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By Schuyler W. Huck

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2. A uniform distribution would be the extreme platykurtic case. * When describing distributional shape, the term uniform means the same thing as rectangular. † Appendix B contains references for all quoted material presented in this section. * One reason for this admonition is the fact that deviations from normality in the form of positive or negative kurtosis can disrupt the functioning of various statistical tests. For example, kurtosis can affect tests on means, variances, and covariances. If measures of kurtosis become as commonplace as measures of central tendency, variability, and skewness in researchers’ efforts to summarize groups of data, it is important that those who compute measures of kurtosis (and those who see them in research reports) understand what kurtosis measures measure.

However, it must be remembered that the data in each situation formed a perfectly flat distribution. Although these differences appear to be small, they illustrate the fact that measures of kurtosis are influenced not just by the degree to which a distribution is peaked or flat. Kurtosis also is influenced by the amount of variability in the data. The second surprising feature of kurtosis is that rectangular distributions, which are flat, are not maximally platykurtic. Bimodal * Some people like to subtract 3 from the formula presented in this paragraph so that a normal distribution has a kurtosis value of 0.

If the average deviation (rather than the standard deviation) is used to measure a person’s standing in the group, the result will not likely match up with the person’s actual z-score. * For these 10 scores—0, 1, 2, 3, 4, 4, 5, 7, 11, and 13—SD = 4. The average deviation for these same data (with deviations taken from the arithmetic mean) is equal to 3. 1 was initially prepared† and then the summary data in the right column were used to compute SD = 160 10 and AD = 30 10 With most sets of scores, the standard deviation will be larger than the average deviation from the mean.

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