Chapter 4 Notes Psychology 202.docx - Chapter 4 Notes...

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Chapter 4 Notes Psychology 202The term variability has much the same meaning in statistics as it has in everyday language; to say that things are variable means that they are not all the same.In statistics, our goal is to measure the amount of variability for a particular set of scores, a distribution.oIf the scores in a distribution are all the same, then there is no variability Small difference b/w scores: variability is smallLarge difference b/w scores: variability is largeVariability: provides a quantitative measure of the differences between scores in a distribution and describes the degree to which scores are spread out or clustered together.The purpose for measuring variability is to obtain an objective measure of how scores are spread out in a distribution.
A good measure of variability serves two purposes:oVariability describes the distribution. It tells whether the scores are clustered close together or are spread out over a large distance. Variability is defined in terms of distance. It tells how much distance to expect b/w one score and another, or how much distance to expect between an individual score and the mean. oVariability measures how well an individual score (or group of scores) represents the entire distribution. This aspect of variability is very important for inferential statistics, in which relatively small samples are used to answer questions about populations. The obvious first step toward defining and measuring variability is the range which is the distance covered by the scores in a distribution, from the smallest score to the largest score.
One commonly used definition of the range simply measures the difference between the largest score (Xmax) and the smallest score (Xmin)oRange = X (max) -X (min)When the scores are measurements of a continuous variable, the range can be defined asthe difference between the upper real limit (URL) for the largest score (Xmax) and the lower real limit (LRL) for the smallest score (Xmax).oRange = URL for X (max) – LRL for X (min)When the scores are whole numbers, the range can also be defined as the number of measurement categories. Defining the range as the number of measurement categories also works for discrete variables that are measured with numerical scores. oX (max) – X (min) + 1The range is the most obvious way to describe

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