Traditional InferenceStatLens

Theory-based confidence intervals and hypothesis tests using t, z, F, and chi-square distributions.

Confidence Intervals (Estimation)

Pick a confidence level — or drag the critical values on the curve — and read the interval.

CI for a Mean
x̄ ± t*·s/√n, with the t-curve behind t*.
CI for a Proportion
p̂ ± z*·SE, with the normal curve behind z*.
CI for Difference in Means
Welch's interval for μ₁ − μ₂.
CI for Paired Differences
d̄ ± t*·s_d/√n for matched pairs.
CI for Difference in Proportions
Unpooled interval for p₁ − p₂.
CI for Regression Slope
b₁ ± t*·SE(b₁), df = n − 2.
Pairwise CIs for 3+ Groups
Every pair of group means with a family-wise interval — Tukey HSD or Bonferroni.

Hypothesis Tests

State the hypotheses, compute the test statistic, and shade the p-value.

One-Sample t-Test
Test a claim about a single mean.
One-Proportion z-Test
Test a claim about a single proportion.
Two-Sample t-Test
Welch's t-test for the difference in two group means.
Paired t-Test
Test the mean of paired differences.
Two-Proportion z-Test
Test the difference in two proportions.
Chi-Square Test of Independence
Theory-based chi-square test for a contingency table.
Chi-Square Goodness-of-Fit
Theory-based test that one categorical variable fits a specified distribution.
One-Way ANOVA
F-test for equality of means across 3+ groups.
Multiple Comparisons
After a discernible F: which pairs differ? Adjusted p-values, Tukey HSD or Bonferroni.
Regression Slope t-Test
Test whether the regression slope β₁ is zero.

The test pages also report a confidence interval. The CI pages above are the estimation-only view — no hypotheses, no p-value — so the interval and the critical value behind it stay in focus.