Fandom

Psychology Wiki

Friedman test

34,202pages on
this wiki
Add New Page
Talk0 Share

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.

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


The Friedman test is a non-parametric statistical test developed by the U.S. economist Milton Friedman. The procedure involves ranking each row (or block) together, then considering the values of ranks by columns.

MethodEdit

  1. Given data \{x_{ij}\}_{m\times n}, that is, a tableau with m rows (the blocks), n columns (the treatments) and a single observation at the intersection of each block and treatment, calculate the ranks within each block. Replace the data with a new tableau \{r_{ij}\}_{m \times n} where the entry r_{ij} is the rank of x_{ij} within block i.
  2. Find the values:
    • SS_t = n\sum_{j=1}^n (\bar{r}_{j} - \bar{r})^2,
    • SS_e = \frac{1}{m(n-1)} \sum_{i=1}^m \sum_{j=1}^n (r_{ij} - \bar{r})^2
    • \bar{r}_{j} = \frac{1}{m} \sum_{i=1}^m {r_{ij}}
    • \bar{r} = \frac{1}{mn}\sum_{i=1}^m \sum_{j=1}^n r_{ij}
  3. The test statistic is given by Q = \frac{SS_t}{SS_e}.
  4. Finally, the p-value is given by \mathbf{P}(\chi^2_{n-1} \ge Q).

Also on Fandom

Random Wiki