Question

The salmonella data was collected in a salmonella reverse mutagenicity assay. The predictor is the dose level of quinoline and the response is the numbers of revertant colonies of TA98 salmonella observed on each of three replicate plates. Show that a Poisson GLM is inadequate and that some overdispersion must be allowed for.

Answer 1

To determine if a Poisson GLM is adequate for the salmonella reverse mutagenicity assay, we need to analyze the data collected and assess for overdispersion. Overdispersion occurs when the variance is greater than the mean, indicating that a Poisson GLM is inadequate. We can assess overdispersion by comparing the deviance and the residual deviance of the GLM model.

Step-by-step explanation:

To determine if a Poisson GLM is adequate, we need to analyze the data collected in the salmonella reverse mutagenicity assay. In this assay, the predictor variable is the dose level of quinoline, and the response variable is the number of revertant colonies of TA98 salmonella observed on each of three replicate plates. In a Poisson GLM, the response variable is assumed to follow a Poisson distribution, where the mean is equal to the variance.

However, if there is overdispersion, the variance is greater than the mean, indicating that a Poisson GLM is inadequate. We can assess overdispersion by comparing the deviance and the residual deviance of the GLM model. If the residual deviance is significantly larger than the deviance, it suggests overdispersion and we will need to allow for it.