## Statistical Analysis in Decision Making

Apr 20th, 2009 by Scott Hebert

When discussing probabilities, it is important to understand the difference between classical and subjective probabilities. Classical probabilities require that each outcome is equally likely to happen. Subjective probabilities require an understanding of the underlying data in order to formulate an educated guess as to their outcome (Triola, 2008). Essentially, classical probabilities relate to data sets in which chance is the only factor. For example, the roll of a 6-sided die is equally likely to result in any number between one and six. This is an example of a classical probability. If the die was warped in such a way that one number was more likely to happen than another, that probability would require an understanding of the nature of the warping in order to predict how frequently any specific number would be generated.

If a bank is trying to decide which of two cash back options to offer on their credit card, they must decide which option would be preferred by the largest percentage of the population. In order to make this determination, the best method is to develop a questionnaire that asks questions relevant to the cash back options and retrieve results from an appropriate sample size. One of the most difficult aspects of questionnaire design is deciding what questions should be asked. To assist in this, David Ambrose and John Anstey (2007) designed a model for questionnaire design that includes seven question categories. In their research, Ambrose and Anstey found that all questions could be assigned to one of these categories, and effective questionnaires include questions from each category.

Determining the appropriate sample size requires the application of a simple mathematical formula. The expression that represents the margin of error relies on the sample size. If the margin of error is a known value, the expression can be solved for the sample size instead (Triola, 2008). A larger sample size produces statistics that are more accurate. Therefore, it is important to choose a sample size that is large enough to render accurate results, but small enough to make the research feasible. In other words, the most accurate data would include results from the entire population, but gathering that data would be an unwieldy process.

If the bank chose instead to offer a credit card that included a sweepstakes entry for each purchase made, a new set of calculations arise. The bank would need to understand how many prizes they would be giving away in a year. For example, if the bank chose to award one prize for every 1000 purchases made and they know that the average credit card user makes 52 purchases per year, research is still necessary to estimate how many people would use the card. Knowing the population of credit card users and, therefore, the maximum number of prizes given per year, would allow the bank to more accurately estimate each user’s chance of winning a prize. Customers want to understand not only how frequently the bank will award prizes, but also how likely they are to win in a given year. This calculation also requires an estimate of how many total purchases will be made. Once this research is complete, the bank will have the information necessary to decide what kind of credit card incentive would be most beneficial to their customers.

References

Ambrose, D., & Anstey, J. (2007). Better Survey Design Is: Stuck for an answer?. *Bank Marketing, 39*(2), 26-31. Retrieved April 20, 2009, from MasterFILE Premier database.

Triola, M. F. (2008). *Elementary statistics* (10th ed.). Boston: Pearson.