1. Graeco-Latin squares
Graeco-Latin squares build on Latin squares by adding yet another blocking factor. Let's introduce them quickly so you can get back to the exercises.
2. Graeco-Latin squares
This slide might look familiar if you watched the last video, and for good reason; a Graeco-Latin square design simply adds one more blocking factor, but shares the same properties of a Latin square experiment otherwise. We again have to have the same number of treatments as levels in the blocking factors and are operating under the assumption that none of those treatment and blocking factors interact.
3. Graeco-Latin squares
Traditionally, Graeco-Latin squares are drawn very similar to Latin squares, with the addition of Greek letters, which indicate the third blocking factors are added next to the Latin letters, which indicate the treatment, as seen in this diagram. For this course, we won't be accessing the Greek alphabet to draw Graeco-Latin squares in R, we'll use the Latin alphabet and numbers.
As before, the treatment occurs only once in each row and column. The rows are one blocking factor, the columns another, and the Greek letters the third, so here we notice that A, B, C, and D appear not only once per column and row, but they are also each paired with alpha, beta, gamma, and delta only once.
4. GLS - explanation
Again, it may be easier to see why this is a Graeco-Latin square when the letters, representing the treatments, are converted to shapes. You can see that the circles appear only once per row and column, and they're only paired up with each Greek letter once for each of alpha, beta, gamma, and delta, which represent the third blocking factor.
5. Let's practice!
Because Graeco-Latin Squares are so similar to Latin Squares, I'm keeping this video short and sweet. Jump in and try the exercises, where we expand the Latin Square experiment from the last lesson.