SRA was invited to participate in a forum sponsored by the Palm Beach Community College Career Center called “Mathematics: Career Opportunities for Success.”
By highlighting career opportunities that stress the field of mathematics, the forum hoped to persuade students to continue their education. Bob Tarburton of SRA joined four other presenters to address an audience of AP high school math students, liberal arts math students, and others interested in learning about career opportunities.
The forum was also graced by the attendance of ‘Elvis,’ who could never quite fully explain how he intended to use mathematics in his career as an impersonator.
The following is an excerpt from Bob’s talk.
Quantitative research requires strong math skills from start to finish. Three areas where we use applied mathematics include sampling, segmentation, and attribute priority.
Directed sampling is used in almost every survey. A sampling plan is developed to ensure that the survey represents the universe being studied. Quotas can be set by factors such as income, zip code, gender, and age. In some cases, the sampling plan mirrors known demographics of a target audience. In other cases, we obtain a significant number of interviews for each group, and weight the results from each group to represent the known demographics.
By significance, I’m referring to the range of error in sampling. We’ve probably all seen survey results reported as a percentage +/- 3% or 4%. This is where a course in probability is applied. Where a random sample is used to represent a population, there is always the possibility that our sample includes a larger percentage of favorable or unfavorable responses than in the actual population. The number of interviews we conduct in a study is determined by the acceptable error range. The larger the sample, the smaller the potential differential between the results of the study and the actual make-up of the population.
Segmentation is used to determine differences between demographic groups, and to estimate how individuals will act based on their age, income, gender and other factors. The theory behind segmentation is that who you are is a more accurate predictor of how you will behave than how you say you will behave.
Differences between demographic groups are measured by how the survey respondents say they will behave. This again involves probability and sampling error. For example, if 4% more women than men are likely to buy a product, but the error range is +/- 5%, we are not confident that women comprise a stronger market. After demographic differences are measured for the group, individuals are assigned a likely behavior based their personal characteristics.
Attribute priority uses ratings of different factors of services or product features in conjunction with overall ratings of the service or product to determine which attributes are most in need of improvement. The idea is that resources should be directed to improve areas that are important to customers, but are not performing well. If customers are already satisfied with a certain feature, or if that feature is not important to them, then improving that feature will not improve sales or overall satisfaction.
To determine attribute priority, we correlate ratings of features with the overall rating of the product or service. If a feature is important, then high ratings of the feature will most likely correspond with high overall ratings, and vice-versa. To determine attribute priority, customer rating of each feature is ranked against other features, as is correlation of each factor with overall satisfaction. The ranks are combined to determine which attributes are most in need of improvement.
It’s safe to say that we use algebra and probability in almost every area of our business. We also use correlation and regression analysis in determining importance of features and areas of service. ‡
