Overview

For aggregate contingency tables, rmorie exposes morie_chi_square_test() and the companion effect-size helpers (Cramer’s V, omega-squared).

A 2x3 contingency table

library(rmorie)
tab <- matrix(c(20, 10, 30,
                15, 25, 35), nrow = 2, byrow = TRUE,
              dimnames = list(group = c("treated", "control"),
                              outcome = c("A", "B", "C")))

result <- morie_chi_square_test(tab)
result$chi_sq
#> [1] 5.934066
result$p_value
#> [1] 0.05145575
result$df
#> [1] 2
result$cramers_v
#> [1] 0.209657

morie_chi_square_test() returns a list with the Pearson \(\chi^{2}\) (chi_sq), the degrees of freedom, the asymptotic p-value, and Cramer’s V. The values agree with stats::chisq.test(tab).

Effect size: Cramer’s V

v <- morie_cramers_v(tab)
v
#> [1] 0.209657

Cramer’s V scales the chi-square statistic to a 0–1 association measure that is more interpretable than the raw statistic.

One-way ANOVA + omega-squared

For continuous outcomes across more than two groups, the one-way ANOVA pattern in R is aov(y ~ g, data = ...). MORIE exposes morie_omega_squared() as the less-biased counterpart to eta-squared:

set.seed(2)
n      <- 90
group  <- rep(c("A", "B", "C"), each = n / 3)
y      <- rnorm(n) + ifelse(group == "C", 0.6, 0)

fit  <- stats::aov(y ~ group)
fsum <- summary(fit)[[1]]
fstat   <- fsum$`F value`[1]
df_b    <- fsum$Df[1]
df_w    <- fsum$Df[2]

fstat
#> [1] 0.9152736
morie_omega_squared(f_stat = fstat, df_between = df_b, df_within = df_w, n = n)
#> [1] -0.00188636

With this seed the F statistic is below 1, so omega-squared comes out slightly negative. The estimator allows that; read a negative value as an effect indistinguishable from zero.

Published chi-square statistics (Sprott, Doob and Iftene)

morie_siu_verify_published_chi_squares() recomputes five Pearson chi-square statistics from contingency tables transcribed from the 2021 Sprott–Doob and Sprott–Doob–Iftene reports on federal Structured Intervention Units, and compares each with the published value:

v <- morie_siu_verify_published_chi_squares()
v$tables[[1]]$data
#>                                 source recomputed_chi2 recomputed_df
#> 1 SD-2021-Feb T11 Region x stay length          201.01            16
#> 2          SD-2021-Feb T15 Region x MH           27.51             4
#> 3     SD-2021-Feb T22 Region x Mandela          208.54             8
#> 4      SDI-2021-May T5 Race x #reviews            8.50             3
#> 5            SDI-2021-May T10 Per-IEDM           26.12            11
#>   published_chi2 published_df pass
#> 1         201.00           16 TRUE
#> 2          27.51            4 TRUE
#> 3         208.54            8 TRUE
#> 4           8.50            3 TRUE
#> 5          26.12           11 TRUE

Where to go next

The effect-sizes vignette covers Cohen’s d, Cramer’s V, omega-squared, proportion confidence intervals, and the E-value.
mrm_otis_mortification_cooccurrence() applies the chi-square test and Cramer’s V to pairs of OTIS alert flags; see the mrm-empirical-callables vignette.