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PSY201H1 (45)
Chapter 4

Chapter 4

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Gillian Rowe

Chapter 4 Variability 41 OverviewVariabilityprovides a quantitative measure of the degree to which scores in a distribution are spread out or clustered togetherif scores are all the same theres no variability A good measure of variability serves two purposes 1 Variability describes the distribution it tells whether the scores are clustered close together or spread out over a large distance Usually defined in terms of distance tells how much distance to expect between one score and another or how much distance to expect between an individual score and the mean 2 Variability measures how well an individual score or group of scores represents the entire distribution This is important for inferential statistics where relatively small samples are used to answer questions about populations Variability provides information about how much error to expect if youre using a sample to represent a population Three measures of variability the range the interquartile range and the standard deviation standard deviance is by far the most important42 The Range and Interquartile RangeRangedistance from the largest score Xmax to the smallest score Xmin in a distribution Typically the range is defined as the difference between the upper real limit of the largest X value and the lower real limit of the smallest X valuerangeURL XmaxLRL Xmin Ex 3 7 12 8 5 10range1252510 you can also obtain the range when scores are whole numbers like this rangehighest Xlowest X1Typically used with intervalratio scales of a continuous variable because its defined in terms of distancepossible to do discrete variables provided theyre measured on intervalratio scalesRange is the most obvious way to describe how spread out the scores are simply find the distance between the max and min scoresproblem with using range however is that its completely determined by two extreme values ignoring other scores in the distribution often doesnt give an accurate description of the variability for the entire distribution unreliableThe Interquartile RangeMeasure variability with the interquartile range in order to avoid excessive influence of one or two extreme scores measures range covered by the middle 50 of the distribution First locate the boundary that separates the lowest 25 from the rest called the first quartile Q1 and then the boundary that separates the top 25 third quartile Q3Interquartile rangerange covered by the middle 50 of the distributionQ3Q1 Simplest way to find Q1 and Q3 is to make a frequency distribution histogram in which each score is represented by a box then determine exactly how many boxes are needed to make up onequarter of the whole setex with 16 scores boxes one quarter is exactly 4 boxesQ3Q184535 points from figure 42 page 5
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