Computational formulae are a throwback to a time when computers were not widely available. Today their teaching obscures important underpinnings of statistical theory and practice.᭜ INTRODUCTION ᭜ T he teaching of computational formulae impairs the ability of students to understand statistics.Definitional formulae are clearly favoured by some statistical educators. Bradstreet (1996), for instance, noted that 'the simple computations performed by the students should be those which reinforce data analytic and data interpretation concepts' (p. 70). He went on to state that definitional formulae provide superior vehicles for the teaching of statistical concepts than do computational formulae. Furthermore, there are texts which only include definitional formulae. An example of such is the text by Phillips (2000).To clarify the above, almost all statistical formulae come in two forms: a definitional formula, which elegantly describes the relationships between its inherent components, and a computational formula, which generates the same answer but is easier to employ when making calculations with pen and paper. This note argues that only definitional formulae ought to be taught in introductory statistics courses.If we go back to the time when I learned statistics, there were hardly any computers, and those which existed were mainframes which had to be fed the program to be run, along with the data, on a series of 3-inch by 8-inch punch cards. Statistical calculations were done with pencil and paper, aided by hand-held calculators which were then becoming widely available. In this environment, any formulae which reduced the number of tedious mathematical calculations were not just convenient, they were a necessity. Thus the algebraic derivation and practical application of computational formulae, sometimes called raw-scores formulae, were essential components of introductory statistics courses.
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COMPUTING THE STANDARD ᭜ DEVIATIONOne fundamental formula directs the calculation of the standard deviation. The definitional formula is given first below, and a typical raw-scores computational formula follows it.As with most computational formulae, the second one above is much less elegant; indeed one would say that it is most clunky to look at. But in practice, if one were to use pen and paper to calculate a standard deviation, it removes the necessity of subtracting the mean from each value. Thus if the sample size was 150, the computational formula would allow the researcher to avoid one hundred and fifty tedious (and possibly error-provoking) calculations.
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