I spoke with my wife, a professional psychologist, about this thread and about my comments above. Her response was that the notion of "Women are better at multi-tasking" is simply an urban myth, supposedly supported by not-very accurate pseudo-scientific commentaries about differences between male & female brain structure, but in fact there is little or no genuine scientific evidence of significant gender-based as compared to individual differences in abilities to switch rapidly & effectively between different tasks, or what is informally called "multi-tasking". Oops, my mistake.
So, if there are genuine differences in quality (and therefore productivity & profitability) between companies with male vs female CEO's (as Karen Rubin's work seems to suggest), then the reason is not due to multi-tasking abilities, and so we must look elsewhere for the cause. My wife's professional viewpoint is that there are potentially two main contributing factors, as follows:
1) Women ARE better than men at networking and at group communication, and this is likely to be far more significant in a corporate leadership context than my naieve notions about multi-tasking. My wife believes that differences between men & women in their group communication skills & styles is likely to have a significant impact on organizational dynamics, and in particular on the potential level of satisfaction of employees within organizations, and this may well be reflected in employee attrition rates as a potential (inverse) predictor of productivity and therefore profitability.
2) There have been significant changes over the years in the way that girls have been brought up as compared to boys. Specifically, back in the 1950's (corresponding to the older generation of current CEOs), boys were generally taught that potentially they could do anything, whereas girls had far more limited career opportunities. As this situation has improved over time, we see larger numbers of women in senior positions now, but generally there is not only an age difference, but also a generational outlook difference between "typical" male & female CEOs.
Based on these suggestions & comments, it is likely that in addition to just CEO gender, it would be worthwhile to look further at two other pieces of corporate data that should be easily available, namely:
1) Employee satisfaction (or lack of), as measured by employee attrition rate (which might or might not be related to CEO gender), and
2) Year of birth of the CEO, as indicative of generational changes in outlook.
By considering employee attrition rates and CEO's year of birth, it may be possible to reduce bias effects and thereby significantly strengthen the findings of this study, as well as uncovering other hidden factors in addition to just the gender of the CEO.