Chapter 4: Measures of Variability

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variability

describes distance of the spread of scores or distance of a score from the mean; measures how well an individual score represents the distribution

range

distance covered by the scores in a distribution

range equation

range = Xmax - Xmin

standard deviation

a measure of the standard distance from the mean; describes whether scores are clustered around the mean

deviation score

x - mean

Sum of Squares (SS)

remove negative deviations, square each score, sum the squared deviations

variance

average of the squared deviations; variance measured in squared units

standard deviation equation

square root of variance

definitional formula for Sum of Squares (SS)

SS = Σ(x-mean)^2

computational formula for Sum of Squares (SS)

SS = Σx^2 - (Σx^2)/(N)

degrees of freedom

n-1; # of scores in sample that are independent and free to vary

adding a constant to each score

mean is changed, SD unchanged

multiplying each score by a constant

mean is changed, SD is changed (multiplied by that constant)

goal of inferential stats

detect significant/meaningful patterns in research results

variance of sample formula

s^2 = SS/n-1

standard deviation (SD) of sample formula

s = square root of SS/n-1