Crisp Sets and Boolean Algebra: A Research Strategy for Student Affairs

By Banning, James; Eversole, Barbara et al. | College Student Journal, September 2008 | Go to article overview

Crisp Sets and Boolean Algebra: A Research Strategy for Student Affairs

Banning, James, Eversole, Barbara, Most, David, Kuk, Linda, College Student Journal

A review of student affairs journals clearly points out that most, if not all, research strategies within the field fall within traditional approaches based on quantitative methods and, more recently, qualitative methods. The purpose of this article is not to discourage use of these time honored research strategies, but to suggest the inclusion of a method using crisp sets and Boolean algebra as a research strategy, and to illustrate this method by example, and to discuss how this method can be of value to student affairs researchers.

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To the authors' knowledge all research that has been published focusing on students in higher education has been based on the traditional research strategies associated with quantitative and qualitative methods. Most research texts that focus on student affairs include only these two strategies (Stage, Anaya, Bean, Hosssler, and Kuh, 1996). While these methods have a long history in academia and are certainly well within Kuhn's (1970) concept of normal science, there are strengths and weaknesses associated with each of these two traditional methods. Ragin (1987, 1994, & 2006) articulated these issues. He noted that quantitative research works best when using a variable-oriented approach and when you can satisfy the demands of statistical techniques needed to draw a random sample from the population at interest. Such a characterization of quantitative research is reasonable if inference is a presumed goal, though statistical methods can be used very effectively for descriptive purposes with a small number of cases. However, quantitative methods are less helpful when the focus is on cases rather than variables and when the number of cases is not large. On the other hand, qualitative methods work best when focused on cases, but these methods work best when there are relatively few cases. Neither research strategy is designed to accommodate research that includes cases in the range of 15-35. It is difficult to do in-depth qualitative work with sets larger than 15 (although not impossible) and not very meaningful to do traditional statistical approaches on sets this small.

The crisp set and Boolean logic approach as presented by Ragin (1987) and others (Alasuutari, 1995) is based on the qualitative tradition of focusing on cases and conditions within the cases and then using Boolean algebra to look at all the configuration of conditions to test relationships with specific outcomes.

Boolean algebra is the type of mathematics on which computers and digital equipment are based. Values are 0 and 1, which is analogous to yes/no or true/false dichotomies. These dichotomies are referred to as being binary, or having two possible values. These two possible values are manipulated by the operators AND, OR, and NOT.

Boolean algebra is used to develop Boolean logic. Simply put, Boolean logic is the algebraic interpretation of truth tables. In logic, a statement is an assertion that can be determined to be true or false. The truth value of a statement is true if the statement can be determined to be true. From truth values comes the truth table. This is the same type of logic used on the GRE logic section.

```   Ragin (1987) stated the following:
By examining differences and similarities
in context it is possible to
determine how different combinations
of conditions have the same
causal significance and how similar
causal factors can operate in opposite
directions, p. 49

In summary, Ragin (1987) notes:
In common with the variable-oriented
strategy, it allows examination
of large numbers of cases. In common,
with the case oriented strategy,
it allows assessment of complex patterns
of multiple and conjunctural
causation, p. 71
```

Before introducing the basic concepts of the crisp set and Boolean algebra method, a hypothetical research scenario focusing on a student affairs research interest will be presented. …

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