Chapter 5 of “Introduction to the Use of Statistics in Criminal Justice and Criminology” focuses on the importance of dispersion. The term dispersion refers to the measurement of the spread of variables in the given distribution (Gau, 2019). Dispersion is important as it is not enough to merely know the measures of central tendency to make assumptions about a distribution. Two distributions can have similar or even equal means yet be highly diverse due to the different spreads of their variables. According to Gau (2019), kurtosis is a dispersion analog of a skew. Leptokurtosis is a term used to describe values that are tightly clustered whereas platykurtosis “is evident when values are markedly spread out” (Gau, 2019, p. 141). Clearly, measures of dispersion are essential for the analysis of distribution.
Several kinds of measures of dispersion are present in the study of distributions. The variation ratio measures variables which are not present in the modal category and is calculated as the proportion of the data located outside the mode (Gau, 2019). To calculate the range, the minimum value should be subtracted from the maximum. According to Gau (2019), the variance is “a measure of dispersion calculated as the mean of the squared deviation scores” (p. 150). Unlike the range, the variance uses every value in the distribution. Gau (2019) suggests that standard deviation is computed as the square root of the variance and refers to “the mean of the deviation scores” (p. 156). In combination, the notions outlined in the chapter are useful for making accurate assumptions about the data set.
The chapter is successful at providing the reader with the basic concepts of dispersion. By providing detailed illustrations and incorporating relevant examples, the author efficiently conveys the information. The chapter clearly states which kind of data should be used for each concept. For example, the variation ratio can be used with categorical data whereas the other measures of dispersion discussed in the chapter can only be operated within continuous data (Gau, 2019). Therefore, variation ratio is the only measure of dispersion which can be calculated within qualitative data such as in-depth interviews or case studies. The remaining four measures, on the other hand, can only be computed with numerical data in quantitative research methods such as surveys and experiments.
Reference
Gau, J. M. (2019). Chapter 5: Measures of dispersion. Statistics for criminology and criminal justice (3rd ed., pp. 139-170). Sage.