Statistical Sciences 1024A/B Lecture Notes - Lecture 16: Central Limit Theorem, Simple Random Sample, Statistical Inference
14 May 2016
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Document Summary
When using a statistical inference, you are acting as if your data are a probability sample or come from a randomized experiment. Statistical confidence intervals and tests cannot remedy basic flaws in producing the data, such as voluntary response samples or uncontrolled experiments. Requirements: the data must be an srs, simple random sample, of the population. More complex sampling designs require more complex inference methods: the sampling distribution must be approximately normal. This is not true in all instances: we must know s, the population standard deviation. Nothing can overcome a poor design: outliers influence averages and therefore your conclusions as well. The margin of error in a confidence interval only covers random sampling errors. Practical difficulties such as under coverage and nonresponse are more serious than random sampling error. The margin of error doesn"t take these difficulties into account. If you believe that h0 is probably true, you will want strong evidence (a small p-value) to reject it.
