2 Some Tests Based on the Binomial Distribution
Definition 2.1 (Binomial distribution). A random variable \(X\) counting the occurrences of some outcome in a fixed number \(n\) of observations is Binomial, written \(X\thicksim B(n,P)\), if
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- each observation falls into one of just two categories, success or failure;
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- the \(n\) observations are independent;
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- the probability \(P\) of success is the same for every observation.
The tests of this chapter — the sign test, the binomial test and the quantile test — all reduce the data to a count of successes and so all rest on this one distribution. The reduction is what makes them distribution-free: whatever the shape of the population, the count of observations falling on one side of a hypothesised value is binomial, and nothing further need be assumed.
2.1 Sign Test
2.2 Confidence Interval for the Median
2.3 Order Statistics
2.4 Quantile Functions
2.5 Percentile and Quartile
2.6 Quartile Test
2.7 Practice Problems
2.2 Confidence Interval for the Median
2.3 Order Statistics
2.4 Quantile Functions
2.5 Percentile and Quartile
2.6 Quartile Test
2.7 Practice Problems
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