What This Calculator Does
This calculator finds the chi square test statistic for common statistics work. It supports goodness of fit data, contingency tables, and variance test inputs. You can paste raw counts, expected counts, probabilities, or grouped tables. The result explains the statistic, degrees of freedom, p value, and decision.
Why Chi Square Matters
The chi square method compares what you observed with what a model predicts. A small statistic means the counts are close to expectation. A large statistic means the gap is stronger. Researchers use it for survey categories, genetics examples, product choices, classroom data, and quality checks.
Goodness of Fit Use
Use goodness of fit when one categorical variable is measured. Enter observed counts for each group. Then enter expected counts, or enter expected proportions. The calculator scales proportions to match the observed total. This helps when a theory gives percentages instead of counts.
Independence Table Use
Use the table mode when two categorical variables are compared. Each row is one group. Each column is one outcome. The calculator builds expected counts from row totals, column totals, and the grand total. It then adds each cell contribution to form the final statistic.
Variance Test Use
Use variance mode when a sample variance is compared with a claimed population variance. Enter sample size, sample standard deviation, and hypothesized standard deviation. The calculator returns the one sample chi square statistic.
Interpreting Results
The p value shows how unusual the data would be under the null idea. If p is less than alpha, the result is statistically significant. This does not prove a cause. It only shows that the observed pattern is unlikely under the tested assumption.
Clean Reporting
Use the output table to copy results into reports. Export the CSV file for spreadsheets. Export the PDF file for printable records. Check all expected counts before using the conclusion. Very small expected counts can weaken a chi square approximation.
Good inputs create better decisions. Use whole counts whenever possible. Do not enter percentages as observed counts. Keep categories mutually exclusive. Avoid empty rows and empty columns. When data are sparse, combine sensible categories or choose another test. Record your assumptions with every exported result for later review and approval.