---
title: "Chi-square tests and one-way ANOVA"
output:
  rmarkdown::html_vignette:
    toc: true
vignette: >
  %\VignetteIndexEntry{Chi-square tests and one-way ANOVA}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment  = "#>",
  eval     = requireNamespace("morie", quietly = TRUE)
)
```

# Overview

For aggregate contingency tables --- the kind that sit behind the
MRM chi-square family --- MORIE exposes `morie_chi_square_test()`
and the companion effect-size helpers (Cramer's V, omega-squared)
as first-class functions.

# A 2x3 contingency table

```{r chi-square}
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 <- morie_chi_square_test(tab)
result$statistic
result$p_value
result$df
```

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

# Effect size: Cramer's V

```{r cramers-v}
v <- morie_cramers_v(tab)
v
```

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:

```{r anova}
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]

morie_omega_squared(f_stat = fstat, df_between = df_b, df_within = df_w, n = n)
```

# MRM chi-square family

The MRM framework's chi-square family 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")`).

# Where to go next

- The `effect-sizes` vignette covers Cohen's d, Cramer's V,
  omega-squared, proportion-CI, and the E-value in one place.
- The `mrm-otis-walkthrough` vignette shows the chi-square family
  applied to OTIS provincial data.