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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
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D.M. 1994. A new and simpler approximation for ANOVA under variance
heterogeneity. Journal of Educational Statistics 19(2): 91-101.
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*Corresponding author; email: suhaida@uum.edu.my
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