Friedman rank-sum test (non-parametric repeated-measures omnibus)

The non-parametric repeated-measures omnibus test: compares k >= 2 matched treatments (columns) measured on the same N blocks/subjects (rows), by ranking within each block and testing whether the rank totals differ. It is the within-subject, distribution-free counterpart of the one-way ANOVA (oneWayAnova). The tie-corrected chi-square statistic and its p-value reproduce base R stats::friedman.test bit-for-bit and scipy.stats.friedmanchisquare to machine precision.

Usage

friedmanTest(x, ...)

Arguments

x

A blocks-by-treatments numeric matrix (rows = subjects/blocks, columns = conditions/treatments), or a list of k equal-length numeric vectors (one per treatment, aligned by block). Rows with any missing value are dropped (complete blocks only).

...

Additional treatment vectors when x is a single vector.

Value

A list with statistic (the tie-corrected Friedman chi-square), p_value, df (k - 1), k (treatments) and n (complete blocks).

See also

oneWayAnova, pairedTTest

Examples

m <- matrix(rnorm(40) + rep(c(0, 0.5, 1, 1.5), each = 10), nrow = 10)
friedmanTest(m)
#> $statistic
#> [1] 5.16
#> 
#> $p_value
#> [1] 0.1604491
#> 
#> $df
#> [1] 3
#> 
#> $k
#> [1] 4
#> 
#> $n
#> [1] 10
#>