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 (σ₀²).
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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 (σ₀²).
Is the process variability on target?
In quality control, keeping the mean on target is only half the job; the other half is keeping variability under control. A process whose spread has grown produces inconsistent parts even with a perfect mean. The one-sample variance test checks whether the observed variability matches a specified reference value.
It is, for dispersion, what the one-sample t-test is for the mean. The statistic compares the sample variance with the hypothesized variance, and under normality it follows a chi-square distribution, with degrees of freedom equal to the sample size minus one. A very high value indicates variability above expectation; a very low one, below expectation.
Enter the sample and the hypothesized variance you want to test. The tool returns the chi-square statistic, the degrees of freedom and the two-sided p-value. Like any chi-square-based method for variance, it assumes the data come from an approximately normal population, and it is more sensitive to departures from that assumption than tests about the mean.
Related Tools
CI for Variance and Standard Deviation
Computes the confidence interval for the variance and standard deviation of a normal population, from a sample. While most tools estimate the mean, this one estimates the spread — useful in quality control, where consistency matters as much as the central value. The calculation uses the chi-square distribution, which is asymmetric, so the interval is not centered on the sample variance. Enter the sample and the confidence level.
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.
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.
McNemar's Test (Paired)
Computes McNemar's test, used to compare two paired proportions — 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 2×2 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.
Mood's Median Test
Computes Mood's median test, a non-parametric test that checks whether several groups share the same median. The idea is simple and robust: you compute the grand median of all the data together and count, in each group, how many values fall above it. If the groups had the same median, those counts would be proportional to the sizes; an imbalance produces a large chi-square statistic. It's quite resistant to outliers, working only with counts. Enter the groups separated by semicolons.
Eta-Squared (Effect Size)
Computes eta-squared (η²), an effect-size measure for analysis of variance, from the F-statistic and the degrees of freedom. While the F-test says whether there's a significant difference between groups, η² says how much of that difference the grouping variable explains — the proportion of total variance attributable to the groups. It's essential for reporting ANOVA results beyond the p-value. Enter the F-statistic and the numerator and denominator degrees of freedom.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.