Kruskal-Wallis Non-Parametric Analysis

Other Non-Parametric Tests:

Wilcoxon Intra-Well Comparison

Wilcoxon Inter-Well Comparison

Non-Parametric Prediction Limits

Non-Parametric Tolerance Limits

 

Description:

 

The Kruskal-Wallis test is a non-parametric Analysis of variance that compares each compliance well to a group of background wells. It is recommended in the 1992 guidance document for data that do not follow a normal distribution, or have 15% to 90% non-detects.

 

ChemStat compares each compliance well to the background wells. Two comparisons are provided. The first comparison is performed at a minimum of 1% individual well comparison error level. The second comparison is performed at an experimentwise 5% error level, however the minimum error level may fall below the USEPA required value of 1%. The first comparison is compliant with USEPA guidance. The second comparison is less likely to produce false positives, but is more statistically accurate.

 

All wells should have at least 4 samples. The test will work with fewer samples, but it is not likely to show statistical significance.

 

 

Use:

 

For comparison of compliance wells to background wells when data do not follow a normal distribution, or there are 15% to 90% non-detects.

 

 

Remarks:

 

The Kruskal-Wallis test can only determine which compliance well is elevated with respect to background, but can not determine which specific samples cause the statistical trigger.

 

The 1992 guidance example problem for the Kruskal-Wallis method has an error. On page 43, the rank sum and rank mean for Well 3 are given as 51 and 10 respectively. The rank sum and rank mean should be 61 and 12.2 respectively.