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Dergiler / International Journal of Assessment Tools in Education / 2026 / Volume: 10 Issue: 4

Comparison of cronbach’s alpha and McDonald’s omega for ordinal data: Are they different?

Fatih Orçan(Kahramanmaraş Sütçü İmam Üniversitesi)0000-0003-1727-0456
Sayfa
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Yayın Tarihi
2023-12-23
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Therefore, alpha should be used for the reliability estimations.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Among all, Cronbach’s Alpha and McDonald’s Omega are commonly used for reliability estimations.
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Temel Bulgular & Veri:Their performances were compared according to the sample size, number of items, and deviance from tau equivalence.
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Sonuç & Katkı:Therefore, alpha should be used for the reliability estimations.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Cronbach’s Alpha · McDonald’s Omega · Reliability

Özet

Among all, Cronbach’s Alpha and McDonald’s Omega are commonly used for reliability estimations. The alpha uses inter-item correlations while omega is based on a factor analysis result. This study uses simulated ordinal data sets to test whether the alpha and omega produce different estimates. Their performances were compared according to the sample size, number of items, and deviance from tau equivalence. Based on the result, the alpha and omega had similar results, except for the small sample size, the smaller number of items, and the low factor loading values. When there were 5 or more items in the scale and factor analysis which the omega was calculated from showed fit to the data set, using omega over alpha could be preferred. Also, as the number of items exceeds 5, the alpha and omega differences disappear. Since calculating the alpha is easier compared to the omega (omega requires fitting a factor model first) using alpha over omega can also be suggested. However, when the number of items and the correlations among the items were small, omega performed worse than alpha. Therefore, alpha should be used for the reliability estimations.

Abstract

Among all, Cronbach’s Alpha and McDonald’s Omega are commonly used for reliability estimations. The alpha uses inter-item correlations while omega is based on a factor analysis result. This study uses simulated ordinal data sets to test whether the alpha and omega produce different estimates. Their performances were compared according to the sample size, number of items, and deviance from tau equivalence. Based on the result, the alpha and omega had similar results, except for the small sample size, the smaller number of items, and the low factor loading values. When there were 5 or more items in the scale and factor analysis which the omega was calculated from showed fit to the data set, using omega over alpha could be preferred. Also, as the number of items exceeds 5, the alpha and omega differences disappear. Since calculating the alpha is easier compared to the omega (omega requires fitting a factor model first) using alpha over omega can also be suggested. However, when the number of items and the correlations among the items were small, omega performed worse than alpha. Therefore, alpha should be used for the reliability estimations.

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Bu Makaleye Atıf Yap

Orçan, F. (2023). Comparison of cronbach’s alpha and McDonald’s omega for ordinal data: Are they different?. International Journal of Assessment Tools in Education, Volume: 10 Issue: 4. https://doi.org/10.21449/ijate.1271693

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Kaynakça (21)

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