The following data show the number of fruit y killed at varying concentrations of nicotine.
The number of ies killed in n exposures can be assumed to follow a binomial distribution
(from Hand et al [2]).
(a) Fit both logistic and probit models, modelling proportion killed as a function of nicotine concentration. Are there any obvious differences in the fit of these models?
(b) Plot the observed proportions killed and the two fitted models on the same plot.
Comment on the fit of the models and any differences between models.
(c) Using the models in (a), estimate the nicotine concentration that would kill 50% of flies. Also estimate the dose hat would kill 90% of flies.
(d) Often the experimental factor X is replaced by ln(X) in these quantal assay experiments. Repeat (a) using ln(X) and comment on the fit of these models.
(e) What issues need to be considered when deciding which single model is 'best' between the four models (i.e. the two in (a) and two in (c))? Are any of the four models obviously superior in this example?
| Nicotine concentration |
Flies |
Number |
Percent |
| (g/100cc) |
exposed |
killed |
killed |
| 0.1 |
47 |
8 |
17 |
| 0.15 |
53 |
14 |
26.4 |
| 0.2 |
55 |
24 |
43.6 |
| 0.3 |
52 |
32 |
61.5 |
| 0.5 |
46 |
38 |
82.6 |
| 0.7 |
54 |
50 |
92.6 |
| 0.95 |
52 |
50 |
96.2 |