Sains Malaysiana 40(10)(2011): 1187–1191

 

Kaedah Alexander-Govern Terubah Suai sebagai Alternatif

kepada Ujian-t dan Ujian F ANOVA

(Modified Alexander-Govern Test as Alternative to t-test and ANOVA F Test)

 

 

Suhaida Abdullah*

Kolej Sastera dan Sains, Bangunan Sains Kuantitatif, Universiti Utara Malaysia,

06010 Sintok, Kedah, Malaysia

 

Sharipah Soaad Syed Yahaya

Kolej Sastera dan Sains, Bangunan Sains Kuantitatif, Universiti Utara Malaysia

06010 Sintok, Kedah, Malaysia

 

Abdul Rahman Othman

Institut Pengajian Siswazah, Universiti Sains Malaysia, Minden Pulau Pinang, Malaysia

 

Received: 7 July 2010/Accepted: 17 January 2011

 

ABSTRAK

Ujian Alexander-Govern merupakan ujian kesamaan sukatan memusat yang teguh pada keadaan varians heterogen. Malangnya ujian ini tidak teguh pada keadaan data tidak normal. Adaptasi penganggar teguh seperti penganggar M satu langkah terubah suai (MOM) sebagai sukatan memusat menggantikan min didapati berupaya meningkatkan keteguhan ujian ini apabila dijalankan pada data terpencong. Penganggar ini mempunyai kelebihan berbanding min kerana tidak dipengaruhi oleh data yang tidak normal. Kajian ini mendapati bahawa ujian Alexander-Govern yang telah diubah suai ini berupaya mengawal Ralat Jenis I dengan baik pada data terpencong untuk semua keadaan. Kadar Ralat Jenis I yang dihasilkan kebanyakannya berada di dalam selang kriteria teguh ketat (0.045 hingga 0.055) pada aras keertian 0.05. Berbeza dengan kaedah pengujian asal yang mana pada kebanyakan keadaan, ujian teguh tetapi hanya dengan kriteria liberal (0.025 hingga 0.075), malahan ada kedaan yang mana ujian tidak teguh. Prestasi kaedah yang diubah suai ini juga setanding dengan keadah asal pada keadaan data normal. Kajian ini juga membandingkan kaedah Alexander Govern yang diubah suai dengan kaedah pengujian klasik seperti ujian-t dan ANOVA dan menyaksikan bahawa kaedah klasik tidak teguh pada keadaan varians heterogen.

 

Kata kunci: Penganggar M satu langkah terubah suai; ujian Alexander-Govern; ujian teguh

 

 

ABSTRACT

Alexander-Govern test is a test of equality of central tendency measure that is robust to the heterogeneity of variances. Unfortunately, this test is not robust to nonnormal data. Adaptation of robust estimator such as modified one step M estimator (MOM) as the central tendency measure in place of the mean improves the robustness of the test when dealing with skewed data. This estimator has the advantage over the mean since it is not easily influenced by non normal data. This study showed that the modified Alexander-Govern test has good control Type I Error for all conditions under skewed data. The rates of Type I Error produced are mostly within the stringent criteria of robustness (0.045 to 0.055) at the significance level of 0.05. Even though the original test is robust in most conditions, the values of Type I error are only within the liberal criteria of robustness (0.025 to 0.075), and there are conditions where the test is not robust. The performance of the modified test is also as good as the original test in normal data. This study also compared the modified Alexander Govern test with classical tests such as t-test and ANOVA and it is shown that the classical tests are not robust to condition of variance heterogeneity.

 

Keywords: Alexander-Govern test; modified one step M estimator; robust test

 

REFERENCES

Alexander, R.A., & Govern, D.M. 1994. A new and simpler approximation for ANOVA under variance heterogeneity. Journal of Educational Statistics 19(2): 91-101.

Bradley, J.V. 1978. Robustness? British Journal of Mathematical and Statistical Psychology (31): 144-152.

Efron, B. & Tibshirani, R.J. 1993. An Introduction to the Bootstrap New York: Chapman & Hall, Inc.

Hoaglin, D.C., Mosteller, F. & Tukey, J.W. 1983. Understanding Robust and Exploratory Data Analysis: New York: John Wiley & Sons, Inc.

Myers, L. 1998. Comparability of the James’ second-order approximation test and the Alexander and Govern A statistic for non-normal heteroscedastic data. Journal of Statistical Computational Simulation 60: 207-222.

SAS Institute Inc. 2009. SAS/IML 9.2 User’s guide. SAS Institute Inc, Cary, NC.

Schneider, P.J. & Penfield, D.A. 1997. Alexander and Govern’s approximation: Providing an alternative to ANOVA under variance heterogeneity. Journal of Experimental Education 65(3): 271-287.

Syed Yahaya, S.S., Othman, A.R. & Keselman, H.J. 2006. Comparing the “typical score” across independent groups based on different criteria for trimming. Metodološki zvezki, 3(1): 49-62.

Wilcox, R.R. 2005. Introduction to robust estimation and hypothesis testing (2nded.): California: Academic Press.

 

 

*Corresponding author; email: suhaida@uum.edu.my

   

 

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