Two-sided Exact Tests and Matching Confidence Intervals for Discrete Data

Two-sided Exact Tests and Matching Confidence Intervals for Discrete Data

There is an inherent relationship between two-sided hypothesis tests and confidence intervals. A series of two-sided hypothesis tests may be inverted to obtain the matching 100(1-α)% confidence interval defined as the smallest interval that contains all point null parameter values that would not be rejected at the α level. Unfortunately, for discrete data there are several different ways of def...

Confidence Intervals for the Power of Two-Sided Student’s t-test

For the power of two-sided hypothesis testing about the mean of a normal population, we derive a 100(1 − alpha)% confidence interval. Then by using a numerical method we will find a shortest confidence interval and consider some special cases.

Exact Confidence Intervals

Exact average coverage probabilities and confidence coefficients of confidence intervals for discrete distributions

For a confidence interval (L(X),U(X)) of a parameter θ in one-parameter discrete distributions, the coverage probability is a variable function of θ . The confidence coefficient is the infimum of the coverage probabilities, infθ Pθ (θ ∈ (L(X),U(X))). Since we do not know which point in the parameter space the infimum coverage probability occurs at, the exact confidence coefficients are unknown....

Confidence Intervals and Hypothesis Tests

Overview: Recall that a point estimator for a parameter of interest is a statistic which is a function of the random variables from which our sampling method chooses values. The properties of such an estimator, such as having a small bias or a small mean square error, are usually dependent only upon certain features of the sampling distribution of the statistic, such as its mean or variance. Ho...