📊 Proportion & Variance Tests Calculator
Evaluate population proportions and variances against textbook hypothesis tests. This toolkit covers one-proportion z-tests, two-proportion comparisons, chi-square variance tests, and F-tests for variance ratios. Each module outputs the test statistic, degrees of freedom, p-value, critical region, effect size, and a narrated step-by-step summary.
1. Select Test Type
Tail Direction
For chi-square and F tests, the two-tailed option doubles the more extreme tail probability.
Significance Level (α)
Custom α must be between 0.001 and 0.25.
2. Provide Sample Information
Test Output
Results readyKey Values
- Statistic
- Degrees of freedom
- p-value
Decision
Critical Region & Effect
- Critical value(s)
- Effect size
- Effect interpretation
Step-by-Step Workflow
Formula Reference
One-proportion z-test
\\[ z = \dfrac{\hat{p} - p_0}{\sqrt{p_0(1 - p_0)/n}}, \qquad \hat{p} = \tfrac{x}{n} \\]
Two-proportion z-test
\\[ z = \dfrac{(\hat{p}_1 - \hat{p}_2) - \Delta_0}{\sqrt{\hat{p}(1 - \hat{p})(1/n_1 + 1/n_2)}}, \quad \hat{p} = \tfrac{x_1 + x_2}{n_1 + n_2} \\]
Chi-square variance test
\\[ \chi^2 = \dfrac{(n - 1)s^2}{\sigma_0^2}, \qquad \text{df} = n - 1 \\]
F variance ratio test
\\[ F = \dfrac{s_1^2}{s_2^2}, \qquad \text{df}_1 = n_1 - 1,\ \text{df}_2 = n_2 - 1 \\]
How to Use This Calculator
- Choose the test that aligns with your data type (proportion or variance) and study design.
- Enter the requested counts, sample sizes, or standard deviations. Ensure variances are positive and sample sizes are integers.
- Select the alternative hypothesis direction and set the significance level \\(\alpha\\).
- Click “Run Test” to obtain the statistic, p-value, decision, and effect-size interpretation.
- Review the step-by-step summary and references to communicate your findings accurately.
References
- Agresti, A., & Finlay, B. (2009). Statistical Methods for the Social Sciences (4th ed.). Pearson.
- Casella, G., & Berger, R. L. (2002). Statistical Inference (2nd ed.). Duxbury.
- Montgomery, D. C., & Runger, G. C. (2014). Applied Statistics and Probability for Engineers (6th ed.). Wiley.
- Wackerly, D. D., Mendenhall, W., & Scheaffer, R. L. (2008). Mathematical Statistics with Applications (7th ed.). Cengage.
Disclaimer
Ensure conditions for normal approximations (e.g., \\(np_0\\) and \\(n(1 - p_0)\\) ≥ 5 for proportion tests) and independence are satisfied. Variance tests assume normal populations; results may be sensitive to deviations from normality.