Overview

For aggregate contingency tables \u2014 the kind that sit behind the Doob \(\chi^{2}\) family in the MRM framework \u2014 MORIE exposes chi_square_test() and the companion effect-size helpers (Cramer\u2019s V, omega-squared) as first-class functions.

A 2x3 contingency table

library(morie)
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 <- chi_square_test(tab)
result$statistic
#> NULL
result$p_value
#> [1] 0.05145575
result$df
#> [1] 2

chi_square_test() returns the Pearson \(\chi^{2}\), the asymptotic p-value, and the degrees of freedom in a tidy list.

Effect size: Cramer\u2019s V

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

Cramer\u2019s V scales the chi-square statistic to a 0\u20131 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 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]

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

Doob \(\chi^{2}\) family

The MRM framework\u2019s \u201cDoob \(\chi^{2}\) family\u201d is a coordinated set of chi-square tests on the published Sprott / Doob / Iftene contingency tables (federal SIU operation, COVID-period operation, torture-classification rates, IEDM analyses). MORIE reproduces all five published statistics to within \(0.01\) of the printed values; details are in the MRM paper (citation("morie")).

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