One-Way ANOVA
Computes one-way analysis of variance (ANOVA), the test that checks whether three or more groups have different means. It decomposes the total variation into between-group and within-group variation, and the ratio between them (the F-statistic) indicates whether the observed differences are larger than would be expected by chance. It's the generalization of the t-test to multiple groups. Enter the groups: values separated by commas, groups separated by semicolons.
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One-Way ANOVA
Computes one-way analysis of variance (ANOVA), the test that checks whether three or more groups have different means. It decomposes the total variation into between-group and within-group variation, and the ratio between them (the F-statistic) indicates whether the observed differences are larger than would be expected by chance. It's the generalization of the t-test to multiple groups. Enter the groups: values separated by commas, groups separated by semicolons.
The t-test generalized to many groups
Comparing two groups is a job for the t-test. But what about three, four, five groups? Running several pairwise t-tests inflates the chance of a false positive. Analysis of variance, or ANOVA, solves this by comparing all groups at once, in a single test, controlling that risk.
The name is a bit misleading: although it compares means, ANOVA does so by analyzing variances. It breaks the data's total variation into two parts, the one occurring between groups and the one within them, and computes the ratio between them, the F-statistic. If the between-group variation is much larger than the within, F gets big and you conclude at least one group differs from the rest.
Enter the groups, with values separated by commas and groups separated by semicolons. The tool returns the F-statistic and the degrees of freedom. Remember ANOVA only says a difference exists, not where it is; for that, post-hoc tests like Tukey's are used, and the effect size via eta-squared.
Related Tools
Kruskal-Wallis H Test
Computes the Kruskal-Wallis H test, the non-parametric version of ANOVA for comparing three or more independent groups. Just as Mann-Whitney does for two groups, it works with the ranks of the data instead of the raw values, dispensing with the normality assumption. The H statistic approximately follows a chi-square distribution. It's the choice when the data are ordinal or clearly non-normal. Enter the groups: values by comma, groups by semicolon.
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.
Levene's Test (Equality of Variances)
Computes Levene's test, which checks whether several groups share the same variance — the homogeneity assumption that ANOVA and the t-test rely on. Instead of working with the original values, it transforms each data point into the absolute deviation from its group mean and runs an ANOVA on those deviations, gauging whether the spread differs across groups. It's more robust to non-normality than Bartlett's test. Enter the groups: values by comma, groups by semicolon.
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.