An omnibus test for several dependent correlations

Generalizing the familiar two-correlation comparison, this paper presents a dependence-robust omnibus test to evaluate whether an outcome is equally correlated with multiple predictors. By accounting for shared sampling variation, the test simultaneously avoids false alarms and missed discoveries. The test also nests the pairwise test as a special case. Monte Carlo studies show near-nominal size ( $\approx 5\%$ at $\alpha =0.05$ ) for $n\ge 50$ across diverse dependence structures and under moderate non-normality (e.g., $t_5$ errors) together with high power for moderate departures from equality. We illustrate the method on publicly available educational data and provide an interactive web app (size/power simulator and point-and-click analysis) to facilitate adoption. Collectively, the results support the omnibus test as a practical default when assessing equality of outcome-predictor correlations to be augmented by pairwise contrasts for succinct context rather than primary inference.