Overview
Reliability analysis evaluates consistency among scored indicators. Survlytics calculates covariance-based Cronbach’s alpha, corrected item–total correlations, alpha if an item is deleted, mean inter-item correlation and—through a separately validated one-factor routine—McDonald’s omega total.
Theoretical foundation
Alpha is a function of the number of items, item variances and total-score variance. It is not a test of unidimensionality. Omega total is derived from a congeneric one-factor measurement model and is conceptually distinct from alpha, composite reliability and rho_A.
Key equations
\alpha=\frac{k}{k-1}\left(1-\frac{\sum_{j=1}^{k}s_j^2}{s_T^2}\right)Algorithm and computation
Alpha is calculated directly from the sample covariance matrix. Listwise mode uses one complete-case covariance matrix; pairwise mode uses pairwise covariances and reports the minimum pair count with a warning. Omega is available as its own procedure after one-factor admissibility checks. Composite reliability and rho_A are reported only in the CFA or PLS-SEM contexts where their required model quantities exist.
Required data
At least two scored numeric items for alpha. Omega requires an admissible one-factor congeneric model and sufficient complete observations.
Assumptions
Items should be coherently oriented and substantively intended to measure a common reflective construct. Alpha is not appropriate evidence for a formative block.
Available settings
Item selection or approved construct; listwise or pairwise covariance handling; optional omega request where the validated routine is available.
Worked example
Synthetic example: three consistently oriented service items are analysed together. The item-deleted table is reviewed for anomalous coding; no item is removed solely because alpha increases.
Limitations and non-claims
Reliability does not prove validity, dimensionality or temporal stability. Universal pass/fail cut-offs are not applied. Pairwise covariance matrices can be non-positive-definite.
Validation notes
Alpha and item diagnostics have deterministic unit tests. Omega has one-factor recovery and admissibility tests. The application does not claim equivalence among alpha, omega, CFA composite reliability and PLS rho_A.
How Surv.lytics computes McDonald’s omega
{}How Surv.lytics computes Reliability analysis
{}References and verification status
Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297–334. https://doi.org/10.1007/bf02310555
VerifiedOpen DOIMcDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates.
Unverified draft
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