Chi-Square Test of Independence
Computes the chi-square test of independence for a contingency table, checking whether two categorical variables are associated or independent. For example: does preference for a product depend on age group? The test compares the observed frequencies with those that would be expected if there were no relationship at all, and the chi-square statistic measures the size of that mismatch. The tool returns the statistic, the degrees of freedom and the p-value. Enter the table: columns by comma, rows by semicolon.
Resultado
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Chi-Square Test of Independence
Computes the chi-square test of independence for a contingency table, checking whether two categorical variables are associated or independent. For example: does preference for a product depend on age group? The test compares the observed frequencies with those that would be expected if there were no relationship at all, and the chi-square statistic measures the size of that mismatch. The tool returns the statistic, the degrees of freedom and the p-value. Enter the table: columns by comma, rows by semicolon.
Are two categorical variables related?
Contingency tables cross two categorical variables β sex and preference, region and vote, age group and chosen plan. The natural question is whether one variable has any relationship with the other or whether they move independently. The chi-square test of independence answers this by comparing what was observed with what would be expected if there were no relationship at all.
The mechanics compute, for each cell, the frequency expected under independence, given by the product of the row and column totals divided by the grand total. The statistic sums, over all cells, the square of the difference between observed and expected divided by the expected. If the variables were independent, observed and expected would track each other and the sum would be small; strong relationships inflate the statistic.
Enter the table with columns separated by commas and rows by semicolons. The tool returns the chi-square statistic, the degrees of freedom, given by rows minus one times columns minus one, and the p-value. Remember the test detects association but doesn't measure it; for its size, use coefficients like CramΓ©r's V.
Related Tools
Bartlett's Test (Equality of Variances)
Computes Bartlett's test, the classic test for checking whether several groups share the same variance. It compares the pooled variance of all groups against the individual variances through a statistic that approximately follows a chi-square distribution, with a bias correction that improves the approximation in small samples. It's more powerful than Levene's test when the data are genuinely normal, but more sensitive to departures from normality. Enter the groups: values by comma, groups by semicolon.
One-Sample Variance Test (Chi-Square)
Computes the chi-square test for the variance of a single sample, which checks whether the population variance equals a reference value. It's the dispersion counterpart of the one-sample t-test for the mean. It shows up often in quality control: is a process's variability within the specified limit, or has it increased? The statistic compares the sample variance with the hypothesized one and follows a chi-square distribution. Enter the sample and the hypothesized variance (ΟβΒ²).
McNemar's Test (Paired)
Computes McNemar's test, used to compare two paired proportions β when the same subjects are measured twice (before and after, or by two methods). Unlike the two-proportion test, which treats the groups as independent, McNemar looks only at the cases that switched classification (the discordant cells b and c of the 2Γ2 table), ignoring those that stayed the same. The continuity-corrected version follows a chi-square with 1 degree of freedom. Enter the two discordant counts.
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