Mack-Wolfe Test — mack

Calculates the Mack-Wolfe test on a single vector of numeric data. The Jonckheere-Terpstra (JT) test or Jonckheere trend test is a special case of the Mack-Wolfe where the peak is set to one of the ends.

Usage

mack_wolfe(x, ...)

# S3 method for class 'formula'
mack_wolfe(formula, data, ...)

# S3 method for class 'numeric'
mack_wolfe(
  x,
  group,
  peak = "jt",
  rm_outliers = FALSE,
  alpha = 0.05,
  nperm = NULL,
  ...
)

Arguments

x: numeric(n). A numeric vector of values. If empty of parameters (see examples), the example from Hollander & Wolfe is computed.
...: Additional arguments passed to downstream S3 methods.
formula: A formula specifying the lhs and rhs.
data: A data.frame containing variables in the formula.
group: factor(n). A vector of groupings matched to x. The factor levels are used as the grouping information.
peak: character(1). A string corresponding to the desired peak factor level. If peak = "jt" (default) a JT-test is performed. If peak = NULL, the "peak unknown" version of the Mack-Wolfe test is performed.
rm_outliers: logical(1). Should statistical outliers (\(6 * mad\) and \(5x\)) be removed? See wranglr::remove_outliers().
alpha: numeric(1). The desired significance level.
nperm: integer(1). The number of Monte-Carlo simulations to perform. If NULL, a p-value approximation is used (if length(x) > 10).

Value

Returns a mack_wolfe class object:

Ap:: The Mack-Wolfe test statistic (if peak known)
Astar:: The Normal approximation of the test statistic
p_value:: The two-sided p-value associated with the Normal approximation (pnorm())
Acrit:: The critical value for the z-distribution at the requested significance level (alpha)
alpha:: The significance level at which the critical value was evaluated
peak:: The peak as determined by test statistic
groups:: The factor levels of supplied group parameter.

References

Myles Hollander and Douglas A. Wolfe (1973). Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 115-120, 215.

Author

Stu Field, Michael Mehan

Examples

x <- c(36.0, 33.6, 26.9, 35.8, 30.1, 31.2, 35.3,   # g1
       39.9, 29.1, 43.4,                           # g2
       44.6, 54.4, 48.2, 55.7, 50,                 # g3
       53.8, 53.9, 62.5, 46.6,                     # g4
       44.3, 34.1, 35.7, 35.6,                     # g5
       31.7, 22.1, 30.7)                           # g6
months <- c(g1 = "Jan-Feb",
            g2 = "Mar-Apr",
            g3 = "May-Jun",
            g4 = "Jul-Aug",
            g5 = "Sep-Oct",
            g6 = "Nov-Dec")
group  <- rep(months, c(7, 3, 5, 4, 4, 3))
group  <- factor(group, months)
peak   <- "Jul-Aug"

mack_wolfe(x, group, peak)
#> ══ Mack-Wolfe test for umbrella alternatives (peak known) ═════════════
#> 
#> • Ap       = '157'
#> • Ap*      = '4.1848'
#> • n        = '26'
#> • p_value  = '0.000028539'
#> • Acrit    = '1.6449'
#> • alpha    = '0.05'
#> • groups   = 'Jan-Feb', 'Mar-Apr', 'May-Jun', 'Jul-Aug', 'Sep-Oct', 'Nov-Dec'
#> • peak     = 'Jul-Aug | k = 4'
#> 
#> ═══════════════════════════════════════════════════════════════════════

# run example from text (same as above)
mack_wolfe()
#> ══ Mack-Wolfe test for umbrella alternatives (peak known) ═════════════
#> 
#> • Ap       = '157'
#> • Ap*      = '4.1848'
#> • n        = '26'
#> • p_value  = '0.000028539'
#> • Acrit    = '1.6449'
#> • alpha    = '0.05'
#> • groups   = 'Jan-Feb', 'Mar-Apr', 'May-Jun', 'Jul-Aug', 'Sep-Oct', 'Nov-Dec'
#> • peak     = 'Jul-Aug | k = 4'
#> 
#> ═══════════════════════════════════════════════════════════════════════

# use Monte-Carlo permutation to estimate p-value
mack_wolfe(NA, nperm = 100L)
#> ℹ Performing Monte-Carlo permutation estimate of p-value.
#> ══ Mack-Wolfe test for umbrella alternatives (peak known) ═════════════
#> 
#> • Ap       = '157'
#> • Ap*      = '4.1848'
#> • n        = '26'
#> • p_value  = '0'
#> • Acrit    = '1.6449'
#> • alpha    = '0.05'
#> • groups   = 'Jan-Feb', 'Mar-Apr', 'May-Jun', 'Jul-Aug', 'Sep-Oct', 'Nov-Dec'
#> • peak     = 'Jul-Aug | k = 4'
#> 
#> ═══════════════════════════════════════════════════════════════════════

# S3 formula method
df <- data.frame(var = x, gr = group)
mack_wolfe(var ~ gr, data = df, peak = peak)
#> ══ Mack-Wolfe test for umbrella alternatives (peak known) ═════════════
#> 
#> • Ap       = '157'
#> • Ap*      = '4.1848'
#> • n        = '26'
#> • p_value  = '0.000028539'
#> • Acrit    = '1.6449'
#> • alpha    = '0.05'
#> • groups   = 'Jan-Feb', 'Mar-Apr', 'May-Jun', 'Jul-Aug', 'Sep-Oct', 'Nov-Dec'
#> • peak     = 'Jul-Aug | k = 4'
#> 
#> ═══════════════════════════════════════════════════════════════════════