QK Box 7.1

Linton et al. (2009) studied the effects of the insecticide pyriproxyfen on ovarian development in an endemic Christmas Island land crab, Geocarcoidea natalis. The insecticide was proposed as a means of controlling numbers of an introduced ant species that was viewed as a major threat, and it is an endocrine disruptor. The experiment was designed to test whether the insecticide might pose risks to the crabs, which have a hormone similar to the one targeted in insects, and consisted of feeding crabs a mixture of leaf litter and a bait. Half of the baits contained the insecticide, and the other half were controls (bait type factor). The baits were supplied at three rates, with two levels corresponding to levels used in field applications (2 kg ha-1 and 4 kg ha-1), with the third rate being ad libitum feeding (bait dosage factor). The experimental units in this case were large plastic tubs, each containing a single female crab, and there were 7 crabs for each combination of factors. The response variable was the dry mass of the ovaries of each crab. A two-factor linear model (7.2) including the fixed main effects of bait type and bait dosage and their interaction was fitted to these data.

John Tann from Sydney, Australia, [CC BY 2.0](https://creativecommons.org/licenses/by/2.0), via Wikimedia Commons

John Tann from Sydney, Australia, [CC BY 2.0](https://creativecommons.org/licenses/by/2.0), via Wikimedia Commons

Here is the paper and the data

Linton, S., Barrow, L., Davies, C. & Harman, L. (2009). Potential endocrine disruption of ovary synthesis in the Christmas Island red crab Gecarcoidea natalis by the insecticide pyriproxyfen. Comparative Biochemistry and Physiology, Part A, 154, 289-97.

Preliminaries

Load packages

library(tidyverse)
library(sjstats)
library(effectsize)
library(afex)
library(emmeans)
library(ggsci)
library(patchwork)

Import linton data file (linton.csv)

linton <- read.csv("data/linton.csv")
head(linton,10)
      type dosage drymass nitrogen
1  Control      2   0.524     3620
2  Control      2   0.535     4030
3  Control      2   1.094     6530
4  Control      2   0.525     3938
5  Control      2   0.707     4312
6  Control      2   0.551     3740
7  Control      2   0.489     3860
8  Control      4   0.461     4329
9  Control      4   0.584     5108
10 Control      4   0.715     5877

Fit model to untransformed data and check residuals

Start with boxlplots. Too few reps for boxplot by cell so boxplot for each factor separately

boxplot(drymass~type,data=linton)

boxplot(drymass~dosage,data=linton)

linton.aov <- aov(drymass~type*dosage, data=linton)
plot(linton.aov)

No strong pattern in residuals or boxplots so examine analysis with untransformed data

summary(linton.aov)
            Df Sum Sq Mean Sq F value Pr(>F)  
type         1  2.606  2.6060   7.360 0.0102 *
dosage       2  0.671  0.3353   0.947 0.3974  
type:dosage  2  1.157  0.5784   1.634 0.2094  
Residuals   36 12.747  0.3541                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Get effect size measures (eta- and omega-squared (effectsize package)

eta_squared(linton.aov)
# Effect Size for ANOVA (Type I)

Parameter   | Eta2 (partial) |       95% CI
-------------------------------------------
type        |           0.17 | [0.03, 1.00]
dosage      |           0.05 | [0.00, 1.00]
type:dosage |           0.08 | [0.00, 1.00]

- One-sided CIs: upper bound fixed at [1.00].
omega_squared(linton.aov)
# Effect Size for ANOVA (Type I)

Parameter   | Omega2 (partial) |       95% CI
---------------------------------------------
type        |             0.13 | [0.01, 1.00]
dosage      |             0.00 | [0.00, 1.00]
type:dosage |             0.03 | [0.00, 1.00]

- One-sided CIs: upper bound fixed at [1.00].

Interaction plot

afex_plot(linton.aov, "type", "dosage", dodge=0.05)+theme_light()
dv column detected: drymass
No id column passed. Assuming all rows are independent samples.

High quality figures

Residual plot

p1 <- ggplot(linton.aov, aes(x = linton.aov$fitted.values, y = linton.aov$residuals)) +
  geom_point(color=sc) +
  theme_classic(base_size = 10)+
  theme(
    axis.text = element_text(colour = ac),
    axis.line = element_line(color = ac),
    axis.ticks = element_line(color = ac),
        )+labs(x = "Predicted ovary mass", y = "Residuals", 
       )

Interaction plot

Use emmeans to get dataframe of means and se

emm1<-emmeans(linton.aov, ~type|dosage)
emm2<-as.data.frame(emm1)
emm2
dosage = 2:
 type            emmean        SE df  lower.CL upper.CL
 Control      0.6321429 0.2249031 36 0.1760182 1.088268
 Experimental 1.1504286 0.2249031 36 0.6943039 1.606553

dosage = 4:
 type            emmean        SE df  lower.CL upper.CL
 Control      0.8801429 0.2249031 36 0.4240182 1.336268
 Experimental 0.9621429 0.2249031 36 0.5060182 1.418268

dosage = ad lib:
 type            emmean        SE df  lower.CL upper.CL
 Control      0.7258571 0.2249031 36 0.2697324 1.181982
 Experimental 1.6201429 0.2249031 36 1.1640182 2.076268

Confidence level used: 0.95

Means and error bars

pd=position_dodge(width=0.05)

p2<-ggplot(emm2,aes(x=dosage,y=emmean,shape=type, group=type, color=type))+
  geom_point(position=pd,aes(shape=type), size=3,show.legend = FALSE)+
  geom_errorbar(aes(ymin = emmean-SE, ymax = emmean+SE), width=0, position = pd,show.legend = FALSE)+
  geom_line(aes(color=type), position=pd, linewidth=1.5)+
  scale_color_uchicago(labels = c("Control", "Experimental"))+
    scale_linetype_manual(values=c("solid", "solid"))+
  labs(x = "Food level", y = "Hg (mg/g dw"
       )+
  theme_classic(base_size = 10)+
  theme(
    axis.text.x = element_text(color="black",size=10),
    axis.text.y= element_text(color=ac),
    axis.line = element_line(color = ac),
    axis.ticks = element_line(color = ac),
        )+
  theme(
  legend.position = c(.6, .95),
  legend.justification = c("right", "top"),
  legend.box.just = "right",
  legend.margin = margin(6, 6, 6, 6),
  legend.title = element_blank(),
)

Combine figures

p1+p2