# [Stata] Calculating McDonald’s Omega

### How it is different from Cronbach’s alpha?

📒 Dunn, T. J., Baguley, T., & Brunsden, V. (2014). From alpha to omega: A practical solution to the pervasive problem of internal consistency estimation. *British journal of psychology*, *105*(3), 399-412.

McDonald’s omega and Cronbach’s alpha are both measures of **internal consistency reliability**, which is the extent to which items in a scale are interrelated and measure the same construct. However, there are several differences between the two coefficients.

- McDonald’s omega is based on a
**factor analytic approach**, whereas Cronbach’s alpha is primarily based on the**correlation between the questions**. This means that**omega is less sensitive to the number of items**in a scale and the distribution of item scores. Omega also provides separate estimates of the reliability of the general factor and the group factors. - McDonald’s omega is
**more robust than Cronbach’s alpha against deviations from the assumptions of tau-equivalence and uncorrelated error variances**. This makes omega a more suitable measure of internal consistency in many situations. - McDonald’s omega is
**less biased**than Cronbach’s alpha when**the number**of items in a scale is small or when the items are not tau-equivalent. This means that omega is a more accurate estimate of internal consistency in these situations.

To calculate McDonald’s omega in Stata, you can use the `omegacoef`

command created by Dr. Brian Shaw. This command estimates the scale reliability of a test using McDonald’s omega coefficient, which has many desirable statistical properties that make it preferable to the widely used Cronbach’s alpha.

### Calculating McDonald’s Omega in Stata: `omegacoef`

Here are the steps to calculate McDonald’s omega using `omegacoef`

command:

Step 1. Install the `omegacoef`

command

`ssc install omegacoef`

Step 2. Estimate the factor analysis model with `sem`

command

The important step for `omegacoef`

command is to run `sem`

command before running it. Let’s say that your summary variable (scale) name is `depression`

and the list of items are `phq1`

–`phq9`

. You can run confirmatory factor analysis using `sem`

command as follows.

`sem (depression -> phq1 phq2 phq3 phq4 phq5 phq6 phq7 phq8 phq9)`

One thing to note is that you need to use the lower case variable names for the list of variables after (->). Here, the list of items refer to phq1-phq9. The general command could be as follows, but you should adapt it for your dataset.

`sem (scale -> var1 var2 var3) `

If you skip this step 2, the omegacoef command will return the error message like “model is not specified.”

Step 3. Run the `omegacoef`

command

`omegacoef var1 var2 var3 `

The output of the `omegacoef`

command will include the estimated McDonald’s omega coefficient.