# Concepts or Computations?

One of the first decisions to be made when teaching a statistics course is whether the course will focus on the conceptual nature of statistics or the computation of the statistics. At the risk of identifying myself as a dinosaur, my first course in statistics focused on the computational aspects of statistics. Using lumbering, sometimes cranky, and always noisy mechanical calculators (anyone out there remember the Marchant?), we furiously calculated sums of squares, cross products, and grand totals. Given the emphasis of drill on calculations and the amount of time needed to do them, there was little time left to understand what was being done by the computations. As long as the F value obtained was not a negative number or r was not greater than 1.0, who cared what the statistic meant? What was important was learning to do statistics “by hand.”

Although the focus of all editions of our text has been to develop statistics conceptually using definitional formulas, computational formulas were included in previous editions for those instructors who wanted students to experience the “by hand” approach. But the revolution in computing in the 1990’s and the ready availability of reasonably easy-to-use statistics software packages changed thinking about the value of computational formulas in the teaching of statistics. Computational formulas provide no value in understanding the nature and function of a statistic, they simply ease computations that few people still do. Thus for the fourth edition of our text we removed all computational formulas.

Katarina Guttmannova, Alan Shields, and John Caruso (2005) argue that computational formulas do not add to a student’s understanding of statistics. For example, a discussion of the variance using the definitional formula allows students to obtain a understanding of the concept of dispersion of scores. The computational formula, however, does not offer the possibility for this understanding (Guttmannova, K., Shields, A. L., & Caruso, J. C., 2005. Promoting conceptual understanding of statistics: Definitional versus computational formulas. Teaching of Psychology, 32, 251-253).

A frequent criticism of the use of statistical hypothesis testing is that it is often misused and misunderstood. Michael Firmin and Elizabeth Proemmel (2008, http://www.cluteinstitute-onlinejournals.com/PDFs/793.pdf) indicate that research from their classes suggests that students themselves recognize the need for a better understanding of the conceptual basis of statistics and their appropriate application. A conceptual approach to teaching statistics should help students to better understand when it is appropriate to apply a particular statistic to a given set of data and what the value of the statistic tells them about the data. Anything that instructors can do to help foster a deeper understanding of the use of statistics will be beneficial to the discipline.