What question did this study set out to answer?

To reformulate standard hypothesis tests of equal means into a single-sample multiple decision framework for ranking means from normal distributions with known variances.

March 1, 1954The Annals of Mathematical StatisticsOpen Access

A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with known Variances

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Authors

RBRobert E. BechhoferCornell University

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Implication

Methodological study demonstrates a sample-size framework for ranking means in normal populations with known variances, suggesting an actionable alternative to standard analysis of variance.

Key Points

To reformulate standard hypothesis tests of equal means into a single-sample multiple decision framework for ranking means from normal distributions with known variances.
Reformulated Model I analysis of variance (ANOVA) tests into multiple decision procedures for population mean rankings.
Derived formulas to calculate predetermined sample sizes per population based on a specified probability of correct ranking and defined minimum mean differences.
Established an experimental design approach that guarantees a target probability of correctly ranking k normal population means.
Provided an exact method to compute required sample sizes when differences between population means and variance levels are specified in advance.

Cite This Study

Robert E. Bechhofer (1954) studied this question.

synapsesocial.com/papers/6a0ef52d25c30b2cc7f9f87d https://doi.org/10.1214/aoms/1177728845

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Implication

Methodological study demonstrates a sample-size framework for ranking means in normal populations with known variances, suggesting an actionable alternative to standard analysis of variance.

A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with known Variances

Discussion

Member takes

Implication

Key Points

Cite This Study

A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with known Variances

Discussion

Member takes

Implication

Key Points

Cite This Study

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