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Tetrad correlations were obtained historically for Gaussian distributionswhen tasks are designed to measure an ability or attitude so that a singleunobserved variable may generate the observed, linearly increasing dependencesamong the tasks. We connect such generating processes to a particular type ofdirected graph, the star graph, and to the notion of traceable regressions.Tetrad correlation conditions for the existence of a single latent variable arederived. These are needed for positive dependences not only in joint Gaussianbut also in joint binary distributions. Three applications with binary itemsare given.

Star graphs induce tetrad correlations: for Gaussian as well as for binary variables