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Lecture Slides PSY201 10.7.13

# The variance of the distribuon of means the standard

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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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