Omega is a reliability coefficient said to be superior to coefficient alpha as it makes fewer assumptions, and can be expected to result in a more accurate estimate of a test's or scale's reliability. Lertap5 uses the "closed-form" method to derive an estimate of omega. This working paper has related reference material and citations.


When the "Item scores and correlations" option is used to generate an "IStats" report, statistics related to coefficient omega will be found towards the bottom of the report.




Inter-item covariance values will be displayed in matrix form, with item variances on the diagonal. If any of the covariance values are negative they will be highlighted in yellow. These are unwanted -- all items will hopefully "go well and hang together" (correlate positively with each other). Reliability coefficients such as alpha and omega will be highest when all covariance values are positive and, ideally, at least 0.30 in magnitude.


Closed-form lamda estimates


These indicate the degree to which each item contributes to, "loads on", or correlates with the single "general factor" postulated by the underlying model, estimated by using the closed-form method. Ideally all lamdas will be above 0.50 in magnitude.


Score variance is the variance of the total test/scale scores as found in the Scores report.


The omega estimate is calculated by summing the lamda estimates, squaring the sum, and then dividing the result by the score variance.


In theory the maximum value the omega estimate can obtain is 1.00 (indicating perfect reliability). However, if the covariance matrix has numerous negative entries, it is possible to find the omega estimate exceeding its theoretical maximum. When this happens, Lertap will raise a warning message and indicate that the omega estimate should be ignored. This does not mean that omega cannot be computed - rather, the indication is that the closed-form method itself has failed and users should make use of another of the methods mentioned in the working paper to obtain an omega estimate.