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The effect of Juvenile hormone on mandible size in stag beetles.

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Introduction

The concentration of juvenile hormone in stag beetles is known to

influence mandible growth. Groups of stag beetles were injected

with different concentrations of juvenile hormone (arbitrary units)

and their average mandible size (mm) determined. The experimenters

planned to analyse their data with regression. The data are

in ../data/stag.txt

The data are organised into 2 columns

'data.frame': 16 obs. of 2 variables:

$ jh : int 0 2 4 6 8 10 12 14 16 18 ...

$ mand: num 0.56 0.35 0.28 1.22 0.48 0.86 0.68 0.77 0.55 1.18 ...

Set up

working directory (in my case, yours will differ)

setwd("M:/web/17C - 2018/scripts")

note: if you are using RStudio projects, this is unnecessary

packages

library(tidyverse)

Hadley Wickham (2017). tidyverse: Easily Install and Load the 'Tidyverse'. R package version

1.2.1. https://CRAN.R-project.org/package=tidyverse

Import and tidy data

data are in ../data

read the data in and check the structure

stag <- read.table("../data/stag.txt", header = T) str(stag)

Exploratory Analysis

looking at the dataset there doesn't seem to be anything very

obviously non-normal (such as lots of values the same, too many

zeros, or extreme values

The goal of the analysis is to determine the effect of a

continuous explanatory variable (JH) on a continuous response

(mand). This is a regression. Linear regression requires any

effect of JH of mand to be linear therefore we will do a quick plot

before proceedding

quick plot

ggplot(stag, aes(x = jh, y = mand) ) + geom_point()

looks linear-ish on the scatter

the sceanrio seems to suit regresion - JH has been choosen or set, mandible has been measured

we will check the other assumptions after we have run the lm

get summaries of the variable

summary(stag)

jh mand

Min. : 0.0 Min. :0.2800

1st Qu.: 7.5 1st Qu.:0.5575

Median :15.0 Median :0.8150

Mean :15.0 Mean :0.9038

3rd Qu.:22.5 3rd Qu.:1.2225

Max. :30.0 Max. :1.6600

Statistical Analysis

Linear regression using lm()

mod <- lm(data = stag, mand ~ jh) summary(mod)

mand = 0.032 * jh + 0.419

the slope of the line is significantly different from zero

/ the jh explains a significant amount of the variation in

mand (ANOVA: F = 16.63; d.f. = 1, 14; p = 0.00113).

the intercept is 0.419 and differs significantly from zero. 54%

variation in mandible size is explained by juvenile hormone

concentration

Assumptions

Examine the residuals to check the assumptions

plot(mod, which = 1)

the variance looks approximately equal along x

hist(mod$residuals)

the residuals look approxiamtely normal

normaility test on the residuals

shapiro.test(mod$residuals)

N.S

These results are consistent with the assumptions being met

but note that the sample size is quite small so large devations

from normality would be required for signifcance.

On balance the use of regression is probably justifiable

but ideally the experiment would be better if multiple individauls were measure at each of the chosen juvenile hormone levels.

The coefficients for the best fitting straight line can be accessed

from the mod object

The intercept is the first coefficient and the slope is the second

and these can be used to make predictions

intercept <- mod$coefficients[1] intercept

(Intercept)

0.4193382

slope <- mod$coefficients[2] slope

jh

0.03229412

Suppose want to know the mandible size for a JH level of 15

jh <- 15 slope * jh + intercept

mandible size is predicted to be 0.9mm

we can get a several predictions using the predict function

first generate the jh values for which we want predictions

newdata <- data.frame(jh = seq(10, 30, 5)) newdata$predictedman <- predict(mod, newdata = newdata)

> newdata

jh predictedman

1 10 0.7422794

2 15 0.9037500

3 20 1.0652206

4 25 1.2266912

5 30 1.3881618

Figure

The following would be a suitable plot

ggplot(stag, aes(x = jh, y = mand) ) + geom_point() + geom_smooth(method = lm, se = FALSE, colour = "black") + ylab("Mandible size (mm)") + ylim(0, 2) + xlim(0, 32) + xlab("Juvenile hormone (arbitrary units)") + theme_classic()

Figure x. The effect of juvenile hormone injections on the mandible size of stag beetles.

carlos-r-git/scriptsearch documentation built on Sept. 1, 2020, 6:38 p.m.