ON THE COMPARISON OF THE WELCH TEST AND THE SINGLE-STAGE TEST: A SIMULATION STUDY

Yıl 2007, , 51 - 61, 01.08.2007

Meltem Ekiz Hamza Gamgam

https://doi.org/10.1501/Commua1_0000000189

Öz

It is known that using the F test for testing the equality of meansin a one-way ANOVA is misleading when the assumption of equal populationvariances is violated. When the variances are unknown and unequal, Welch[1] developed the so-called Welch test and Chen and Chen [2] developed thesingle-stage test for ANOVA. In this paper, Welch and single-stage tests arecompared in terms of their powers and the reject ratios of the hypothesis whenthe hypothesis is true. Simulation results indicate that the power of the singlestage test is better than the Welch test and that this test performs well in termsof the reject ratios for small number of populations and sample sizes

Anahtar Kelimeler

One-way ANOVA, heteroscedasticity, single-stage test, Welch test

Kaynakça

• Welch, B.L., On the comparison of several mean values: an alternative approach, Biometrica, 38, 330-336, 1951. [2] Chen, S.Y., ChenH.J., Single-stage analysisof varianceunderheteroscedasticity, Commun.Statist.-Simula, 27(3), 641-666, 1998.
• Cochran, W.G., Problems arising in the analysis of a series of similar experiments, Journal of the Royal Statistical Society, Suppl. 4, 102-118, 1937.
• James, G.S., The comparison of several groups of observations when the ratios of the population variances are unknown, Biometrika, 38, 324-329, 1951.
• Brown, M.B., Forsythe, A.B, The small-sample behavior of some statistics which test the equality of several means, Technometrics, 16, 129-132, 1974.
• Dudewicz, E.J. and Dalal, S.R., Allocations of observations in ranking and selection with unequal variances, Sankhya, 37B, 28-78, 1975.
• Bishop, T.A. and Dudewicz, E.J., Exact analysis of variance with unequal variances: test procedures and tables, Technometrics, 20, 419-430, 1978.
• Kulinskaya, E., Staudte, R.G. and Gao, H., Power approximations in testing for unequal means in a one-way ANOVA weighted for unequal variances, Communications in Statistics-Theory and Methods, 32(12), 2353-2371, 2003. Current address : Gazi University, Faculty of Arts and Science, Department of statistics, Ankara, Turkey E-mail address : [e-mail], [e-mail]