API reference

plot(t_1 => x_1, t_2 => x_2, ..., t_k =>  x_k; kwargs...)
plot(df, treatment, observation, outcome; kwargs...)

Return a PGFPlots axis which contains a critical difference diagram for n repeated observations of k treatments.

The input data are arranged in treatments t_i => x_i, each of which has a name t_i and n associated observations x_i. You can omit the names, either providing the separate x_i alone or by providing all observations as a single (n, k)-shaped matrix X. Alternatively, you can provide a DataFrame df with the columns treatment, observation, and outcome.

The analysis starts with a FriedmanTest to check if any of the treatments differ. If so, the differences between each pair of treatments is checked with a Holm-adjusted or Bonferroni-adjusted Wilcoxon SignedRankTest. The cliques represent groups of treatments which are not significantly distinguishable from each other.

kwargs

• alpha=0.05 is the significance level in the hypothesis tests.

• maximize_outcome=false specifies whether the ranks represent a maximization or a minimization of the outcomes.

• adjustment=:holm specifies the adjustment method (:holm or :bonferroni).

• title=nothing is an optional string to be printed above the diagram.

• reverse_x=false reverses the direction of the x axis from right-to-left (default) to left-to-right.

2-dimensional sequences of CD diagrams

You can arrange a sequence of CD diagrams in a single 2-dimensional axis. In the following, each item in the sequence consists of a pair s_i => [args_i...] of the item's name s_i and the regular CD diagram arguments args_i... that are documented above.

plot(
    s_1 => [t_11 => x_11, t_12 => x_12, ..., t_1k =>  x_1k],
    s_2 => [t_21 => x_21, t_22 => x_22, ..., t_2k =>  x_2k],
    ...,
    s_j => [t_j1 => x_j1, t_j2 => x_j2, ..., t_jk =>  x_jk];
    kwargs...
)

ranks_and_cliques(t_1 => x_1, t_2 => x_2, ..., t_k =>  x_k; kwargs...)
ranks_and_cliques(x_1, x_2, ..., x_k; kwargs...)
ranks_and_cliques(X; kwargs...)
ranks_and_cliques(df, treatment, observation, outcome; kwargs...)

Return a tuple (avg_ranks, cliques) of the average ranks of k treatments in n repeated observations, together with the cliques of indistinguishable treatments.

The input data are arranged in treatments t_i => x_i, each of which has a name t_i and n associated observations x_i. You can omit the names, either providing the separate x_i alone or by providing all observations as a single (n, k)-shaped matrix X. Alternatively, you can provide a DataFrame df with the columns treatment, observation, and outcome.

The analysis starts with a FriedmanTest to check if any of the treatments differ. If so, the differences between each pair of treatments is checked with a Holm-adjusted or Bonferroni-adjusted Wilcoxon SignedRankTest. The cliques represent groups of treatments which are not significantly distinguishable from each other.

kwargs

• alpha=0.05 is the significance level in the hypothesis tests.
• maximize_outcome=false specifies whether the ranks represent a maximization or a minimization of the outcomes.
• adjustment=:holm specifies the adjustment method (:holm or :bonferroni).

FriedmanTest(x_1, x_2, ..., x_k; kwargs...) = FDistFriedmanTest(x_1, x_2, ..., x_k; kwargs...)
FriedmanTest(X; kwargs...) = FDistFriedmanTest(X; kwargs...)

Test the null hypothesis that n repeated observations of a set of k treatments have the same distribution across all treatments. These observations are arranged in k vectors x_i of n observations each or in an (n, k)-shaped matrix X.

The default version of this test, the FDistFriedmanTest, uses an F-distributed statistic.

See also: FDistFriedmanTest, ChisqFriedmanTest

Keyword arguments

• maximize_outcome=false specifies whether the ranks represent a maximization or a minimization of the outcomes.

FDistFriedmanTest(x_1, x_2, ..., x_k; kwargs...)
FDistFriedmanTest(X; kwargs...)

Test the null hypothesis that n repeated observations of a set of k treatments have the same distribution across all treatments. These observations are arranged in k vectors x_i of n observations each or in an (n, k)-shaped matrix X.

This version of the FriedmanTest uses an F-distributed statistic.

Keyword arguments

• maximize_outcome=false specifies whether the ranks represent a maximization or a minimization of the outcomes.

ChisqFriedmanTest(x_1, x_2, ..., x_k; kwargs...)
ChisqFriedmanTest(X; kwargs...)

Test the null hypothesis that n repeated observations of a set of k treatments have the same distribution across all treatments. These observations are arranged in k vectors x_i of n observations each or in an (n, k)-shaped matrix X.

This version of the FriedmanTest uses a χ²-distributed statistic.

Keyword arguments

• maximize_outcome=false specifies whether the ranks represent a maximization or a minimization of the outcomes.

average_ranks(x) where x <: FriedmanTest

Return the average ranks of methods in the FriedmanTest.