---
title: "Effect sizes and association measures"
output:
  rmarkdown::html_vignette:
    toc: true
vignette: >
  %\VignetteIndexEntry{Effect sizes and association measures}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

# Overview

Effect sizes complement p-values: they answer "how big is the
effect?" rather than "is there an effect at all?". MORIE exposes
the standard families used in carceral, public-health, and
sociolegal research.

# Cohen's d (continuous, two-group)

```{r cohens-d}
library(morie)
set.seed(7)
group_a <- rnorm(60, mean = 0.0)
group_b <- rnorm(60, mean = 0.6)

d <- morie_cohens_d(group_a, group_b)
d
```

Cohen's d expresses the difference between two means in pooled
standard-deviation units. Conventional benchmarks: 0.2 small,
0.5 medium, 0.8 large.

# Cramer's V (categorical association)

```{r cramers-v}
tab <- matrix(c(20, 10, 30,
                15, 25, 35), nrow = 2, byrow = TRUE)
v <- morie_cramers_v(tab)
v
```

Cramer's V scales the chi-square statistic to a 0--1 association
measure for contingency tables. It is particularly useful for the
provincial-vs-federal Mandela-rate cross-comparisons in MRM.

# Omega-squared (one-way ANOVA)

Omega-squared is a less-biased effect-size estimator than
eta-squared for a one-way ANOVA design.

```{r omega-squared}
morie_omega_squared(f_stat = 5.2, df_between = 2, df_within = 87, n = 90)
```

# Proportion confidence intervals

For a binomial proportion, MORIE exposes Wilson, Clopper--Pearson
exact, and Wald CIs. Wilson is the default and is what we recommend
in published papers (it has better small-sample coverage than Wald).

```{r proportion-ci}
morie_proportion_ci(35, 100)                       # Wilson, 95% CI
morie_proportion_ci(35, 100, method = "exact")     # Clopper-Pearson
morie_proportion_ci(35, 100, method = "wald")      # Wald
```

# E-value (sensitivity analysis)

```{r e-value, eval = exists("morie_e_value")}
morie_e_value(rr = 2.0)
```

The E-value is the minimum strength of association that an
unmeasured confounder would need on both treatment and outcome to
fully explain away an observed risk ratio.

# Where to go next

- For survey-weighted versions of `morie_cohens_d` and `morie_cramers_v`, see
  the `survey-weighted` vignette.
- For full causal-inference workflows that include ATE / ATT / ATC
  effect sizes with CIs, see the `causal-inference` vignette.