Inference for Proportions

  • 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.

  • 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.

  • 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.

  • 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).

  • 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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