Mood's Median Test

MEDIAN_TEST() tests whether a continuous variable's population median differs across the levels of one or more grouping variables. It works by dichotomizing all observations at the grand median (or a supplied custom_median) and running a chi-squared test of independence on the resulting 2xk contingency table. If MEDIAN_TEST is supplied within the lazy-loaded pipeline, supply MEDIAN_TEST as a function i.e. prepare_test(.test = MEDIAN_TEST).

Usage

MEDIAN_TEST(.var_id = NULL, .data = NULL, ...)

Arguments

.var_id: A variable mapper <var_id>. Supports x_by() and on(). When supplied, the test executes immediately. x_by() with more than one grouping variable requires via("multi") (see the Supported variable mapper section).
.data: A data frame. Only used on the standalone path.
...: Additional arguments passed to the implementation: custom_median (a hypothesized median to split on, instead of the sample's own grand median), accepted on every path, accepted on default (which is the "base", both x_by() and on()). x_by()'s multi variant instead accepts display_var (whether an index or grouping-variable name choosing which variable's table to compute and show; that the default (base) or on() never have. See the Supported variable mapper section for the full list per path.

Value

A cld_exec object (in statim::conclude()), a stat_infer_spec object, or a test_spec when .var_id = NULL. mmdtest_def_xby's base and multi, and mmdtest_def_on's baseline, all return a class_median_test object. On multi, every grouping variable's test runs and its statistic/df/p_value/median are kept, but only the display_var-selected variable's contingency table is retained in cont_tab, others' tables are discarded. On the on() path, vars is fixed to "on" since there is no grouping variable to label.

Details

H0: all groups share a common population median. H1: at least one group's median differs from the others.

Supported variable mapper `<var_id>`s

x_by(): grouped Mood's median test. The base path handles exactly one grouping variable; the multi variant handles more than one, running one test per grouping variable. See details from mmdtest-xby.
on(): one-sample or k-sample Mood's median test via a compiled backend, run directly on .proc$data without an x_by() split. See details from mmdtest-on.

A note on `custom_median` for single-group tests

With exactly one group and no custom_median supplied, the split point is estimated from that same group's data, so the above/below counts land near a 50/50 split by construction and the test has little power to detect anything. Supply custom_median (a hypothesized population median) whenever you're testing a single group.

Examples

set.seed(123)
x = rcauchy(50, 1, 1.5)
g = sample(letters[1:5], size = 50, replace = TRUE)
MEDIAN_TEST(x_by(x, g))
#> -- Summary ---------------------------------------------------------------------
#> 
#> ────────────────────────────────
#>   vars  statistic  df  p_value  
#> ────────────────────────────────
#>    g      3.066    4    0.547   
#> ────────────────────────────────
#> 
#> 
#> -- Contingency Table -----------------------------------------------------------
#> 
#>                            Cross Tabulation: x by y              
#>               ───────────────────────────────────────────────────
#>                                            y              
#>               ───────────────────────────────────────────────────
#>                 x                  d   e    c   a    b    TOTAL  
#>               ───────────────────────────────────────────────────
#>                 > Median (1.04)    4   5    3   5    8     25    
#>               
#>                 <= Median (1.04)   5   6    5   6    3     25    
#>               ───────────────────────────────────────────────────
#>                 TOTAL              9   11   8   11   11    50    
#>               ───────────────────────────────────────────────────
#> 

# against a hypothesized median rather than the sample's own
MEDIAN_TEST(x_by(x, g), custom_median = 1)
#> -- Summary ---------------------------------------------------------------------
#> 
#> ────────────────────────────────
#>   vars  statistic  df  p_value  
#> ────────────────────────────────
#>    g      3.066    4    0.547   
#> ────────────────────────────────
#> 
#> 
#> -- Contingency Table -----------------------------------------------------------
#> 
#>                             Cross Tabulation: x by y            
#>                 ────────────────────────────────────────────────
#>                                           y              
#>                 ────────────────────────────────────────────────
#>                   x               d   e    c   a    b    TOTAL  
#>                 ────────────────────────────────────────────────
#>                   > Median (1)    4   5    3   5    8     25    
#>                 
#>                   <= Median (1)   5   6    5   6    3     25    
#>                 ────────────────────────────────────────────────
#>                   TOTAL           9   11   8   11   11    50    
#>                 ────────────────────────────────────────────────
#>