# 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

D G Bonett and R M Price Jnr (2015) Varying coefficient meta-analysis methods for odds ratios and risk ratios.

*Psychological Methods***20(3)**394-406. References recommending the use of adding 0.5 to frequencies to minimise bias when evaluating an odds ratio are given in this paper.

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".

- Subbiah and Srinivasan (2008) note the practice of adding a constant to a zero cell to define an odds ratio. They go on to state "Usually a continuity correction, by addition of 0.5, is considered for studies with zero counts in the estimation of the log of the odds ratio or the log of the risk ratio."
M Subbiah and M R Srinivasan (2008) Classification of 2x2 sparse data sets with zero cells.

*Statistics & Probability Letters***78(18)**3212-3215.

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:

David R COX and E J SNELL (1989)

*Analysis of Binary Data*, Chapman and Hall: London

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

Michael J HAUTUS (1995) Corrections for extreme proportions and their biasing effects on estimated values in d'. Behavioral Research Methods, Instruments, & Computers, 27(1), 46-51.

## 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