# Latin Square Design ANOVA in R

I have been searching online for an appropriate way to analyse data obtained using a 4x4 latin-square design (and more specifically how to do this in R).

I have some sources online that say the data should be analysed using a repeated measures ANOVA. I have tried this, but want to make sure that I have entered the error term correctly or whether there is a better method.

The design is repeated-measures: I have my treatment factor (correction) with 4 levels, and another factor (narrative) which also have 4 levels. Correction and narrative have 4 different combinations or orders.

Any help at all would be much appreciated!

• what are two blocking variables to make your design to make this latin square. – John Jun 27 '17 at 13:51
• Hi there - Narrative is the Column blocking variable and I have Order (which corresponds to the combination of Narrative with the treatment variable Correction) as the Row blocking variable. So each subject is allocated to one of four orders which are combinations of Narrative and Correction. I am analyzing the data in R and I know that there are some issues with unbalanced designs for aov and ezANOVA in R so I'm not sure this is the best approach. – Con Des Jul 7 '17 at 10:46
• I think there issues with 'lmer' because of the design – Con Des Jul 7 '17 at 10:54
• To make things even more complicated the qualtrics algorithm didn't allocate subjects to the different orders equally so there are more observations for some conditions than others – Con Des Jul 7 '17 at 11:05

This is complete answer but more than just comment.

Probably you have looked the bloggers article:

https://www.r-bloggers.com/latin-squares-design-in-r/

I think using mixed model analysis is more powerful. You can treat them as row-column design.

The following question may be useful:

lme4 or other open source R package code equivalent to asreml-R

• Thanks so much. I had initially intended on using mixed model analysis but I spoke to someone who knew more about this analysis and they said that design means that LMM might not be appropriate. I also couldn't find any resources online to for using LMM in this way. – Con Des Jun 26 '17 at 10:06
• The other thing I find a little confusing is that some of the resources I have found online suggest using a linear model but this ignores the repeated measures nature of the data. – Con Des Jun 26 '17 at 10:07