library(lmerTest)
## Loading required package: lme4
## Loading required package: Matrix
## 
## Attaching package: 'lmerTest'
## The following object is masked from 'package:lme4':
## 
##     lmer
## The following object is masked from 'package:stats':
## 
##     step
library(ggplot2)

Take-home:

Thorns and Simpson paradox

Imagine you have measured how much a plant species is attacked by big herbivores as a function of how many thorns the plant grows on stems. You have collected data in 5 locations and visualise the relationship between herbivory and quantity of thorns

thorndata <- read.csv("data/thorndata.csv")
str(thorndata)
## 'data.frame':    100 obs. of  3 variables:
##  $ herbivory   : num  4.53 4.6 3.89 4.05 3.73 ...
##  $ thorndensity: num  1.72 1.75 2.2 2.3 2.43 ...
##  $ site        : Factor w/ 5 levels "a","b","c","d",..: 1 1 1 1 1 1 1 1 1 1 ...
ggplot(aes(x=thorndensity, y= herbivory), data = thorndata) +  geom_point()+
  geom_smooth(method = "lm")
## `geom_smooth()` using formula 'y ~ x'

m0 <- lm(thorndensity ~ herbivory, data=thorndata)
summary(m0)
## 
## Call:
## lm(formula = thorndensity ~ herbivory, data = thorndata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.2660 -0.4745 -0.2017  0.3563  2.8093 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.9691     0.5428   3.628 0.000456 ***
## herbivory     0.4447     0.1264   3.520 0.000657 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9627 on 98 degrees of freedom
## Multiple R-squared:  0.1122, Adjusted R-squared:  0.1032 
## F-statistic: 12.39 on 1 and 98 DF,  p-value: 0.0006566
plot(m0)