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AP STATISTICS LESSON 10 -3 (DAY 1)

AP STATISTICS LESSON 10 -3 (DAY 1). MAKING SENSE OF SATISTICAL SIGNIFICANCE. ESSENTIAL QUESTION: When does logic take precedence over statistics?. Objectives: To make decisions using both logic and statistical analysis. To use significance testing properly.

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AP STATISTICS LESSON 10 -3 (DAY 1)

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  1. AP STATISTICSLESSON 10 -3(DAY 1) MAKING SENSE OF SATISTICAL SIGNIFICANCE

  2. ESSENTIAL QUESTION: When does logic take precedence over statistics? Objectives: • To make decisions using both logic and statistical analysis. • To use significance testing properly

  3. Making Sense of Statistical Significance Significance tests are widely used in reporting the results of research in many fields of applied science and in industry. New pharmaceutical products require significant evidence of effectiveness and safety. In all these uses, statistical significance is valued because it points to an effect that is unlikely to occur simply by chance.

  4. Choosing a Level of Significance The purpose of a test of significance is to give a clear statement of the degree of evidence provided by the sample against the null hypothesis. The P-value does this. But sometimes you will make some decision or take some action if your evidence reaches a certain standard. A level of significance α sets such a standard.

  5. α level If you do use afixed α significance test to make a decision, choose α by asking: How much evidence is required to reject Ho? This depends mainly on two circumstances: • How plausible is Ho? If Ho represents an assumption that the people you must convince have believed for years, strong evidence (small α) will be needed to persuade them. • What are the consequences of rejecting Ho? If rejecting Ho in favor of Ha means making an expensive changeover from one type of product packaging to another, you need strong evidence that the new packaging will boost sales.

  6. Significance Level There is no sharp border between “significant” and “insignificant,” only increasingly strong evidence as the P-value decreases.

  7. Statistical Significance and Practical Significance When large samples are available, even tiny deviations from the null hypothesis will be significant. Remember the wise saying: Statistical significance is not the same thing as practical significance. • Plot your data and examine them carefully. • Are there outliers of other deviations from a consistent pattern?Outliers can destroy the significance of otherwise convincing data.

  8. Example 10.18 Page 588 Wound Healing Time • Mean healing time is 7.6 days with a standard deviation of • 1.4 days • Use a 5% significance level • Step 1. Identify the population of interest and the parameter you want to draw conclusions about • Step 2. Choose the appropriate inference procedure. Verify the conditions of using the selected procedure. • Step 3. If the conditions are met, carry out the inference procedure. • Step 4. Interpret your results in the context of the problem: • Since 0.0367 < α = 0.05, we reject Ho and conclude the healing effect is statistically significant, although not practically important (having your scab fall off half a day sooner is no big deal).

  9. Statistical inference is not valid for all sets of data. Badly designed surveys or experiments often produce invalid results.

  10. Example 10.19 Page 590 Does Music Increase Worker Productivity? Hawthorne effect – Any change in the work environment together with knowledge that a study is under way will produce a short-term productivity increase. This is the Hawthorne effect, named after the Western Electric manufacturing plant where it was first noted.

  11. Beware of Multiple Analyses Always ask how the data were produced, and don’t be too impressed by P-values on a printout until you are confident that the data deserve a formal analysis. Statistical significance ought to mean that you have found an effect that you were looking for. The reasoning behind statistical significance works well if you decide what effect you are seeking, design a study to search for it and a test of significance to weigh the evidence you get.

  12. Example 10.20 Page 591 Predicting Successful Trainees Running one test and reaching the α = .05 level is reasonably good evidence that you have found something. Running several dozen tests and reaching that level once or twice is not. The P-value assumes you had that specific difference in mind before you looked at the data. It is very misleading when applied to the largest of many differences. Searching data for suggestive patterns is certainly legitimate. Once you have a hypothesis, design a study to search specifically for the effect you now think is there. If the result of this study is statistically significant, you have real evidence.

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