# One-Way ANOVA 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.

## ANOVA Formulas

One-Way ANOVA Table | |||||
---|---|---|---|---|---|

Source | Degrees of Freedom DF |
Sum of Squares SS |
Mean Square MS |
F-Stat | P-Value |

Between Groups |
k − 1 | SS_{B} |
MS_{B} = SS_{B} / (k − 1) |
F = MS_{B} / MS_{W} |
Right tail of F(k-1,N-k) |

Within Groups |
N − k | SS_{W} |
MS_{W} = SS_{W} / (N − k) |
||

Total: |
N − 1 | SS_{T} = SS_{B}+SS_{W} |

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: **SS _{B} = S^{k}_{i=1}n_{i} (x_{i} − x)^{2}** , where

**n**is the number of subjects in the i-th group

_{i}Sum of Squares Within Groups: **SS _{W} = S^{k}_{i=1}(n_{i} − 1) S_{i}^{2}** , where

**S**is the standard deviation of the i-th group

_{i}Total Sum of Squares: **SS _{T} = SS_{B} + SS_{W}**

Mean Square Between Groups: **MS _{B} = SS_{B} / (k − 1)**

Mean Square Within Groups: **MS _{W} = SS_{W} / (N − k)**

F-Statistic (or F-ratio): **F = MS _{B} / MS_{W}**