tails:

**Header**: You may change groups' name to the real names.**Data**: When entering data, press Enter or , (comma) after each value.

Empty cells or non-numeric cells will be ignored

You may **copy the data** from Excel, Google sheets or any tool that separate data with **Tab** and **Line Feed**.

Copy **one block of 2 consecutive columns includes the header**, and paste below. Click to see example:

The tool will ignore empty cells or non-numeric cells

Hover over the cells for more information.

**Tukey HSD / Tukey Kramer**

tresults

R code.mmmm

Usually the Tukey HSD compare the averages, but the following test run over the differences from the averages.

The following tables compares the mean absolute deviations (MAD), similar to comparing the standard deviations.

**Target**: To check if the difference between the variances of two or more groups is significant, using a sample data

The Levene's tests perform an ANOVA test over the absolute deviations from each group's average or the absolute deviations from each group's median.

When performing ANOVA test, we try to determine if the difference between the averages of the absolute residuals reflects a real difference between the groups, or is due to the random noise inside each group. The F statistic represents the ratio of the variance between the groups and the variance inside the groups. Unlike many other statistic tests, the smaller the F statistic the more likely the averages are equal.

Hypotheses

H_{0}: σ_{1} = .. = σ_{k}

H_{1}: not(σ_{1} = .. = σ_{k})

Test statistic

F = | MSG |

MSE |

F distribution

Independent samples. | |

Normal population distribution or symmetrical distribution. |

Sample data from all compared groups. |

Source | Degrees of Freedom | Sum of Squares | Mean Square | F statistic | p-value |
---|---|---|---|---|---|

Groups(between groups) | k - 1 | MSG = SSG / (k - 1) | F = MSG / MSE | P(x > F) | |

Error(within groups) | n - k | MSE = SSE / (n - k) | |||

Total | n - 1 | SS(total) = SSG + SSE | Sample Variance = SS(total) / (n - 1) |

The following R code should produce the same results