<p>Generalizing the familiar two-correlation comparison, this paper presents a dependence-robust omnibus test to evaluate whether an outcome is <i>equally</i> 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 (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\approx 5\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>≈</mo> <mn>5</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> at <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\alpha {=}0.05$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </math></EquationSource> </InlineEquation>) for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$n\!\ge \!50$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mspace width="-0.166667em" /> <mo>≥</mo> <mspace width="-0.166667em" /> <mn>50</mn> </mrow> </math></EquationSource> </InlineEquation> across diverse dependence structures and under moderate non-normality (e.g., <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$t_5$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>t</mi> <mn>5</mn> </msub> </math></EquationSource> </InlineEquation> 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.</p>

An omnibus test for several dependent correlations

期刊论文
发表日期：

2026年5月12日

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Zvi Drezner,
George A. Marcoulides,
Dawit Zerom

摘要

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 ( $\approx 5\%$ $\approx 5 %$ at $\alpha {=}0.05$ $α = 0.05$ ) for $n\!\ge \!50$ $n \geq 50$ across diverse dependence structures and under moderate non-normality (e.g., $t_5$ $t_{5}$ 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.