Statistical Sciences 1024A/B Chapter 18: Chapter 18 - Inference in Practice

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Statistical Sciences
Statistical Sciences 1024A/B
Lori Murray

March 16, 2017 Chapter 18: Inference in Practice Thinking about inference (a conclusion reached on the basis of evidence and reasoning) o Procedures for statistical inference When the simple conditions are truedata are an SRS, the population has a Normal distribution The standard deviation of the population a confidence interval for the mean is To test a hypothesi0 H : 0 = we use the onesample z statistic: These are called z procedures because they both involve a one sample zstatistic and use the standard Normal distribution 18.1 Conditions for Inference in Practice o Where the data come from matters When you use statistical inference, you are acting as if your data are a random sample or come from a randomized comparative experiment If your data doesnt come from a random sample or random comparative experiment, your conclusions may be challenged Practical problems such as nonresponse or dropouts from an experiment can hinder inference Different methods are needed for different designs There is no cure for fundamental flaws like voluntary response o What is the shape of a population distribution? Many of the basic methods of inference are designed for Normal populations Fortunately, this condition is less essential than where the data comes from Any inference procedure based on sample statistics like the sample mean, x) that are not resistant to outliers can be strongly influenced by a few extreme observations In practice, the z procedures are reasonably accurate for any sample of at least moderate size from a fairly symmetric distribution o ** If the data does not come from a random sample or a randomized comparative experiment, the conclusions may be open to challenge. To answer the challenge, ask whether the data can be trusted as a basis for the conclusions of the study** 18.2 Cautions About Confidence Intervals o A sampling distribution shows how a statistic varies in repeated random sampling o This variation causes random sampling error because the statistic misses the true parameter by a random amount o The margin of error in a confidence interval ignores everything except the sampleto sample variation due to choosing the sample randomly
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