Solved – Combining between and within-subjects designs

anovaexperiment-designrepeated measures

I have a two by two design. Ideally I would run the whole thing within-subjects (all participants get all conditions) but the procedure is too long. I could run one factor between-subjects (each participants gets one condition) and one factor within-subjects(each participant gets both conditions), but then I have more power to see the effect for one factor vs. the other. I was thinking about running it such that one participant gets factor A within and another participant gets factor B within. That way I have to recruit fewer participants and I can see within subject and between subject effects for each factor. But I'm not sure how this would affect the analyses. Advice would be appreciated.

Best Answer

Don't try to come up with a complicated analysis to deal with this, just do within and between analyses separately on the relevant subsets of your data. That way you will not compromise the interpretability of the outcome and you will be able to make sure that the result is both sensible and robust.

Depending on the nature of your data you could potentially combine the outcomes of the two arms of the experiment. For example, if you can generate likelihood functions for each arm then the combined function is simply their product.

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Solved – Analyse within-subject data as between-subject data

The analysis you want to pursue is not uncommon (unfortunately I don't have a reference right now), but you have to split it. You have to run 2 ANOVAs and hope that the analyses agree.

The overall ANOVA uses the full within subject design.
The between-subjects ANOVA just uses the data from the first session and compares those.

If the seond analysis is not significant but shows the same pattern, this may be, as there is less power.

Solved – Random effects for within subjects study in R

I would go for package lme4.

If I understand correctly, mF below should be your model. It has condition as a fixed effect, while judge and subject as a random intercepts.

library(lme4)

# m0 = Null model without the fixed effects.
# m1 = Your model including the fixed effects.
# Set REML = FALSE for a meaningful model comparison

m0 <- lmer(rating ~ 1 + (1|judge) + (1|subject), data = data, REML = FALSE) 
mF <- lmer(rating ~ condition + (1|judge) + (1|subject), data = data, REML = FALSE) 

summary(m0)
summary(mF)

anova(m0, mF)

# If significant, fit the final model using REML = TRUE
# This is often recommended since it usually gives better estimates for random effects.

mF <- lmer(rating ~ condition + (1|judge) + (1|subject), data = data, REML = FALSE)

Edit: Per discussion below.

Best Answer

Related Solutions

Solved – Analyse within-subject data as between-subject data

Solved – Random effects for within subjects study in R

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