tails:

Calculates the KW test and multiple comparisons and validates the data normality, test power, outliers and generates the R syntax.

**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

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

The Kruskal-Wallis test is a non parametric test.

When the groups have a similar distribution shape, the null assumption is stronger and states that the medians of the groups are equal.

When performing Kruskal-Wallis test, we try to determine if the difference between the ranks reflects a real difference between the groups, or is due to the random noise inside each group. The Chi-square statistic is an approximation for the exact calculation.

Hypotheses

H_{0}: MR_{1} = .. = MR_{k}

H_{1}: not(MR_{1} = .. = MR_{k})

MR - Mean rank.Test statistic

R_{j} - the rank sum of group j.

n_{j} - the sample size of group j.

n - the total sample size across all groups, n = n_{1} +...+ n_{j}.

H'= | 12 | Σ( | R_{j}^{2} | ) - 3(n+1) |

n(n+1) | n_{j} |

H= | H' |

1 - correction |

n

n - the total sample size across all groups, n = n

χ^{2} distribution

Independent samples from independent groups. One subject can't be in more than one group. |

Sample data from all compared groups. |

The following R code should produce the same results