Description of Calculation of Individual Difference Scores
Individual difference scores for variables representing counts were calculated using logistic- transformed test results for corresponding batteries under alcohol and placebo. The count variables were DAT and SIM correct answer counts, and SIM collisions and speed exceedances.
AD_CORR/(50-AD_CORR) is the odds for correct response under alcohol, and
PD_CORR/(50-PD_CORR) is the odds for correct response under placebo, so that
LOG (OR) =
LOG((0.5+AD_CORR)/(0.5+50-AD_CORR)) - LOG((0.5+PD_CORR)/(0.5+50-PD_CORR))
is the log odds ratio for comparing correct responses under alcohol to correct responses under placebo. Note, log(OR) > 0 if the odds for a correct response under alcohol exceeds the corresponding odds under placebo, and log(OR) < 0 in the opposite case. Log(OR) = 0 if the alcohol has no effect on correct response frequency.
For counted variables, statisticians, and various researchers, tend to prefer log-odds ratios to simple difference scores because of its interpretation: log odds is approximately equal to percent difference in correct answers minus percent difference in incorrect answers. In contrast, a simple difference score of say 7 may represent a huge difference between 1 and 8 or a relatively small difference between 24 and 31.
Also, log-odds lead to more stable variances than do simple difference scores and, often the statistical distribution of log-odds ratios are better approximated by the normal distribution than the distribution of the untransformed variable. Finally, when linear regression is used to predict, or to estimate, a simple difference score, the estimated value will, on occasion fall, outside the legitimate range (say, one may end up with a negative probability!). Difference estimates based on logistic regression can not yield such meaningless numbers.
The log-odds ratios for the other three count variables were defined in the same spirit as:
LOG((1/6+AS_COR)/(1/6+ 72-AS_COR)) - LOG((1/6+PS_COR)/(1/6+ 72-PS_COR))
LOG((1/6+AS_COLL)/(1/6+ 79-AS_COLL)) - LOG((1/6+PS_COLL)/(1/6+79-PS_COLL))
LOG((1/6+AS_SPEX)/(1/6+ 58-AS_SPEX)) - LOG((1/6+TPCB9)/(1/6+ 58-AS_SPEX)).
Note. The authors followed customary practice of adding 0.5 to avoid zero-counts.
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