The real question here is if there is a way to know X is causing Y rather than simply being associated with it. In my example Y seems to be telling more of X(if not causing it) than X says about Y.
This is not about causality per se, I know that correlational studies can not show that. But we will never be able to do random assignment, it would not even be legal. So correlation is what we have. My problem is that I am having growing doubts about the use of regression to show that X causes a change in Y. For example in our survey of satisfaction we measure a wide range of predictors of satisfaction, like satisfaction with pay, and then use it to predict overall satisfaction. Satisfaction with pay (a dummy predictor variable) has the highest odds ratio in the survey (the DV is a two level variable satisfied/not - I am running logistic regression). If you are satisfied with pay you are 19 times more likely to be overall satisfied than if you are not satisfied with pay. The odds ratio suggests that this is a key factor in overall satisfaction therefore at least compared to 30 other predictors.
The problem is that there is little indication this really matters. 90 plus percent of our staff are satisfied (that the number is so high might be part of the problem because there are only 47 usable cases that are dissatisfied out of 448 total cases - also we have 31 predictors). And dissatisfaction with pay is extremely high. So pay looks like a key driver of overall satisfaction based on the odds ratios, but satisfaction with pay is very low and overall satisfaction is quite high. It seems that while overall satisfaction reflects real differences between those who are satisfied with pay and not, those differences don't change whether customers are satisfied or not. Which confuses me given my understanding of regression.
It is interesting that two variables with much lower odds ratios have higher levels of statistical significance. Pay is significant at the ,1 level they are at the .05 level.