Unformatted text preview: ;on for degrees of freedom (for now) Unbiased es4mate of the popula>on variance using nota>on for degrees of freedom Summary of diﬀerent types of standard devia>on and variance Sta4s4cal Term Sample standard devia>on Popula>on standard devia>on Es4mated popula4on standard devia4on
Sample variance Popula>on variance
Es4mated popula4on variance
Symbol SD σ S SD2 σ2 S2 5 10/6/13 When es4ma4ng the popula4on variance, you divide the sum of squared devia>ons by the degrees of freedom (N – 1) BUT when ﬁguring the variance of the distribu4on of means, you divide the es+mated popula>on variance by the full sample size (N) When using the es4mated the popula4on variance for calcula>ng the variance and standard devia>on of the distribu>on of means, the equa>ons should look familiar… The variance of the distribu>on of means: The standard devia4on of the distribu>on of means: Es>ma>ng the popula>on variance loses some accuracy. We make up for this by sehng the cutoﬀ score for signiﬁcance a liSle more extreme. In fact, sta>s>cians have ﬁgured an exact distribu>on that takes this into account
called the t distribu>on. 6 10/6/13 What do you no>ce about the t distribu>on, compared to the normal distribu>on? Similar to a normal curve, but with thicker (heavier) tails, making more cases in the extremes Thus, for any par>cular cut
oﬀ (e.g., 5%), the score will fall farther out than on the normal curve The t distribu>on varies in shape depending on df ▪ The more degrees of freedom, the less heavy the tails, the more the curve approximates a normal distribu>on There is a diﬀerent t distribu>on for each number of degrees of freedom. The more degrees of freedom (larger the sample size), the closer the t distribu>on is to the normal curve. This is because you are es>ma>ng with increas...
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 Winter '13
 bernard
 Psychology, the00

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