Replicated Latin Square Analysis in R Language with ANOVA

Question

I am executing a 1 factor(tool) experiment with 2 treatments and 2 block variables (participant and process). In other words, a 2x2 Latin square.

One of the block variables is the participants. As my sample has 8 participants, I have 4 2x2 latin squares.

To do the analysis of just 1 Latin square, I am using ANOVA through the following commands in R:

result = aov(time~participant+process+tool);
print(summary(result));

My questions is: How can I execute an ANOVA test with replicated latin squares in R?

Answer 1

I found a good reference to understand how to analyse replicated latin squares in:

http://halweb.uc3m.es/esp/Personal/personas/jmmarin/esp/Disenno/CursoDisExpSAS.pdf

In page 42 is possible to observe that my case is: "new rows and same columns"

So, the ANOVA table should be according to the table in page 46. Special attention to the sources and degree of freedom (df).

To code the expressed concepts in R, I did the following:

result = aov(time~tool+participant:replic+process+replic);

The bold part is the changes in order to represent the table presented in page 46.

Answer 2

library(nlme) # Avoid lme4 for starter, documentation is not that good yet
result = lme(time~process*tool, data=...., random = ~1|participant)
summary(result)