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Lecture 2

PS296 Week 2C (Measures of Variability)

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Max Gwynn

PS296 Week 2C (Measures of Variability) • Also called measures of dispersion. • Indicate how spread out (dispersed) the scores in a distribution are. • Dispersion (Variability): – the degree to which individual data points are distributed around the mean • All yield numerical values, i.e., a quantification of variability. Measures of variability • Range • Variance • Sum of squares • Standard deviation Range: Calculated as the difference between the highest score and the lowest score in a data set. • Range = (Highest score - Lowest score) • advantage: simple to calculate • disadvantage: takes into account only two scores, no matter how large your data set • so, it is sensitive to all scores Deviation scores • how much each score varies (deviates) from the mean • involves deviation scores: deviation score = (x-x) • problem: sum of the deviation scores in a data set always equals 0 (within rounding error), i.e., Σ(X - X) = 0 • So the average deviation score also always equals 0 Mean absolute deviation • MAD = • Not difficult to calculate, but doesn’t have the nice statistical properties that other measures of dispersion have. • Rather than use the absolute deviation, another way of getting rid of the negative values is to square each deviation score. Sum of squares • SS = the sum of the squared deviation scores 2 • SS = Σ(X - X) • Steps: – Calculate the mean: X – Calculate the deviation scores: (X – X) – square each deviation score: (X - X) 2 2 – Sum the squared deviation scores: Σ(X - X) Variance • variance is like an average squared deviation.
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