The (Large) Effect of (Small) Correlations in Anova, and Correction Procedures

SYNOPTIC ABSTRACT

Rarely is the independence assumption verified in an ANOVA. (Even with independent data, correlation estimates can vary much from zero, and many observations are needed to actually verify independence.) It is shown that by increasing the number of observations per cell in a factorial experiment, even slight correlations (which would perhaps be ignored even if known) can have a strong influence on the F-statistic and greatly inflate the Type I error. A method for adjusting an ANOVA in the presence of correlated data is given.

Key Words:

• factorial experiment
• intraclass correlation
• Type I error
• random effects