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 conclusions about a population using 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 likely get a somewhat different result. ! The bigger the sample the better. Population Sample Terms ! Parameter – a measure that describes a population. ! This value is fixed, yet almost always unknown ! Example: the population mean, μ ! Statistic – A measure that describes a sample. ! This value can vary from sample to sample but is known when we have the sample. ! Example: the sample mean, 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 . If we take many random samples of the same size from a given population, the variation from sample to sample—the sampling distribution —will follow a predictable pattern.
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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. 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. Bias and Variability ! Bias – concerns the center of the sampling distribution. ! Unbiased: when the mean of the sampling distribution is equal to the parameter. ! Variability – described by the spread of the sampling distribution ! Determined by design ! Larger samples yield smaller spreads 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. !
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This note was uploaded on 02/16/2010 for the course STAT 212 taught by Professor Holt during the Fall '08 term at UVA.

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Lecture03 - Toward statistical inference The techniques of...

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