Probability in decision making

¶ … Decision-making in the Age of Information can be a daunting enterprise by any measure, but there are some steps that researchers can take to help improve the accuracy of their decisions while limiting the uncertainty that is involved. A typical business context that requires a decision using probability concepts involves the use of probability proportionate to size sampling wherein cluster groups being studied vary in size. An example of this decision-making process is described further below, including a discussion concerning how probability concepts were applied and the process involved for limiting the uncertainty. The outcomes of the statistical analysis that would be used for this context are followed by an assessment of the respective tradeoffs that are involved between accuracy and precision required by various probability concepts and the effect on the resulting data. Finally, the decision that was reached based on the statistical data using this approach is presented.

Review and Analysis

Hypothetical Business Decision Requirement

The hypothetical business decision involved in this study concerns a human resources (HR) director for a medium-sized computer retailer, "Computers R. Us," located in the mid-western United States. The HR director wants to visit and conduct face-to-face interviews with a sample of 100 college students who are representative of the population of all college students in the United States who are majoring in computer science to ascertain their views concerning the viability of a new product launch envisioned by Computer R. Us.

How the probability proportionate to size concepts are applied to formulate a decision.

The HR director, "Ms. Smith," selects a random sample of 20 colleges in the United States with computer science degree programs and visits selected institutions where she selects ten students at each college who are enrolled in a degreed computer science program at random for face-to-face interviews to gauge their opinion concerning her company's envisioned product launch.

Application of appropriate probability concepts and to find resulting data to limit uncertainty in the decision

Because the 20 colleges selected for the sample vary in size and have different numbers of students enrolled, Ms. Smith must take steps to ensure that larger colleges with more students have a better chance of being selected than their smaller counterparts in order to ensure that every student has an equal chance of being selected for the face-to-face interviews. Ms. Smith would accomplish this requirement by adjusting the chances of selecting a given college during the initial stages of sampling. According to Becker and Bryman (2004), "Probability proportionate to size sampling adjusts the probability of a higher order unit (cluster) being selected in proportion to the number of units in that cluster" (p. 402). Moreover, Daly and Ree (2006) suggest that the probability proportionate to size method is particularly useful for sampling educational institutions for ensuring that a representative sampling is achieved. Therefore, Ms. Smith would assign larger colleges with higher enrollment rates a greater chance of being selected for her visits and correspondingly lower chances to smaller colleges with lower enrollments. In order to reduce the uncertainty involved and maximize the chances of each student having an equal opportunity of being selected for interview, this step is achieved by adjusting the probability of selecting a college during the initial stages of college selection based on the proportion of all students in the general population who are enrolled at the college. As a result, a college that had 40,000 students enrolled in its computer science program would be 100 times more likely to be selected by Ms. Smith than a smaller college with just 400 students so enrolled.

Identify each outcome from the statistical analysis, providing rationale for each.

The colleges initially selected by Ms. Smith, their respective enrollment rates and sorted according to the adjusted cluster unit that was assigned to each are shown in Table 1 below.