Knowledge of statistics is by far the most important quantitative skill for doctoral programs in business in general, but as Praetorian said, the specific quantitative subdisciplines that you should expect to master depend on your specific business discipline.
In general, do not think in terms of what quantitative skills predominate in a particular discipline's academic requirements. Rather, think in terms of what quantitative skills are generally the most difficult to master. Although statistics will figure prominently throughout your doctoral program and all of your empirical research, it is not one of the difficult quantitative skills. Instead, you may take a course or two in something very difficult, possibly never to see those algorithms ever again after the course is over. Here is a rough guideline, off the top of my head, of the one of the toughest subdisciplines of the quantitative arts that I can think of that you might see in each of several business disciplines:
1. Accounting. Stochastic differential equations.
2. Finance. Stochastic differential equations.
3. Human Resource Management. Differential calculus.
4. Management. Differential calculus.
5. Management Information Systems. Differential calculus.
6. Management Science. Differential calculus.
7. Managerial Economics. Differential calculus.
8. Marketing. Differential calculus.
9. Operations Management. Stochastic processes.
I certainly welcome further updates to this little table. Some people may disagree that what I've listed is both difficult and likely to crop up in each listed discipline.
Quantitative challenges that you should expect to see in all disciplines, somewhere along the way, include game theory, Pareto optimization, linear programming, and Bayesian analysis, in addition to statistics. These are not difficult subjects, however, so it might be worthwhile to build your confidence by tackling all of these up front, if you have the time. Then go on to the more interesting topics listed above.
Lastly, regarding statistics per se
, plan on mastering everything up to multivariate analysis, including hierarchical regression analysis. Again, these are not difficult disciplines to master, but sometimes you can get bogged down in details and forget what you're doing. Possibly a good strategy to follow in mastering statistics is to work hard to figure out exactly why a formula is the way it is. Even the simplest principles should be scrutinized this way if you wish to master the more difficult ones. Once you have worked it that far, you are a lot less likely to get confused by the notation.
Richard S. Voss, Ph.D.
Chair, Graduate Business Programs
Troy University, Southeast Region
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