Chapter 4: Analysing the Data |

## Standard deviationTo overcome the problem of dealing with squared units, statisticians take the square root of the variance to get the standard deviation. The So if the scores in the data were 5, 7, 6, 1, and 8, their squared differences from the mean would be 0.16 (from [5-5.4] The above formula is the definition for a The standard deviation in our sexual behaviour data is 2.196, from the SPSS printout in Output 4.2. So the mean number of sexual partners is 1.864 with a standard deviation of 2.196. The units are now the same as the original data. But, is this a large standard deviation? It is hard to say. In a normal distribution the mean and standard deviation are independent of each other. That is one could be large or small and the other large or small without any influence on each other. However, in reality they are often linked so that larger, means tend to have larger standard deviations. This leads into the area of transformations that are a way of reestablishing this independence. A useful measure of a distribution that is sometimes used is the ratio of the standard deviation to the mean (Howell p. 48) The standard deviation has one undesirable feature. Like the mean, one or two extreme scores easily influence the standard deviation. So really atypical scores in a distribution ("outliers") can wildly change the distributionŐs standard deviation. Here, adding a score of 200 increases the sd from 2.196 to 15.0115, a seven-fold increase! Because both of these descriptive statistics are influenced by extreme cases, it is important to note when extreme values exist in your data and might be influencing your statistics. How to define "extreme," and what to do if you have extreme data points is a controversial and complex topic out of the scope of this class. |

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