Adding 0.5 to cells when calculating odds ratios, d' and the empirical logit transform

On the use of adding 0.5 to cells to define an odds ratio

In particular Bonett and Price Jnr (2015, p.395) say "The addition of [1/2] to the cell frequencies in Equations 2 and 3 was suggested by Gart (1966), and it can be shown (see Agresti, 2002, p. 595) that the bias of ln(odds ratio) is minimized with the addition of [1/2] to each cell frequency".

A pdf copy of this paper is available to read and print from here.

On the use of the +0.5 smoothing for calculating the empirical logit transform see:

On the use of the +0.5 smoothing for calculating the d' signal detection parameter see:

See also

Signal Detection Parameters from SPSS There a different convention is followed of putting 1/2N and 1-1/2N in place of 0% and 100%.

A discussion on the optimal quantity to add to 0% and 100% hit and false alarm rates to give finite dprime values is here.

There are details here which suggests a nonparametric alternative to dprime called aprime which represents an average area under all possible ROC curves. If this link is broken here are the details copied from there on how to compute ROC diagnostics using in R.


These pages are maintained by Ian Nimmo-Smith and Peter Watson

Last updated on 27 July, 2006