Kruskal-Wallis Test

The Kruskal-Wallis calculates if the Median of two or more data sets at least one data-set is significant different. The calculation calculates the test only from the checked data sets in the Kruskal-Wallis dialogue. This is the non parametric counterpart of the One way Anova test is for not normally distributed data but before using this test try to find out why the data is not normally distributed.

Interpretation

• The smaller the p value is the more likely there is a data-set with a significant difference.
• Develve uses the commonly accepted value of p < 0.05 for significance.
• If all data-sets are normally distributed use the One way Anova
• With no significant difference you can not say that the data is the same.

For a good result the data must

• Data is randomly and independent.
• The data is continuous.
• The shape of the distribution of all data-sets are the same.

Colors of the cells

• Green
  No significant difference
• Yellow
  Significant difference

Formula

All selected data-sets are sorted and ranked in order. The sum of the ranks of each data-set is calculated ()

With tie correction

Ties are data point with the same value.

With the H and the amount of df-1 value the p value can be calculated with the distribution.

Sample size

Sample size calculation is the same as with the One way Anova but with 15% more samples.
The result is the minimum sample size for all the data sets.

Legend

= Mean of ranks of group j
= Mean of ranks all ranks of all groups
= Amount of samples of group j
= total Amount of samples
= amount of ties of a rank
= degrees of freedom (amount of groups)

Example

From the selected data-sets there is at least one data-set that is significant different median compared to the other data sets.

Data file

External links

• http://en.wikipedia.org/wiki/Kruskal%E2%80%93Wallis_one-way_analysis_of_variance
• http://www.le.ac.uk/bl/gat/virtualfc/Stats/kruskal.html