Chapter_15

# Chapter_15 - Chapter 15 Thinking about Inference BPS 5th Ed...

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BPS - 5th Ed. Chapter 15 1 Chapter 15 Thinking about Inference

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BPS - 5th Ed. Chapter 15 2 If we know the standard deviation σ of the population, a confidence interval for the mean μ is: To test a hypothesis H 0 : = 0 we use the one-sample z statistic: These are called z procedures because they both involve a one-sample z statistic and use the standard Normal distribution. z Procedures n σ μ x z 0 - = n σ z x ±
BPS - 5th Ed. Chapter 15 3 Conditions for Inference in Practice The data must be an SRS from the population (ask: “where did the data come from?”). Different methods are needed for different designs. The z procedures are not correct for samples other than SRS. Outliers can distort the result. The sample mean is strongly influenced by outliers. Always explore your data before performing an analysis. The shape of the population distribution matters. Skewness and outliers make the z procedures untrustworthy unless the sample is large. In practice, the z procedures are reasonably accurate for any sample of at least moderate size from a fairly symmetric distribution. The population standard deviation σ must be known. Unfortunately is rarely known, so z procedures are rarely useful. Chapter 17 will introduce procedures for when is unknown.

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BPS - 5th Ed. Chapter 15 4 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 tests cannot remedy basic flaws in producing data, such as voluntary response samples or uncontrolled experiments. Also be aware of nonresponse or dropouts in well-designed studies. If the data do not come from a probability sample or a randomized 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. Where Did the Data Come From?
BPS - 5th Ed. Chapter 15 5 Case Study Mammary Artery Ligation Surgeons tested a procedure to alleviate pain caused by inadequate blood supply to the heart, and the patients reported a statistically significant reduction in angina pain. Barsamian, E. M., “The rise and fall of internal mammary artery ligation,” Costs, Risks, and Benefits of Surgery , Bunker, Barnes, and Mosteller (eds.), Oxford University Press, 1977, pp. 212-220.

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BPS - 5th Ed. Chapter 15 6 Case Study Mammary Artery Ligation Statistical significance indicates that something other than chance is at work, but it does not say what that something is. Since this experiment was not controlled, the reduction in pain could be due to the placebo effect. A controlled experiment showed that this was the case, and surgeons immediately stopped performing the operation.
BPS - 5th Ed. Chapter 15

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## This note was uploaded on 08/27/2011 for the course MA 116 taught by Professor Muntheralraban during the Summer '11 term at Montgomery CC.

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Chapter_15 - Chapter 15 Thinking about Inference BPS 5th Ed...

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