Perform z-tests, t-tests, and chi-squared tests with visual rejection regions, p-values, and power curves.
Choose a z-test, t-test, or chi-squared test to turn an observed result into a test statistic, p-value, and graphical decision. The visualizer places the statistic on its reference distribution, shades the rejection region selected by the significance level and alternative hypothesis, and displays how power changes across alternatives. The most important interpretive trap is the p-value: it measures extremeness under the null hypothesis, not the probability that the null hypothesis is true.
A concrete input and expected output from the current implementation.
Input
Test: one-sample z-test Null mean: 0 Sample mean: 2 Known population standard deviation: 2 Sample size: 4 Alternative: two-sided Significance level: 0.05
Expected output
z statistic = 2.00000; two-sided p-value = 0.04550; critical values = -1.95996 and 1.95996; reject the null hypothesis at alpha = 0.05. The observed statistic lies in the right rejection region.
The standard error is 2 / sqrt(4) = 1, so z = (2 - 0) / 1 = 2. The probability beyond |z| = 2 in both normal tails is approximately 0.04550, which is below 0.05.
The chosen test family determines the curve used for comparison. A z-test uses the standard normal distribution. A t-test uses a Student t distribution governed by its degrees of freedom. A chi-squared test uses a chi-squared distribution, also governed by degrees of freedom. The observed statistic's location on that curve determines its tail probability.
For a fixed significance level, the shaded rejection region contains the outcomes designated sufficiently extreme under the null hypothesis. A two-sided z or t test divides that region between both tails, while a directional test uses its specified tail. The power curve represents the probability that the same rejection rule detects candidate alternatives, rather than another version of the observed p-value.
For a two-sided z or t test, results at least as far from the null in either direction count against the null hypothesis. The visualizer therefore combines both extreme tails. With these symmetric distributions, that is twice the corresponding one-tail area for a nonzero statistic. For a directional alternative, no: the opposite tail is not included in the p-value.
No. It means the entered result does not meet the selected rejection rule at the chosen significance level. The plot does not assign a probability that the null is true, and low power can leave meaningful alternatives undetected. Use the power display and the study's effect estimates to judge how informative a non-rejection actually is.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
Calculate percentages, percentage change, and what percent one number is of another with step-by-step breakdowns.
Calculate tips and split bills between multiple people with customizable tip percentages and rounding options.
Calculate monthly payments, total interest, and generate amortization schedules for loans and mortgages.
Calculate Body Mass Index from height and weight with category classification and healthy range guidance.
Calculate sale prices, savings amounts, and final costs after single or stacked percentage discounts.
Compute mean, median, mode, standard deviation, variance, and other descriptive statistics from a data set.