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The standard deviation proves to be a more valuable measure than the range for assessing the variability within a distribution of scores. It signifies the average extent to which scores in a distribution deviate from the mean, which, in the case of Table 11.1, is 7.665. As discussed in Chapter 10, “Establishing Evidence of Reliability and Validity,” a larger variance indicates that the scores are dispersed farther from the mean. Conversely, a smaller variance implies greater similarity among the scores, with them clustering closer to the mean.
In most cases, testing software reports the standard deviation, which is the square root of the variance, in their test analysis reports. This standard deviation provides information about the average degree of divergence of scores from the mean, indicating how much scores differ, either positively or negatively, from the mean. A smaller standard deviation signifies that scores were closely grouped around the mean, while a larger standard deviation suggests that scores were widely dispersed from the mean.
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The standard deviation is particularly valuable for drawing insights from the normal curve, a grading approach discouraged for classroom testing, as discussed in Chapter 13, “Assigning Grades.” In the classroom context, the primary utility of the standard deviation lies in aiding comprehension of the reliability coefficient and the standard error of measurement (SEM) for a test.
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