In robschick/tangled: Creates data objects and plots for Knowlton, Schick et al. manuscript on entanglement

The goal of this vignette is to conduct a simple statistical analysis of the calving data for females that have experienced different entanglement severity. We'll start by creating the data frame using data from Amy Knowlton at NEAq:

knitr::opts_chunk$set(warning=FALSE, message=FALSE)

library(tangled)
library(magrittr)
library(dplyr)
library(ggplot2)

calves <- matrix(c(76,  302,    34, 10, 0, 128, 521,    60, 23, 8), nrow = 2, byrow = TRUE,
                 dimnames = list(c('Calf', 'No Calf'), 
                                 c('Not impacted',  'Recovered', 'Minor',   'Moderate', 'Severe')))
knitr::kable(calves)

What the above table shows is that 0 animals who have experienced a severe entanglement have gone on to have a calf. The calf to no-calf ratio for all is:

calves[1, ] / calves[2, ] * 100

Statistical Analysis

The first obvious test is a Chi-square test, however this does not allow for 0 values in the contingency table. There are two alternatives: Fisher's Exact test, and Barnard's test - the latter of which seems to be preferred in the statistical literature. We need to use a new package to conduct the test - the Exact package.

This looks for a comparison of a 2x2 contingency table, so in the next chunk we'll run a test comparing these 4 cases to the Not Impacted reference case:

1. Recovered
2. Minor
3. Moderate
4. Severe

The test will return the p-value for a two-sided test. Specifically, we are running a Barnard's unconditional exact test. The model is a Binomial, and the method for finding the "as or more extreme" tables is "Z-pooled."

library(Exact)
csubrp <- calves[, c(1, 2)]
csubMinp <- calves[, c(1, 3)]
csubModP <- calves[, c(1, 4)]
csubsp <- calves[, c(1, 5)]

recp <- exact.test(csubrp ,alternative="two.sided", to.plot = FALSE)$p.value
minp <- exact.test(csubMinp, alternative="two.sided", to.plot = FALSE)$p.value
modp <- exact.test(csubModP, alternative="two.sided", to.plot = FALSE)$p.value
sevp <- exact.test(csubsp, alternative="two.sided", to.plot = FALSE)$p.value

Let's summarise those in a table:

df <- data.frame(test = c('Recovered', 'Minor', 'Moderate', 'Severe'),
                 pval = c(recp, minp, modp, sevp))
knitr::kable(df)

This shows that severe are significantly different from the Not Impacted reference case.

robschick/tangled documentation built on May 9, 2022, 4:07 p.m.