# Student's t

## Definition

### Health Economics

- A test based on the t-distribution: where is the sample mean, is the population mean and s is the sample standard deviation. This is a method of comparing a sample mean with a hypothesized value, or of comparing two sample means, or of testing whether the slope of a regression line differs statistically significantly from zero. The decision rule is to reject the null hypothesis when estimated t is larger than a critical value, that is, reject the null if the p-value of t is less than 0.05. It was invented by William Gossett (1876-1937) a chemist employed by Guinness in Dublin and, later, London. He used the nom-de-plume 'Student' because Guinness employees were not permitted to publish. The only other students in question seem to have been Mr. Gossett's consumers (of his extensive statistical work, of course).

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