### Abstract

This study proposes an approach for determining appropriate sample size for Welch's F test when unequal variances are expected. Given a certain maximum deviation in population means and using the quantile of F and t distributions, there is no need to specify a noncentrality parameter and it is easy to estimate the approximate sample size needed for heterogeneous one-way ANOVA. The theoretical results are validated by a comparison to the results from a Monte Carlo simulation. Simulation results for the empirical power indicate that the sample size needed by the proposed formulas can almost always achieve the desired power level when Welch's F test is applied to data that are conditionally nonnormal and heterogeneous. Two illustrative examples of the use of the proposed procedure are given to calculate balanced and optimal sample sizes, respectively. Moreover, three sample size tables for two-, four-, and six-group problems are provided, respectively, for practitioners.

Original language | English |
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Pages (from-to) | 959-971 |

Number of pages | 13 |

Journal | Educational and Psychological Measurement |

Volume | 68 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2008 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Education
- Developmental and Educational Psychology
- Applied Psychology
- Applied Mathematics

### Cite this

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**Approximate sample size formulas for testing group mean differences when variances are unequal in one-way ANOVA.** / Guo, Jiin Huarng; Luh, Wei-Ming.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Approximate sample size formulas for testing group mean differences when variances are unequal in one-way ANOVA

AU - Guo, Jiin Huarng

AU - Luh, Wei-Ming

PY - 2008/1/1

Y1 - 2008/1/1

N2 - This study proposes an approach for determining appropriate sample size for Welch's F test when unequal variances are expected. Given a certain maximum deviation in population means and using the quantile of F and t distributions, there is no need to specify a noncentrality parameter and it is easy to estimate the approximate sample size needed for heterogeneous one-way ANOVA. The theoretical results are validated by a comparison to the results from a Monte Carlo simulation. Simulation results for the empirical power indicate that the sample size needed by the proposed formulas can almost always achieve the desired power level when Welch's F test is applied to data that are conditionally nonnormal and heterogeneous. Two illustrative examples of the use of the proposed procedure are given to calculate balanced and optimal sample sizes, respectively. Moreover, three sample size tables for two-, four-, and six-group problems are provided, respectively, for practitioners.

AB - This study proposes an approach for determining appropriate sample size for Welch's F test when unequal variances are expected. Given a certain maximum deviation in population means and using the quantile of F and t distributions, there is no need to specify a noncentrality parameter and it is easy to estimate the approximate sample size needed for heterogeneous one-way ANOVA. The theoretical results are validated by a comparison to the results from a Monte Carlo simulation. Simulation results for the empirical power indicate that the sample size needed by the proposed formulas can almost always achieve the desired power level when Welch's F test is applied to data that are conditionally nonnormal and heterogeneous. Two illustrative examples of the use of the proposed procedure are given to calculate balanced and optimal sample sizes, respectively. Moreover, three sample size tables for two-, four-, and six-group problems are provided, respectively, for practitioners.

UR - http://www.scopus.com/inward/record.url?scp=56749151318&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56749151318&partnerID=8YFLogxK

U2 - 10.1177/0013164408318759

DO - 10.1177/0013164408318759

M3 - Article

VL - 68

SP - 959

EP - 971

JO - Educational and Psychological Measurement

JF - Educational and Psychological Measurement

SN - 0013-1644

IS - 6

ER -