2値データの解析には一般化線形モデルを使いましょう：割算値の利用からの脱却のススメ

抄録

Proportion data obtained from binary responses in ecotoxicity tests (e.g., survival, mortality, and hatchability) are conventionally analyzed using statistical analyses based on the assumption of normality (e.g., analysis of variance), often by applying arcsine square root transformation. However, proportion data are rarely normally distributed and use of proportion loses the sample size information. In this review, we sum up several issues of the conventional statistical analyses and introduce generalized linear model (GLM) with a binomial distribution to overcome them. To demonstrate the benefits of using GLM in an easy-to-understand manner, we simulate simplified toxicity data and compare the statistical power of three different methods (i.e., t-test without transformation, t-test with arcsine square root transformation, and GLM) for detecting a treatment effect in the simulated data. Simulations indicate that the GLM provides as high or higher statistical power than other methods. We recommend that proportion data such as survival be analyzed using the binomial GLMs.