McDonald's Omega

McDonald's omega is a reliability coefficient for a multi-item scale, computed from a one-factor model as the share of total score variance due to the common factor, without assuming equal item loadings.

맥도널드 오메가는 단일요인 모형에서 공통요인이 설명하는 총점 분산의 비율로 계산하는 다문항 척도의 신뢰도 계수로, 문항 적재량이 같다고 가정하지 않는다.

What should I report instead of Cronbach's alpha when my items do not contribute equally to the scale?

문항들의 기여도가 같지 않을 때 크론바흐 알파 대신 무엇을 보고해야 하나요?

McDonald's omega estimates the internal-consistency reliability of a scale from the loadings of a single-factor model, so items may differ in how strongly they reflect the construct. Alpha equals omega only when all loadings are equal, and when they differ alpha tends to underestimate reliability, which is why many journals now ask for omega.

When to use McDonald's Omega

• Reporting the reliability of a unidimensional multi-item scale
• Items with clearly unequal loadings, where alpha's equal-loading assumption fails
• Alongside a confirmatory factor model of the same scale

When to use something else

• Multidimensional scales with a general factor and subfactors: use hierarchical omega from a bifactor model
• Agreement between raters rather than items: use the intraclass correlation

Assumptions and requirements

• A single common factor underlies the items
• Items continuous or with enough response categories to be treated as interval
• Item errors uncorrelated with one another
• Complete responses (rows with missing items are removed)

What the analysis reports

• Omega coefficient
• Standardised loading of each item from a maximum-likelihood one-factor solution
• Number of items
• Warning for items with loadings below 0.4

How to report it

Internal consistency of the [k]-item [scale] was [good], McDonald's ω = [value].

Related methods

• Cronbach's Alpha Reliability Analysis
• Composite Reliability & AVE Test
• Confirmatory Factor Analysis (CFA)

Run McDonald's Omega on Quorant