Chapter16

# The Basic Practice of Statistics (Paper) & Student CD

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Inference in practice BPS chapter 16 © 2006 W.H. Freeman and Company

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Objectives (BPS chapter 16) Inference in practice Where did the data come from? Cautions about z procedures Cautions about confidence intervals Cautions about significance tests The power of a test Type I and II errors
When you use statistical inference, you are acting as if your data are a probability sample or come from a randomized experiment. Statistical confidence intervals and hypothesis tests cannot remedy basic flaws in producing the data , such as voluntary response samples or uncontrolled experiments. Where did the data come from?

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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 σ , the population standard deviation. This is often an unrealistic requisite. We'll see what can be done when σ is unknown in the next chapter. Caution about z procedures
We cannot use the z procedure if the population is not normally distributed and the sample size is too small because the central limit theorem will not work and the sampling distribution will not be approximately normal. Poorly designed studies often produce useless results (e.g., agricultural studies before Fisher). Nothing can overcome a poor design. Outliers influence averages and therefore your conclusions as well. Distr. of 1 observation Distr. for avg. of 2 observations Distr. for avg. of 10 observations Distr. for avg. of 25 observations

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The margin of error does not cover all errors: The margin of error in a confidence interval covers only random sampling error. Undercoverage, nonresponse, or other forms of bias are often more serious than random sampling error (e.g., our elections polls). The margin of error does not take these into account at all. Cautions about confidence intervals
How small a P -value is convincing evidence against H 0 ?

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