In this exercise you will:
The data in the table are the number of embryogenic anthers of the plant species Datura innoxia produced when numbers of anthers were produced under several different conditions. There is one qualitative factor, storage under special conditions or storage under standard conditions, and one quantitative factor, the centrifuging force. In the data given below y is the number of plants which did produce anthers and n is the total number tested at each combination of storage and force.
Storage | Centrifuging force | |||
40 | 150 | 350 | ||
Standard | y | 55 | 52 | 57 |
n | 102 | 99 | 108 | |
Special | y | 55 | 50 | 50 |
n | 76 | 81 | 90 |
Fit a logistic model to these data. Consider whether there is an interaction between storage and centrifuging force and whether the effect of force is linear on a logistic scale. Write a report on the analysis for the benefit of a biologist, explaining what the coefficients mean with the logit link.
<- data.frame(Storage=rep(c("Standard","Special"), c(3,3)), Force=factor(rep(c(40, 150, 350), 2)), y=c(55, 52, 57, 55, 50, 50), n=c(102, 99, 108, 76, 81, 90))
Plant <- glm((y/n)~Storage*Force, data=Plant, weights=n, family=binomial)
Plant.glm |> summary() Plant.glm
Call:
glm(formula = (y/n) ~ Storage * Force, family = binomial, data = Plant,
weights = n)
Deviance Residuals:
[1] 0 0 0 0 0 0
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.9628 0.2565 3.753 0.000174 ***
StorageStandard -0.8056 0.3244 -2.483 0.013023 *
Force150 -0.4848 0.3436 -1.411 0.158279
Force350 -0.7397 0.3329 -2.222 0.026276 *
StorageStandard:Force150 0.4287 0.4450 0.963 0.335377
StorageStandard:Force350 0.6937 0.4329 1.602 0.109061
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 1.0452e+01 on 5 degrees of freedom
Residual deviance: 9.5479e-15 on 0 degrees of freedom
AIC: 41.568
Number of Fisher Scoring iterations: 3
|> anova(test="Chisq") Plant.glm
Analysis of Deviance Table
Model: binomial, link: logit
Response: (y/n)
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 5 10.4520
Storage 1 5.2790 4 5.1730 0.02158 *
Force 2 2.5670 2 2.6059 0.27706
Storage:Force 2 2.6059 0 0.0000 0.27173
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
N.B. Take note of the following:
It looks like the centrifuging force has no impact on the proportion of plants that developed anthers, but the way they are stored does. The proportion for standard storage is lower than for special storage.
You only need to present a proportion for each kind of storage in your presentation.