Calculate p-values for Z-tests, T-tests, and Chi-square tests — one-tailed or two-tailed. Includes a live distribution curve with the rejection region, significance verdict at α=0.05 and 0.01, and plain-English interpretation.
Select the test type and tail direction, then enter your statistic.
Select the test type, enter your statistic (or raw inputs), and press Calculate to get the exact p-value with distribution curve and significance verdict.
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Use the calculator above to compute p-values for Z-tests, T-tests and Chi-square tests, one-tailed or two-tailed, with a live distribution curve, the rejection region shaded and a verdict at α=0.05 and α=0.01. The p-value is the standard tool for deciding whether an observed difference is real or could plausibly be due to chance.
A p-value is the probability of observing data at least as extreme as your sample, assuming the null hypothesis is true. A small p-value (typically < 0.05) is evidence against the null and grounds for accepting the alternative. A large p-value means your data is consistent with the null — not that the null is proven correct.
The calculator computes the test statistic appropriate to the test (Z, t, or chi-square), then converts it to a p-value using the relevant distribution. The p-value is the area under the curve more extreme than the observed test statistic, on one tail or both depending on the test direction.
A team changes a machine setting and measures defect rates before and after. A two-sample t-test gives t = 2.78 with 58 degrees of freedom. P-value = 0.0073, well below α = 0.05.
The team rejects the null hypothesis of "no difference" and concludes the change has reduced defect rates. They still report the size of the effect (the difference in means with a confidence interval), because significance alone is not the same as practical importance.
P-values replace gut feel with a defensible test of whether an observed difference is real. They prevent celebrating a random fluctuation as a genuine improvement.
Use p-values whenever you compare two groups, test a process change, or validate a Designed Experiment. They are the closing test in any Lean Six Sigma improve phase.
P-values are the verdict line in hypothesis testing — the inferential backbone of Six Sigma. They work alongside confidence intervals, effect sizes and DOE to convert data into reliable decisions.
Always report the effect size and CI alongside the p-value. If p < α, validate with a small confirmation run before locking in the change. If p > α, do not conclude "no effect" — conclude "no evidence of effect at this sample size".
Pair p-values with confidence intervals, effect-size reporting and DOE for a complete inferential workflow.
The probability of observing data at least as extreme as your sample, assuming the null hypothesis is true. A small p-value is evidence against the null.
There is less than a 5% chance of seeing data this extreme if the null hypothesis were true. By convention this is treated as sufficient evidence to reject the null.
No. It means the data is unlikely under the null hypothesis. Replication, effect size and confidence intervals matter as much as the p-value itself.
A one-tailed test looks for an effect in a specific direction (e.g. defect rate went down); a two-tailed test looks for any difference. Choose direction before seeing the data, not after.
It is not evidence of no effect — only that the current sample does not provide sufficient evidence to reject the null. Consider increasing the sample, or report the result transparently with the effect size and CI.
Want to understand how to interpret p-values and choose the right hypothesis test? The Green Belt covers this in full.
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