cramers_v.Rmd

---
title: "Cramer's V"
author: "Clay Ford"
date: "1/20/2021"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

Cramer's V returns the same measure of association regardless of ordering of labels, where 1 is perfect association. Using Jennie's example, notice both equal 0:

```{r}
library(DescTools) # for CramerV() function
X <- c(rep("A", 3), rep("B", 3))
Y <- c(rep("X", 3), rep("Y", 3))
t1 <- table(X, Y)
t1

Y <- c(rep("Y", 3), rep("X", 3))
t2 <- table(X, Y)
t2

CramerV(t1)
CramerV(t2)
```

There is no hypothesis test associated with Cramer's V, however you can calculate confidence intervals using four different methods. I couldn't immediately tell you why you should choose one over the other, though the fisher methods do seem to provide a little tighter upper bound for small samples.

1. "ncchisq" (using noncentral chisquare, the default)
2. "ncchisqadj"
3. "fisher" (using fisher z transformation)
4. "fisheradj" (using fisher z transformation and bias correction)


```{r}
X <- c(rep("A", 10), rep("B", 10))
Y <- c(rep("Y", 9), rep("X", 8), "X", "Y", "Y")
t3 <- table(X, Y)
t3
CramerV(t3, conf.level = 0.95) # "ncchisq" (default)
CramerV(t3, conf.level = 0.95, method = "ncchisqadj")
CramerV(t3, conf.level = 0.95, method = "fisher")
CramerV(t3, conf.level = 0.95, method = "fisheradj")

```