Create boxplot for detection probabilities in r

Question

I have a dataset that looks similar to this:

sex	observed	date	idtag
M	0	10/20/2019	12
M	0	10/20/2019	12
F	0	10/20/2019	21
F	0	10/20/2019	21
M	0	10/21/2019	12
M	1	10/21/2019	14
F	0	10/21/2019	21
M	1	10/21/2019	14
M	1	10/21/2019	14
F	1	10/21/2019	21
M	0	10/23/2019	12
M	0	10/23/2019	12
F	0	10/23/2019	21
F	0	10/23/2019	22
M	0	10/23/2019	14
M	1	10/23/2019	12
F	0	10/23/2019	22
M	1	10/23/2019	14
M	1	10/23/2019	12

I would like to create a boxplot of detection rate by sex. I.e., I would like to compare (total number of observations by sex/number of 1s per sex). I used this code to calculate detection rate by sex:

drrate_sex <- detectiondata %>% 
    group_by(sex) %>% 
   summarise(dr = mean(observed))

This is the standard boxplot code I typically use:

boxplot(? ~ sex, data=drdata, main="Detection by sex",
        xlab="Sex", ylab="Detection rate (%)", notch=T, par(mar=c(4,12,4,12)))

I am not sure how to incorporate detection rate (where I entered ? in the code) into the code to produce a boxplot in r that compares detection rate of females versus males. Any help would be appreciated.

A boxplot seems like a very poor choice for binary data. Most of the components of boxplots are quantiles - median, min, max, 1st and 3rd quartiles. With binary data, all of those values will be either 0 or 1. — Gregor Thomas, Nov 05 '21 at 19:44
Maybe you should just do a point estimate percentage with error bars showing a [binomial confidence interval](https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval). — Gregor Thomas, Nov 05 '21 at 19:45
Based on your response, I believe I left out an important component/did not adequately explain my question. Each male/female has an id number (idtag). I have close to 100 different idtags. Can I calculate detection rate for each male and female, then calculate the median and quartiles based on the detection rates of each male/female and compare them with boxplots? For example, if males 12 and 14 have a detection rate of 36% and 54%, respectively, I should be able to take that info and put it into a boxplot, no? — , Nov 05 '21 at 20:29
Okay, so it's not a boxplot of binary data, it's a boxplot of porportions. Calculate the proportions first, then make the boxplot. You can calculate the proportions using your favorite answer from [How to calculate mean by group](https://stackoverflow.com/q/11562656/903061), — Gregor Thomas, Nov 06 '21 at 01:43

score 0 · Accepted Answer · answered Nov 05 '21 at 20:33

The closest you could come to a boxplot for this type of data is probably a plot of the proportions with a confidence interval shown by an error bar.

One way to get the numbers you need is to run a logistic regression, and use the coefficients from this to get a confidence interval for the proportions:

# Logistic regression model
regression <- glm(observed ~ sex, data = detectiondata, family = binomial)

# Extract coefficients
coefs <- summary(regression)$coef

# Convert coefficients to odds
coefs[2, 1] <- coefs[1, 1] + coefs[2, 1]
odds <- exp(cbind(mean = coefs[,1], 
                  upper = coefs[,1] + 1.96 * coefs[,2], 
                  lower = coefs[,1] - 1.96 * coefs[,2]))

# Convert odds to probabilities
probs <- odds/(1 + odds)

# Create data frame and add column for sex
df <- as.data.frame(probs)
df$sex <- c("Female", "Male")

Which gives the following data frame:

df
#>                  mean     upper      lower    sex
#> (Intercept) 0.1428571 0.5806110 0.01966987 Female
#> sexM        0.5000000 0.9168654 0.08313460   Male

Which we can plot like this:

library(ggplot2)

ggplot(df, aes(sex, mean)) +
  geom_errorbar(aes(ymin = lower, ymax = upper, color = sex), size = 3,
                width = 0.3) +
  geom_point(size = 4, shape = 21, fill = "black")

Data

detectiondata <- structure(list(sex = c("M", "M", "F", "F", "M", "M", "F", "M", 
"M", "F", "M", "M", "F", "F", "M", "M", "F", "M", "M"), observed = c(0L, 
0L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 
1L, 1L), date = c("10/20/2019", "10/20/2019", "10/20/2019", "10/20/2019", 
"10/21/2019", "10/21/2019", "10/21/2019", "10/21/2019", "10/21/2019", 
"10/21/2019", "10/23/2019", "10/23/2019", "10/23/2019", "10/23/2019", 
"10/23/2019", "10/23/2019", "10/23/2019", "10/23/2019", "10/23/2019"
)), class = "data.frame", row.names = c(NA, -19L))

^{Created on 2021-11-05 by the reprex package (v2.0.0)}

Create boxplot for detection probabilities in r

1 Answers1