An Accumulate-Toward-the-Mode Approach to Confidence Intervals and Hypothesis Testing With Applications to Binomially Distributed Data

The Merits of Confidence Intervals Relative to Hypothesis Testing

Infection Control and Hospital Epidemiology ◽

10.1086/646596 ◽

1992 ◽

Vol 13 (9) ◽

pp. 553-555 ◽

Cited By ~ 2

Author(s):

Leon F. Burmeister ◽

David Bimbaum ◽

Samuel B. Sheps

Keyword(s):

Hypothesis Testing ◽

Confidence Intervals ◽

Null Hypothesis ◽

Finite Population ◽

Extreme Values ◽

Statistical Tests ◽

Point Estimate ◽

Distributed Data ◽

Average Difference ◽

Average Value

A variety of statistical tests of a null hypothesis commonly are used in biomedical studies. While these tests are the mainstay for justifying inferences drawn from data, they have important limitations. This report discusses the relative merits of two different approaches to data analysis and display, and recommends the use of confidence intervals rather than classic hypothesis testing.Formulae for a confidence interval surrounding the point estimate of an average value take the form: d= ±zσ/√n, where “d” represents the average difference between central and extreme values, “z” is derived from the density function of a known distribution, and “a/-∨n” represents the magnitude of sampling variability. Transposition of terms yields the familiar formula for hypothesis testing of normally distributed data (without applying the finite population correction factor): z = d/(σ/√n).

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Uncertainty and Inference for Verification Measures

Weather and Forecasting ◽

10.1175/waf989.1 ◽

2007 ◽

Vol 22 (3) ◽

pp. 637-650 ◽

Cited By ~ 74

Author(s):

Ian T. Jolliffe

Keyword(s):

Hypothesis Testing ◽

Confidence Intervals ◽

Multiple Testing ◽

Prediction Intervals ◽

Hypothesis Tests ◽

Statistical Inferences ◽

The Difference ◽

Main Ideas

Abstract When a forecast is assessed, a single value for a verification measure is often quoted. This is of limited use, as it needs to be complemented by some idea of the uncertainty associated with the value. If this uncertainty can be quantified, it is then possible to make statistical inferences based on the value observed. There are two main types of inference: confidence intervals can be constructed for an underlying “population” value of the measure, or hypotheses can be tested regarding the underlying value. This paper will review the main ideas of confidence intervals and hypothesis tests, together with the less well known “prediction intervals,” concentrating on aspects that are often poorly understood. Comparisons will be made between different methods of constructing confidence intervals—exact, asymptotic, bootstrap, and Bayesian—and the difference between prediction intervals and confidence intervals will be explained. For hypothesis testing, multiple testing will be briefly discussed, together with connections between hypothesis testing, prediction intervals, and confidence intervals.

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