7_Sampling_Distributions

7_Sampling_Distributions - First. Distribution of sample...

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Sampling Distributions First. .. • Distribution of sample means – collection of sample means for all the possible random samples of a particular size ( n ) that can be obtained from a population • vs • Sampling distribution – distribution of statistics obtained by selecting all the possible samples of a specific size from a population First. .. • Distribution of sample means is a • Sampling distribution You should know everything there is to know about . . . • Sampling distribution of the mean – Its composition – Properties – Sample size – Central limit theorem
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Background • A basic goal in a lot of research is to describe populations Background • A basic goal in a lot of research is to describe populations – what are members of a population typically like? Background • A basic goal in a lot of research is to describe populations – what are members of a population typically like? • Do depressed individuals have unusually high IQs? • How much do individuals with a B.A. make?
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Background • A basic goal in a lot of research is to describe populations – what are members of a population typically like? • Do depressed individuals have unusually high IQs? • How much do individuals with a B.A. make? • We want to know parameters — often µ One Approach • Hypothesize • Sample • Determine probability of sample given hypothesized population • Decide whether hypothesis is true One Approach • Hypothesize about µ for the population of interest One Approach • Hypothesize about µ for the population of interest – For the population of all depressed people, we hypothesize that the mean IQ ( µ ) is 116
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One Approach • Hypothesize about µ for the population of interest – For the population of all depressed people, we hypothesize that the mean IQ ( µ ) is 116 H: µ = 116 • Hypothesize about µ for the population of interest – For the population of all depressed people, we hypothesize that the mean IQ ( µ ) is 116 H: µ = 116 Realize that this implies that we have a distribution of scores that is centered around 116 µ = 116 IQ One Approach • Draw a sample from the population – say, 300 depressed individuals One Approach • Draw a sample from the population – say, 300 depressed individuals – Compute M (in this case, their mean IQ)
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One Approach • Draw a sample from the population – say, 300 depressed individuals – Compute M (in this case, their mean IQ) • say, M = 100 One Approach • Determine probability of drawing a sample with a mean of M = 100 given the hypothesized population mean of µ = 116 • Hypothesize about µ for the population of interest – For the population of all depressed people, we hypothesize that the mean IQ ( µ ) is 116 H: µ = 116 µ = 116 IQ M = 100 • Hypothesize about µ for the population of interest – For the population of all depressed people, we hypothesize that the mean IQ ( µ ) is 116 H: µ = 116 Probability of M = 100?
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7_Sampling_Distributions - First. Distribution of sample...

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