On Confidence Limits and Sufficiency, with Particular Reference to Parameters of Location

Welch, B. L.

doi:10.1214/aoms/1177732246

Cited by 56 publications

(31 citation statements)

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“…Better intervals are shorter on average, excluding false values more often (Lehmann, 1959;Neyman, 1937;1941;Welch, 1939). Consider a particular false value of the parameter, θ = θ .…”

Section: The Theory Of Confidence Intervalsmentioning

confidence: 99%

“…In this section, we present an example taken from the confidence interval literature (Berger and Wolpert, 1988;Lehmann, 1959;Pratt, 1961;Welch, 1939) designed to bring into focus how CI theory works. This example is intentionally simple; unlike many demonstrations of CIs, no simulations are needed, and almost all results can be derived by readers with some training in probability and geometry.…”

Section: Example 1: the Lost Submarinementioning

confidence: 99%

“…The third statistician, citing Welch (1939), describes a procedure that can be thought of as a slight modification of the nonparametric procedure. Suppose we obtain a particular confidence interval using the nonparametric procedure.…”

Section: The Uniformly Most-powerful Proceduresmentioning

confidence: 99%

“…In Bayesian terms, this procedure generates "credible intervals" for this prior. It can also be justified under Fisher's fiducial theory; see Welch (1939).…”

Section: An Objective Bayesian Proceduresmentioning

confidence: 99%

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The Fallacy of Placing Confidence in Confidence Intervals

Morey¹,

Wagenmakers²,

Hoekstra³

et al. 2014

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Interval estimates -estimates of parameters that include an allowance for sampling uncertainty -have long been touted as a key component of statistical analyses. There are several kinds of interval estimates, but the most popular are confidence intervals (CIs): intervals that contain the true parameter value in some known proportion of repeated samples, on average. The width of confidence intervals is thought to index the precision of an estimate; CIs are thought to be a guide to which parameter values are plausible or reasonable; and the confidence coefficient of the interval (e.g., 95 %) is thought to index the plausibility that the true parameter is included in the interval. We show in a number of examples that CIs do not necessarily have any of these properties, and can lead to unjustified or arbitrary inferences. For this reason, we caution against relying upon confidence interval theory to justify interval estimates, and suggest that other theories of interval estimation should be used instead. Electronic supplementary materialThe online version of this article

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“…Better intervals are shorter on average, excluding false values more often (Lehmann, 1959;Neyman, 1937;1941;Welch, 1939). Consider a particular false value of the parameter, θ = θ .…”

Section: The Theory Of Confidence Intervalsmentioning

confidence: 99%

Section: Example 1: the Lost Submarinementioning

confidence: 99%

Section: The Uniformly Most-powerful Proceduresmentioning

confidence: 99%

“…In Bayesian terms, this procedure generates "credible intervals" for this prior. It can also be justified under Fisher's fiducial theory; see Welch (1939).…”

Section: An Objective Bayesian Proceduresmentioning

confidence: 99%

See 2 more Smart Citations

The Fallacy of Placing Confidence in Confidence Intervals

Morey¹,

Wagenmakers²,

Hoekstra³

et al. 2014

PsycEXTRA Dataset

View full text Add to dashboard Cite

show abstract

“…( 4.15.4) Welch (1939), referring to R as labelling 'samples of the same configuration' , and to r as labelling 'the actual configuration observed' , expresses this:…”

Section: When Operating Characteristics Are Irrelevantmentioning

confidence: 99%