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Calculating and graphing within-subject confidence intervals for ANOVA.

¹Division of Psychology, School of Social Sciences, Nottingham Trent University, Nottingham NG1 4BU, UK. Thomas.Baguley@ntu.ac.uk

Behavior Research Methods

|August 23, 2011

Summary

This study introduces new methods for calculating confidence intervals (CIs) in repeated measures ANOVA. The proposed techniques improve the accuracy of statistical inference for both individual means and patterns of means.

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Area of Science:

Psychology
Statistics
Quantitative Methods

Background:

Existing literature offers various methods for confidence intervals (CIs) in within-subjects ANOVA.
A critical distinction exists between CIs for mean patterns and CIs for individual means.

Purpose of the Study:

To propose and evaluate methods for calculating and plotting confidence intervals for within-subjects ANOVA designs.
To provide practical solutions for researchers needing to infer patterns of means and individual means.

Main Methods:

Adapting existing confidence interval methods (Cousineau, 2005; Morey, 2008) for inference on mean patterns.
Utilizing multilevel modeling for confidence intervals focused on individual means.
Recommending a two-tiered CI approach when both inference types are required.

Main Results:

The adapted Cousineau and Morey intervals provide confidence for mean differences when they do not include zero.
Multilevel modeling offers a robust method for individual mean inference.
A two-tiered CI approach effectively addresses combined inference needs.

Conclusions:

The study presents a unified approach to within-subjects confidence intervals.
Free, open-source R software is provided to implement the proposed methods.
These tools simplify the calculation and visualization of within-subjects confidence intervals.