, right tailed, or two tailed test. You can also enter an assumed alternative value to estimate power.
Why Power Matters
A test statistic describes how far the sample result sits from the null value. The p value then converts that distance into tail probability. Power asks a different question. It estimates the chance that the test rejects the null hypothesis when the alternative value is true. Higher power means a better chance of detecting a real effect.
Important Inputs
Start with the null value. For a mean, this may be a target weight, time, score, or cost. For a proportion, this may be a defect rate, response rate, pass rate, or conversion rate. Then enter the sample result, sample size, and standard deviation when needed. Select the significance level carefully. Common choices are 0.10, 0.05, and 0.01.
Reading The Result
The calculator reports the standard error, observed test statistic, p value, critical value, beta, and power. It also gives a decision based on alpha. A reject decision means the sample result is unlikely under the null model. It does not prove the alternative. A do not reject decision means evidence is not strong enough at the chosen level.
Planning Better Studies
Power is most useful during planning. Enter the smallest effect worth detecting as the alternative value. Then review the estimated sample size for your target power. Many studies use 80% or 90% power. A larger effect, lower variation, or larger sample size increases power. A smaller alpha usually lowers power.
Practical Notes
Results are rounded for clear reporting. Proportion inputs must stay between zero and one. Mean inputs can use any consistent unit. This calculator is a planning aid, not a replacement for expert statistical review. Always match the method to your sampling design and assumptions.
Use exported results to document assumptions, inputs, and decisions. Keep notes beside each scenario, so later reviews can trace the study plan with less confusion and fewer errors overall.
FAQs
What does this calculator test?
It tests one population mean or one population proportion. It also estimates statistical power using an assumed alternative value.
What is a test statistic?
A test statistic measures how far the sample result is from the null value after adjusting for standard error.
What is statistical power?
Power is the probability of rejecting the null hypothesis when the selected alternative value is actually true.
What does beta mean?
Beta is the probability of missing the effect under the selected alternative value. It equals one minus power.
When should I use a two tailed test?
Use a two tailed test when differences in either direction matter. It checks both higher and lower outcomes.
Can I use proportions as percentages?
Enter proportions as decimals. For example, use 0.25 for 25 percent and 0.08 for 8 percent.
Why is sample size estimated?
The estimate helps plan how many observations may be needed to reach the selected target power.
Is this suitable for final research reporting?
It is useful for planning and checking. Final reports should match your study design and statistical assumptions.