Lecture03

# Lecture03 - Toward statistical inference The techniques of...

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Producing data: - Towards Inference Section 3.3 © 2009 W.H. Freeman and Company Toward statistical inference The techniques of inferential statistics allow us to draw inferences or conclusions about a population in a sample. ! Your estimate of the population is only as good as your sampling design. " Work hard to eliminate biases. ! Your sample is only an estimate—and if you randomly sampled again you would probably get a somewhat different result. ! The bigger the sample the better. Population Sample Sampling variability Each time we take a random sample from a population, we are likely to get a different set of individuals and a calculate a different statistic. This is called sampling variability . The good news is that, if we take lots of random samples of the same size from a given population, the variation from sample to sample—the sampling distribution —will follow a predictable pattern. All of statistical inference is based on this knowledge. The variability of a statistic is described by the spread of its sampling distribution. This spread depends on the sampling design and the sample size n, with larger sample sizes leading to lower variability. # Large random samples are almost always close estimates of the true population parameter. However, this only applies to random samples. Consider “QuickVote” online surveys. They are worthless no matter how many people participate because they use a voluntary sampling design and not random sampling.

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Managing Bias and Variability ! To reduce bias , use random sampling. The values of a statistic computed from an SRS neither consistently overestimate or underestimate the value of a population parameter. ! To reduce the variability of a statistic from an SRS, use a larger sample. You can make the variability as small as you want by taking a large enough sample. ! Population size doesn’t matter : The variability of a statistic from a random sample does not depend on the size of the population, as long as the population is at least 100 times larger than the sample. Practical note Large samples are not always attainable. ! Sometimes the cost, difficulty, or preciousness of what is studied limits drastically any possible sample size ! Blood samples/biopsies: No more than a handful of repetitions acceptable. We often even make do with just one. ! Opinion polls have a limited sample size due to time and cost of operation. During election times though, sample sizes are increased for better accuracy. Producing data: - Data Ethics Section 3.4 © 2009 W.H. Freeman and Company Read This Section Yourself! Pay Particular Attention To: ! Institutional review boards ! Informed consent ! Confidentiality ! Clinical trials ! Behavioral and social science experiments See the Reading Notes for more details.
Probability and Sampling Distributions - Randomness and Probability Models Sections 4.1 and 4.2 © 2009 W.H. Freeman and Company A phenomenon is random if individual outcomes are uncertain, but there is nonetheless a regular distribution of

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## This note was uploaded on 12/11/2009 for the course STAT 212 taught by Professor Holt during the Spring '08 term at UVA.

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Lecture03 - Toward statistical inference The techniques of...

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