推断比例
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Kerrich: Is a Coin Fair?
Inference for One Proportion
Using outcomes for 10,000 flips of a coin, use descriptive statistics, confidence intervals and hypothesis tests to determine whether the coin is fair. Key ideas: Practical Importance Versus Statistical Significance, Low Power.
JMP features demonstrated:
Analyze > Distribution, Formula Editor, Analyze > Fit Y by X
Statistical/Graphical Tools Used:
Bar charts, confidence intervals for proportions, hypothesis testing for proportions, Likelihood Ratio, simulating random data, scatterplot, fitting a regression line.
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Lister and the Germ Theory
Two Sample Proportions
Use results from a 1860’s sterilization study to determine if there is evidence that the sterilization process reduces deaths when amputations are performed. Key ideas: Practical importance and statistical significance, observational studies, relative risk, scope of inference.
JMP features demonstrated:
Analyze > Fit Y by X
Statistical/Graphical Tools Used:
Mosaic plots, contingency tables, Pearson and likelihood ratio tests, Fisher's exact test, two-sample propotions test, one- and two-sided tests, confidence interval for the difference, relative risk.
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Salk Vaccine
Relative Risk
Using data from a 1950’s study, determine whether the polio vaccine was effective in a cohort study, and, if it was, quantify the degree of effectiveness. Key ideas: Relative risk, observational study, cohort study, randomized experiments.
JMP features demonstrated:
Analyze > Distribution
Statistical/Graphical Tools Used:
Bar charts, two-sample proportions test, relative risk, two-sided Pearson and likelihood ratio tests, Fisher's exact test, and the Gamma measure of association.
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Smoking and Lung Cancer
Odds Ratio for Retrospective Analysis
Use the results of a retrospective study to determine if there is a positive association between smoking and lung cancer, and to (through mathematical manipulations) estimate the risk of lung cancer for smokers relative to non-smokers. Conditional Probability, Odds, Retrospective Observational Study.
JMP features demonstrated:
Analyze > Fit Y by X, the Value Ordering column property
Statistical/Graphical Tools Used:
Mosaic plots, two-by-two contingency tables, odds ratios and confidence intervals for odds ratios, hypothesis tests for proportions (likelihood ratio, Pearson's, Fisher's Exact, two sample tests for proportions).
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Mendel’s Laws of Inheritance
Chi-squared Goodness-of-Fit Test and Chi-squared Test for Two-Way tables
Use the data sets provided to explore Mendel’s Laws of Inheritance for dominant and recessive traits. Key ideas: Genetic linkage, independence, laws of probability.
JMP features demonstrated:
Analyze > Distribution, Analyze > Fit Y by X, the Value Ordering column property
Statistical/Graphical Tools Used:
Bar charts, frequency distributions, goodness-of-fit tests, mosaic plot, hypothesis tests for proportions.
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