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Unformatted text preview: Sampling Distributions Central Limit Theorem PSY 2801: Summer 2010 Sampling Distributions Jeﬀ Jones University of Minnesota Jeﬀ Jones Ch 8 Sampling Distributions Central Limit Theorem Sampling Distributions A Sampling Distribution is a distribution of a statistic . If we take one person from a distribution of heights, they most likely will not be equal to the population average height; if we take a ﬁnite sample of people from a distribution, their average will probably not equal the population average either. Jeﬀ Jones Ch 8 Sampling Distributions Central Limit Theorem Sampling Dist of the Mean We will focus on the sampling distribution of ¯ x , as that is the most common sampling distribution. Staying with our height example, suppose we wanted to ﬁnd out the mean height of American men 1 American men is our welldeﬁned population of interest 2 μ of height is our parameter of interest Parameter of Interest : The parameter you’re attempting to make conclusions about for your population. Jeﬀ Jones Ch 8 Notes Notes Notes Sampling Distributions Central Limit Theorem Sampling Dist of the Mean So, to get an idea of mean male height from the population, we take a random sample of 9 American men, measure them on height, and take their mean. But there’s a diﬀerence between a statistic and a parameter (we only have a statistic), so we decide to take another random sample of 9 American men, measure them on height, and take their mean. Jeﬀ Jones Ch 8 Sampling Distributions Central Limit Theorem Sampling Dist of the Mean Since there’s a discrepancy between our ﬁrst sample mean and our second sample mean, we decide to take another sample to settle the score. Random Sample of 9 American men Calculate Height Take Mean But each sample mean is a little diﬀerent than every other sample mean → why is this happening? Jeﬀ Jones Ch 8 Sampling Distributions Central Limit Theorem Sampling Dist of the Mean Standard Error : The standard deviation of a sampling distribution If we took a regular distribution, we would have a range of values for people; with a sampling distribution we would have a range of values for means. It is what we would expect to obtain for a statistic! If we are trying to estimate a parameter, we would say that the variation of means is due to sampling error . Sampling error is very important → it is what we are trying to estimate in order to make conclusions about parameters for the rest of the semester. Jeﬀ Jones Ch 8 Notes Notes Notes Sampling Distributions Central Limit Theorem Sampling Distributions These are the steps to obtaining a sampling distribution: 1 Pick a population of interest, a statistic, and a sample size ( N ) 2 Randomly sample N observations from the population of interest 3 Calculate the statistic on those N observations 4 Throw everybody back into the pool 5 Repeat steps 24 an inﬁnite number of times 6 Plot the means, calculate statistics on the means An important point to note is that a sampling distribution is...
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This note was uploaded on 10/08/2010 for the course PSY 2801 taught by Professor Guyer during the Summer '08 term at Minnesota.
 Summer '08
 GUYER

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