If you’ve ever been puzzled by odds ratios in a logistic regression that seem backward, stop banging your head on the desk.
Odds are (pun intended) you ran your analysis in SAS Proc Logistic.
Proc logistic has a strange (I couldn’t say odd again) little default. If your dependent variable Y is coded 0 and 1, SAS will model the probability of Y=0. Most of us are trying to model the probability that Y=1. So, yes, your results ARE backward, but only because SAS is testing a hypothesis opposite yours.
Luckily, SAS made the solution easy. Simply add the ‘Descending’ option right in the proc logisitic command line. For example:
PROC LOGISTIC DESCENDING;
MODEL Y = X1 X2;