In experiments of life sciences application of logistic regression techniques are fairly common. Often it is imperitive to compare the slopes of a series of logistic regressions(arising from applications of different treatments) to that of a standard. We present an exact method for performing this many-to-one comparison based on simple functions of the sufficient statistics without conditioning on the nuisance parameters. We compare our proposed method with asymptotic methods like Reiersol~(1961)based on Minimum Logit Chi-squres, sequentially rejective Bonferroni (Holm,1971) based on Wald statistics and a step-down method based on likelihood ratio tests and show that our method outperforms its competitors in terms of both Type I errors and marginal power (Spurrier, 1992). The research was motivated by problems in plant pathology and Environmental sciences and we include these as our data examples.

References:

1. Holm, S., (1979). A simple sequentially rejective test procedure. Scandanavian Journal Statistics 9, 65-70.
2. Reiersl, O. (1961). Linear and nonlinear multiple comparisons in logit analysis. Biometrika 48, 359-365.
3. Spurrier, J. D. (1992). Optimal designs for comparing the variances of several treatments with that of a standard treatment. Technometrics 34, 332-339.