# JMP Case Study Library

## Inference for Proportions

• ### 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.

• ### 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.

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