Z Test
Calculate hypothesis tests, p-values, regression lines, critical Z/t scores, and statistical inference for z test.
Input Test Parameters
Enter sample data and significance level α.
Calculated p-Value
Decision Rule
If p-value ≤ α, reject the null hypothesis H₀ (statistically significant). If p-value > α, fail to reject H₀.
Calculation Methodology & Details
Formula
Applies ordinary least squares (OLS) regression, Student's t-test, Mann-Whitney non-parametric ranks, and Welch's ANOVA equations.
Important Disclaimer
Calculations assume random sampling, independent observations, and normality or large sample sizes unless non-parametric tests (Wilcoxon, Kruskal-Wallis) are selected.
How to Calculate Step-by-Step
Follow these steps to complete the calculation:
Step 1
Enter sample statistics (sample mean, standard deviation, sample size n) or test statistic (Z, t, F).
Step 2
Select tail direction (two-tailed, left-tailed, right-tailed) and alpha level α.
Step 3
View exact p-value, critical rejection region, statistical power (1 - β), or regression R² fit.
Detailed Insights & Expert Guide
ℹ️ About this Calculation
The Z Test provides complete hypothesis test inference, regression modeling (linear, quadratic, exponential), ANOVA variance analysis, non-parametric rank tests, and statistical power estimation.
Variable Glossary
Test Statistic
Calculated sample score measuring standard error deviations from H₀.
p-Value
Probability of obtaining a test statistic at least as extreme as observed, assuming H₀ is true.