A Hierarchical Map and Application to Traverse and Unify Analyses Subsumed by Canonical Correlation

Area of Science:

• Statistics
• Quantitative Psychology

Background:

• Canonical correlation unifies analyses within the general linear model.
• Previous portrayals of this hierarchy have been overly simplified.
• Understanding the relationships between univariate and multivariate analyses is crucial for researchers.

Purpose of the Study:

• To present a hierarchical map of analyses encompassed by canonical correlation.
• To develop a user-friendly application (canCORRgam) to illustrate these analytical connections.
• To aid researchers in understanding the transitive properties of statistical analyses.

Main Methods:

• Developed a hierarchical map of statistical analyses.
• Created a Shiny application (canCORRgam) to visualize the hierarchy for 15 models.
• Provided tools and formulas for relating test statistics to effect sizes.

Main Results:

• Demonstrated that the hierarchy of analyses under canonical correlation is more complex than previously depicted.
• The canCORRgam application effectively illustrates the hierarchical paths for various statistical models.
• Facilitated the transformation of test statistics and effect sizes.

Conclusions:

• The proposed hierarchy offers a more nuanced understanding of statistical analysis relationships.
• The canCORRgam application serves as a valuable educational tool for researchers.
• This work encourages meta-analytic practices by linking diverse statistical measures.