FANDOM


Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |

Statistics: Scientific method · Research methods · Experimental design · Undergraduate statistics courses · Statistical tests · Game theory · Decision theory


In statistics, the Kruskal-Wallis one-way analysis of variance by ranks (named after William Kruskal and Allen Wallis) is a non-parametric method. Intuitively, it is identical to a one-way analysis of variance, with the data replaced by their ranks.

Since it is a non-parametric method, the Kruskal-Wallis test does not assume a normal population, unlike the analogous one-way analysis of variance.

MethodEdit

  1. Rank all data from all groups together.
  2. The test statistic is given by: $ K = (N-1)\frac{\sum_{i=1}^g n_i(\bar{r}_{i\cdot} - \bar{r})^2}{\sum_{i=1}^g\sum_{j=1}^{n_i}(r_{ij} - \bar{r})^2} $, where:
    • $ n_g $ is the number of observations in group $ g $
    • $ r_{ij} $ is observation $ j $ from group $ i $
    • $ N $ is the total number of observations across all groups
    • $ \bar{r}_{i\cdot} = \frac{\sum_{j=1}^{n_i}{r_{ij}}}{n_i} $,
    • $ \bar{r} $ is the average of all the $ r_{ij} $, equal to $ (N+1)/2 $.
      Notice that the denominator of the expression for $ K $ is exactly $ (N-1)N(N+1)/12 $.
  3. Finally, the p-value is approximated by $ \mathbf{P}(\chi^2_{N-g} \ge K) $. If some ni's are small the distribution of K can be quite different from this.

See alsoEdit

ReferencesEdit

  • William H. Kruskal and W. Allen Wallis. Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association 47 (260): 583–621, December 1952.es:Prueba de Kruskal-Wallis

nl:Kruskal-Wallis

This page uses Creative Commons Licensed content from Wikipedia (view authors).