6_ParameterEst

# 6_ParameterEst - Estimating Parameters Parameter Estimation...

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Estimating Parameters

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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
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 .

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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?
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

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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. 1 ) ( ˆ 2 2 - - = N X X σ 1 ) ( ˆ 2 - - = N X X (hat means sample estimate of parameter)
Standard Error We would like the statistic to be unbiased so we know that on average, the statistic equals the mean. We would like all the estimates to be close to

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## This note was uploaded on 05/21/2011 for the course PSY 3213 taught by Professor Staff during the Fall '08 term at University of South Florida.

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6_ParameterEst - Estimating Parameters Parameter Estimation...

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