Exploration and description

We have now realised that we do not have sufficient diet replication to allow us to undertake further statistical analysis. We had presumed that it would be possible to use the individual measurements recorded per chicken in an analysis of variance, but we had neglected the fact that there is competition among chickens for feed when they are fed together. The consequence is that we cannot assume individual observations to be independent – one of the assumptions in an analysis of variance.

Thus, only one single mean value for birds on a group-fed diet can be used for comparison purposes, and we have no means for calculating standard errors. In other words the experimental or observational unit in this study is the surround or compartment.

Mortality

Four of the 50 chickens in the control group died by eight weeks of age. In contrast, no chicken died in the group fed 0.5 g/kg of spent yeast, and just one and two, respectively, in the other two groups. Bird mortality is different from variables such as weight or feed efficiency in that deaths, especially when few, are generally likely to be individual occurrences and unrelated to the group to which the bird belongs. Thus, assuming that mortalities can be treated as independent observations we can combine the three spent yeast treated groups and compare 3/150 deaths against 4/50 deaths for the control group by a Chi² test. Using Stats → Statistical Tests → Contingency Tables in GenStat and creating a 2-way table with values 3, 147, 4 and 46 we obtain Chi² = 4.00 (P = 0.046), seemingly just significant. However, note the warning message in the GenStat output.