= Calculating 95% confidence interval for the group means from one-way ANOVAs =

(See also the plots in the Post-hoc Graduate Statistics talk)

Between Subjects ANOVA

A 95% Confidence interval for a group mean is given by

group mean + $$t_text{df(MS(subjects) ,0.025} \sqrt{\mbox{MS(subjects)/ng}}$$

for ng subjects in group g, degrees of freedom, df, and

Baguley (2012a) suggests alternative approaches which give more informative confidence intervals for group means in between subejcts ANOVA (see [http://seriousstats.wordpress.com/2012/03/18/cis-for-anova/ here.])

Repeated Measures ANOVA

The most commonly used method for specifying a 95% CI for a group mean from a repeated measures design is was proposed by Loftus and Masson (1994) (A pdf copy of the paper attachment:lofmas.pdf is here).]

A 95% Confidence interval for a group mean is given by

group mean + $$t_text{n,0.025} \sqrt{\mbox{MS Error(W x subjects)/n}}$$

for a within subject factor, W, with n subjects in each group.

If the variances are heterogeneous Loftus and Masson advocate using the MS Error and its degree of freedom adjusted by the Greenhouse-Geisser correction. Applications of both corrected and uncorrected calculation of these confidence intervals for group means from repeated measures ANOVA in SPSS as suggested by Loftus and Masson are illustrated [attachment:lsSPSS.doc here.]

Baguley (2012b) suggests alternative approaches which give more informative confidence intervals for group means in repeated measures (see [attachment:Baguley.pdf here.])

References

Baguley, T. (2012a, in press). Serious stats: A guide to advanced statistics for the behavioral sciences. Basingstoke: Palgrave.

Baguley, T. (2012b). Calculating and graphing within-subject confidence intervals for ANOVA. Behavior Research Methods, 44, 158-175.