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Unformatted text preview: but an unknown variance 2 10/6/13 If the variance of a popula>on is not known, we can es4mate it. Usually, the only informa>on we have available about a popula>on is the informa>on that we know about a sample We assume that Popula>ons 1 and 2 have the same variance If the sample that we collect informa>on about is representa(ve of the popula>on... Then the variance of the sample should tell us something about the popula>on ▪ If the sample has liSle variance, then the popula>on probably has liSle variance ▪ If the sample has a lot of variance, then the popula>on probably has a lot of variance The variances of the samples (boSom row) is similar to the variances in the popula>ons they are drawn from (top row) 3 10/6/13 The sample’s variance cannot be used directly as an es>mate of the popula>on variance. It can be shown mathema>cally that a sample’s variance will, on average, be a bit smaller than its popula>on’s variance. Because of this, the variance of the sample would be considered a biased es(mate of the popula>on variance It is “biased” because it systema>cally underes>mates the actual variance of the popula>on Remember, the equa>on for the variance of a sample is: SD2 = Σ(X – M)2/N or SD2 = SS/N No>ce we are no longer using σ2 because we’re talking about a sample sta>s>c (not a popula>on parameter) In order to get an unbiased es4mate of the popula>on variance, we adjust the equa>on slightly… Remember, the equa>on for the variance of a sample is: SD2 = Σ(X – M)2/N or SD2 = SS/N No>ce we are no longer using σ2 because we’re talking about a sample sta>s>c (not a popula>on parameter) Unbiased es4mate of the popula>on variance 4 10/6/13 Degrees of freedom Number of scores that are “free to vary” There are N – 1 because when ﬁguring the devia>ons, each score is subtracted from the mean… Thus, if you knew all the devia>on scores but one, you could ﬁgure the last one given the mean Equa>...
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 Winter '13
 bernard
 Psychology

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