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The bell curve provides a foundation for the majority of statistical procedures in sociology. Conceptually it is a histogram, but with such fine distinctions between outcomes that it is a line in the shape of a bell. Beneath this curve are all possible outcomes, with the outcomes on the x-axis and the y-axis describing the proportion or probability for each outcome. The ”tails of the curve extend indefinitely. The shape is symmetrical and unimodal, so that the distribution s mean, median, and mode are identical and in the center of the distribution. In the distribution one standard deviation from the mean is 34.13 percent of the area under the curve, two standard deviations is 47.72 percent of the area under the curve, and three standard deviations is 49.87 percent of the area under the curve. Since the distribution is symmetrical, the distance from the mean will be the same regardless of whether the standard deviations are above or below the mean.
The bell curve can be used for hypothesis testing. The central limit theorem states that, even when individual scores are not normally distributed, in random samples of a sufficient size, the distribution of sample means will be approximately normally distributed around the population mean. Thus, sociologists can examine the probability of producing a specific sample mean, based on a hypothesized population mean. If a sample mean is unlikely to occur based on the hypothesized population mean, the sociologist can reject the hypothesized population mean. Similarly, relationships between variables can be tested by studying how likely it would be to find a specific relationship in a sample if there was no relationship in the population.
- Agresti, A. & Finlay, B. (1997) Statistical Methods for the Social Sciences. Prentice Hall, Upper Saddle River, NJ.
- Healey, J. F. (2005) Statistics: A Tool for Social Research. Thomson Wadsworth, Belmont, CA.
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