Common pitfalls when testing additivity of treatment mixtures with chi-square analyses

Studying interactions of multiple pesticides applied simultaneously in a mixture is a common task in phytopathology. Statistical methods are employed to test whether the treatment components influence each other's efficacy in a promotive or inhibitory way (synergistic or antagonistic interaction) or rather act independent of one another (additivity). The trouble is that widely used procedures based on chi-square tests are often seriously flawed, either because people apply them in a preposterous way or because the method simply does not fit the problem at hand. Browsing recent volumes of entomological journals, we found that numerous researchers have (in all likelihood unwittingly) analysed their data as if they had had a sample size of 100 or, equally bad, a sample size of one! We show how to avoid such poor practices and further argue that chi-square testing is, even if applied correctly (meaning that no technical errors are made), a limited purpose tool for assessing treatment interactions.