 # Statistics in Plain English

## Synopsis

This book presents statistical concepts and techniques in simple, everyday language. It provides short, simple descriptions and explanations of a number of statistics or concepts. Part 1 provides a brief description of the statistic, including how it is used and what information it provides. Part 2 reviews how it works, how to calculate the formula, the strengths and weaknesses of the technique, and the conditions needed for its use. Part 3 concludes with an example that uses and interprets the statistic. A glossary of terms and symbols is also included. This brief paperback is an ideal supplement for statistics, research methods, or any course that uses statistics, or as a handy reference tool to refresh one's memory about key concepts. The actual research examples are from a variety of fields, including psychology and education.

## Excerpt

Measures of central tendency, such as the mean and the median described in Chapter 1, provide useful information. But it is important to recognize that these measures are limited and, by themselves, do not provide a great deal of information. To illustrate, consider this example: Suppose I gave a sample of 100 fifth-grade children a survey to assess their level of depression. Suppose further that this sample had a mean of 10.0 on my depression survey and a median of 10.0 as well. All we know from this information is that the mean and median are in the same place in my distribution, and this place is 10.0. Now consider what we do not know. We do not know if this is a high score or a low score. We do not know if all of the students in my sample have about the same level of depression or if they differ from each other. We do not know the highest depression score in our distribution or the lowest score. Simply put, we do not yet know anything about the dispersion of scores hi the distribution. In other words, we do not yet know anything about the variety of the scores in the distribution.

There are three measures of dispersion that researchers typically examine: the range, the variance, and the standard deviation. Of these, the standard deviation is perhaps the most informative and certainly the most widely used.

Range

The range is simply the difference between the largest score (the maximum value) and the smallest (the minimum value) score of a distribution. This statistic gives researchers a quick sense of how spread out the scores of a distribution are, but it is not a particularly useful statistic because it can be quite misleading. For example, in our depression survey described earlier, we may have 1 student score a 1 and another score a 20, but the other 98 may all score 10. In this example, the range will be 19 (20 - 1 = 19), but the scores really are not as spread out as the range might suggest. Researchers often take a quick look at the range to see whether all or most of the points on a scale, such as a survey, were covered in the sample.

Another common measure of the range of scores in a distribution is the interquartile range (IQR). Unlike the range, which is the difference between the largest and smallest score in the distribution, the IQR is the difference between the score that marks the 75th percentile (the third quartile) and the score that marks the 25th percentile (the first quartile). If the scores in a distribution were arranged in order from largest to smallest and then divided into groups of equal size, the IQR would contain the scores in the two middle quartiles.

Variance

The variance provides a statistical average of the amount of dispersion in a distribution of scores. Because of the mathematical manipulation needed to produce a variance statistic (more about this in the next section), variance, by itself, it not often used by researchers to gain a sense of a distribution. In general, variance is used more as a step in the calculation of other statistics (e.g., analysis of variance) than as a stand-alone statistic. But with a simple manipulation, the variance can be transformed into the standard deviation, which is one of the statistician's favorite tools.

Standard Deviation

The best way to understand what a standard deviation is to consider what the two words mean. Deviation, in this case, refers to the difference between an individual score in a distribution and the . . .

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