# ANOVA Calculator: One-Way Analysis of Variance Calculator

This One-way ANOVA Test Calculator helps you to quickly and easily produce a one-way analysis of variance (ANOVA) table that includes all relevant information from the observation data set including sums of squares, mean squares, degrees of freedom, F- and P-values.

To use the One-way ANOVA Calculator, input the observation data, separating the numbers with a comma, line break, or space for every group and then click on the "Calculate" button to generate the results.

One-Way ANOVA Calculator

## ANOVA Formulas

One-Way ANOVA Table
Source Degrees of Freedom
DF
Sum of Squares
SS
Mean Square
MS
F-StatP-Value
Between Groupsk − 1SSBMSB = SSB / (k − 1)F = MSB / MSWRight tail of
F(k-1,N-k)
Within GroupsN − kSSWMSW = SSW / (N − k)
Total:N − 1SST = SSB+SSW

Between Groups Degrees of Freedom: DF = k − 1 , where k is the number of groups

Within Groups Degrees of Freedom: DF = N − k , where N is the total number of subjects

Total Degrees of Freedom: DF = N − 1

Sum of Squares Between Groups: SSB = Ski=1ni (xix)2 , where ni is the number of subjects in the i-th group

Sum of Squares Within Groups: SSW = Ski=1(ni − 1) Si2 , where Si is the standard deviation of the i-th group

Total Sum of Squares: SST = SSB + SSW

Mean Square Between Groups: MSB = SSB / (k − 1)

Mean Square Within Groups: MSW = SSW / (N − k)

F-Statistic (or F-ratio): F = MSB / MSW