## Friedman test |

The **Friedman test** is a
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*block*) together, then considering the values of ranks by columns. Applicable to

Classic examples of use are:

*n*wine judges each rate*k*different wines. Are any of the*k*wines ranked consistently higher or lower than the others?*n*welders each use*k*welding torches, and the ensuing welds were rated on quality. Do any of the*k*torches produce consistently better or worse welds?

The Friedman test is used for one-way repeated measures analysis of variance by ranks. In its use of ranks it is similar to the

Friedman test is widely supported by many

- Given data , that is, a
matrix with rows (the*blocks*), columns (the*treatments*) and a single observation at the intersection of each block and treatment, calculate theranks *within*each block. If there are tied values, assign to each tied value the average of the ranks that would have been assigned without ties. Replace the data with a new matrix where the entry is the rank of within block . - Find the values:
- ,

- The test statistic is given by . Note that the value of Q as computed above does not need to be adjusted for tied values in the data.
- Finally, when n or k is large (i.e. n > 15 or k > 4), the
probability distribution of Q can be approximated by that of achi-squared distribution . In this case thep-value is given by . If n or k is small, the approximation to chi-square becomes poor and the p-value should be obtained from tables of Q specially prepared for the Friedman test. If the p-value issignificant , appropriate post-hocmultiple comparisons tests would be performed.

Other Languages

Deutsch: Friedman-Test (Statistik)

español: Prueba de Friedman

فارسی: آزمون فریدمن

français: ANOVA de Friedman

polski: Test rang Friedmana

português: Teste de Friedman

русский: Критерий Фридмана