Standard Deviation
The standard deviation is a more useful measure than the range of the variability of a score distribution. Standard deviation indicates the average distance that scores in a distribution vary from the mean (7.665 in Table 11.1). A large variance indicates that the scores are spread out from the mean, as Chapter 10, “Establishing Evidence of Reliability and Validity,” discusses. Conversely, the smaller the variance, the greater the similarity of the scores and the closer they are to the mean. Most software programs report the standard deviation, which is the square root of the variance, in their test analyses reports. The standard deviation tells you the average distance of the scores from the mean, or how much the scores differ, either positively or negatively, from the mean. A small standard deviation means that the scores were bunched together around the mean, while a large standard deviation means that the scores were spread out from the mean.
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The standard deviation is most useful for making interpretations about the normal curve, which is a grading method that is discouraged for classroom testing, as Chapter 13, “Assigning Grades,” discusses. In the classroom setting, the most useful application of the standard deviation is to help you to understand the reliability coefficient and the standard error of measurement (SEM) for a test.
