The Investigation of Bartlett and Levene' s Test Statistics in Terms of Type I Error Rates in SmaII Samples
Öz
In this study, It was aimed that the investigation of Bartlett and Levene' s test statistics in terms of Type I error rates a. = 0.50, 0.25, 0.20, 0.15, 0.10, 0.05 and 0.01 in small samples. For this, samples had 3 and 4 treatment groups were drawn from a normal N 0.1 population and balanced equal sample sizes were increased from 2 to 30. In these samles, Type I error rates were obtained empirically. In order to obtain Type I error rates, 100000 replications were done for each sample sizes. In addition, the critical values of Bartlett and Levene's test statistics at a = O. 05 ve 0.01 Type I error levels were obtained from 1000000 replications for each sample sizes. As a result, It was emphasised that Bartlett's test is better
Anahtar Kelimeler
Bartlett's test Levene's test Type I error homogeneity of variance
Kaynakça
- Bishop, T. A. ve E. J. Dudewicz, 1978. Exact analysis of variance with unequal variances: Test procedures and tables, Technometrics, 20 (4) 419-424.
- Conover, W. J., M. E. Johnson, M. M. Johnson, 1981. A comperative study of test for homogeneity of variances with applications to the outer continental shelf bidding data, Technometrics, 23 (4) 351-361.
- Gartside, P. S. 1972. A study of methods for comparing several variances, JASA 67(338) 342-346.
- Geng, S., W. J. Wang, C. Miller, 1979. Small sample size comparisons of tests for homogeneity of variances with monte- carlo, Sim. Comp. B8 (4) 379-389.
- Keselman, H, J., P. A. Games, J. J. Clinch, 1979. Test for homogeneity of variance , Sim. Comp. B8 (2) 113-129.
- Lim, T. S., W. Y. Loh, 1996. A comparison of tests of equality of variances, Comput. Statis. and Data Analysis, 22, 287-301
- Lix, L. M. 1996. Consequences of assumption violations revised: A quantiative review of alternatives to the one-way analysis of variances F test, Review of Edu. Research 66 (4) 579- 619.
- Loh, W. Y. 1987. Some modifı cations of Levene's test of variance homogenity. J. Statist. Comput. Simul., 28, 213-226
Öz
Bu çal ışmada, Bartlett ve Levene test istatistiklerinin I. Tip hata bak ı m ı ndan incelenmesi amaçlanm ışt ı r. Bu amaçla; normal da ğı l ı m N 0,1 gösteren populasyondan 3 ve 4 gruplu örnekler al ı nm ış ve örnek genişliğ i her grupta eş it olacak şekilde 2' den ba ş lat ı larak 30' a kadar art ı rı lm ışt ı r. Bu örneklerde kararlaşt ı rı lan I. Tip hata; a = 0.50, 0.25, 0.20, 0.15, 0.10, 0.05 ve 0.01 oldu ğ unda, Bartett ve Levene test istatistikleri için gerçekle şen I. Tip hatalar ampirik olarak elde edilmiştir. Bunun için her örnek geni şliğinde 100000 deneme yap ı lm ışt ı r. Buna ilaveten a = O. 05 ve 0.01'deki Bartlett ve Levene istatistiklerinin kritik de ğ erleri de belirlenmi ştir. Bu değerlerin belirlenmesi için 1000000 deneme yap ı lmışt ı r. Sonuçta, Bartlett testinin I. Tip hata bak ı mı ndan daha iyi olduğu vurgulanm ışt ı r.
Anahtar Kelimeler
Bartlett testi Levene testi I. Tip hata varyanslar ı n homojenliği
Kaynakça
- Bishop, T. A. ve E. J. Dudewicz, 1978. Exact analysis of variance with unequal variances: Test procedures and tables, Technometrics, 20 (4) 419-424.
- Conover, W. J., M. E. Johnson, M. M. Johnson, 1981. A comperative study of test for homogeneity of variances with applications to the outer continental shelf bidding data, Technometrics, 23 (4) 351-361.
- Gartside, P. S. 1972. A study of methods for comparing several variances, JASA 67(338) 342-346.
- Geng, S., W. J. Wang, C. Miller, 1979. Small sample size comparisons of tests for homogeneity of variances with monte- carlo, Sim. Comp. B8 (4) 379-389.
- Keselman, H, J., P. A. Games, J. J. Clinch, 1979. Test for homogeneity of variance , Sim. Comp. B8 (2) 113-129.
- Lim, T. S., W. Y. Loh, 1996. A comparison of tests of equality of variances, Comput. Statis. and Data Analysis, 22, 287-301
- Lix, L. M. 1996. Consequences of assumption violations revised: A quantiative review of alternatives to the one-way analysis of variances F test, Review of Edu. Research 66 (4) 579- 619.
- Loh, W. Y. 1987. Some modifı cations of Levene's test of variance homogenity. J. Statist. Comput. Simul., 28, 213-226
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Research Article |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Ocak 2002 |
| Gönderilme Tarihi | 1 Ocak 2002 |
| Yayımlandığı Sayı | Yıl 2002 Cilt: 08 Sayı: 01 |
Cited By
BİLİMSEL HİKÂYELERLE DESTEKLENEN FEN ÖĞRETİMİNİN İLKOKUL ÖĞRENCİLERİNİN AKADEMİK BAŞARILARINA ETKİSİ
Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi
https://doi.org/10.17240/aibuefd.2022..-1097144
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