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# notes6 - Slide 1 Estimating Parameters Slide 2 Parameter...

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Unformatted text preview: Slide 1 Estimating Parameters ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 2 Parameter Estimation We use statistics to estimate parameters, e.g., effectiveness of pilot training, psychotherapy. We want to know how good our estimates are. Most common ways to examine goodness of a statistic as an estimator are bias and standard error . We will define both, but first: µ → X σ → SD ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 3 Sampling Distribution • A sampling distribution is a distribution of a statistic over many samples. • To get a sampling distribution, – 1. Take a sample of size N (a given number like 5, 10, or 1000) from a population – 2. Compute the statistic (e.g., the mean) and record it. – 3. Repeat 1 and 2 a lot (infinitely). – 4. Plot the resulting sampling distribution, a distribution of a statistic over repeated samples . ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 4 Sampling Distribution • Class exercise • Find some people’s height, graph it. Find the mean. • Take subsamples of different sizes N and compute mean height. Graph the results. • What happens as N gets larger? ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 5 Bias • If the mean of the sampling distribution equals the parameter, the statistic is said to be unbiased . • If the mean of the sampling distribution does not equal the parameter, the statistic is biased. • The mean is an unbiased estimator. The average value of is . X µ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 6 Bias • The sample standard deviation and variance are biased estimators of their population values. Fortunately, the estimators can be made unbiased with a simple correction. Use N-1 instead of N in the denominator. All stat packages (SPSS) do this....
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notes6 - Slide 1 Estimating Parameters Slide 2 Parameter...

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