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Lecture 10

Lecture 10 - Sampling Pt 2.docx

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Western University
Psychology 2800E
Doug Hazlewood

Sampling (Part 2): Sample Size & Sampling Error Prologue All of Today’s Discussion  Involves statistics - (W&M ch 15, p. 387-389)  Assumes we have probability (random) samples. Generated through a simple random sampling process  When dealing with non-random samples, it is difficult to talk about sample size or sampling error Part 1: Sampling Error (and a “thought experiment”) A. Estimating mean midterm grade from random sample of 10 midterm grades.  120 grades in a hat; with replacement; add and divide by ten for mean; suppose  sample mean = 75%  Is this an accurate estimate of population (class) mean?  No! (class mean was 70%).  Lesson: Sample means contain “random” error.  Another sample might be 5% lower, etc B. How much random error is associated with our sample mean?  Generate more random samples of 10 (with replacement: select 10, put back; select 10…)  S1 = 75%; S2 = 65%... S1000 = 73%  If we plot these means, we’ll get a “sampling distribution” (distribution of sample means that are randomly selected from the same population).  Things to note about sampling distribution:  The means from a “normal” distribution (bell shaped curve)  With large number of samples, the mean of the sampling distribution is the same as the mean of the population  Standard deviation of sampling distribution (how “spread out” means are) is a measure of how much error is in the sample means (more spread, more error) Q: What would happen if we chose 1000 samples of 20 (instead of 1000 samples of 10)?  We’d get another sampling distribution  Mean would be the same, but  Because the size of each sample is larger, the distribution will have a smaller standard deviation  Each sample mean will be closer to the population mean (indicating each mean has less error)  Can use a formula to estimate how much sampling error is associated with samples of any size:  Standard error of population mean (SEM) = standard deviation of population, divided by the square root of the sample size (see p. 387) Next 2 sides are on handout (#8 & 9) Part 2: Back to Reality  We don’t choose 1000’s of samples to study!  Instead, we choose one sample with one mean (and some “random error” – sample mean won’t necessarily be the same as the population mean)  Can estimate t
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