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This Ms. has now been withdrawn form submission to peerJ, as we wish to make substantial changes.
In particular, it should be noted that modesl CANNOT be compared using BIC. This is becasue the optimisation metrics depend on the model, and are always larger for logit than probit becasue logit (p) > rpobit (p).
All the rest of the comparisons are valid.
In particular the findings that:
1. standard anova and probit or logit estimates of population proportion are singificantly different (95%)
2. between 7% and 20% of classifications according to p-null are different for raw and probit or logit models. d
Apologies that these corrections were not mader earlier