The one-way ANOVA calculator determines the differences between means of three or more independent samples or treatments.

- First, enter the set of numbers for at least three and up to five samples.
- Make sure the entered numbers should be space or comma separated. Example: 12,15,23 or 12 15 23.
- Also, input at least two or more data points in each sample.
- After entering the values, press the 'Calculate' button.
- Finally, the tool returns the ANOVA results including F-statistic, P-value, sum of squares, degrees of freedom, and mean square.
- The interpretation is divided into three categories: Between Treatments, Error (Within Treatments), and Total.

The one-way ANOVA (Analysis of Variance) is a test used to check the statistically significant difference between three or more group means.

This statistical concept is widely used in education, business, engineering, healthcare, environmental studies, agriculture, and many more fields.

The following table shows the formulas of each one-way ANOVA results:

Source | Treatments (Between Treatments) |
Error (Within Treatments) |
Total |
---|---|---|---|

Degrees of Freedom | k - 1 | n - k | n - 1 |

Sum of Squares | SS_{between} = Σ n_{i} (x̄_{i} - x̄)^{2} |
SS_{within} = Σ (n_{i} - 1) S_{i}^{2} |
SS_{total} = SS _{between} + SS_{within} |

Mean Square | MS_{between} = SS _{between} / (k-1) |
MS_{within} = SS _{within} / (n-k) |
MS_{total} = SS _{total} / (n-1) |

F Statistic | F = MS_{between} / MS_{within} |
||

P-value | P(x > F) |

Where,

k = Number of samples (groups),

n = Total number of observations,

n_{i} = Number of observations in the i^{th} group,

x̄_{i} = Mean (Average) of the i^{th} group,

x̄ = Overall mean,

S_{i} = Standard deviation of the i^{th} group.