Interpretation of marginal means
A researcher wants to compare how kids solve three different types of arithmetic word problems, and to see if the order in which they experience the three types of problems makes a difference in how well they achieve. The problems are all based on the relationship Distance = Rate x Time. In Distance problems, the kids are given a Rate (speed) that a vehicle is going, in addition to a Time that the vehicle travels, and asked to find out the Distance travelled. In the Rate problems they are asked to find out Rate from the other two quantities, and similarly for Time in the Time problems.
In order to control (and test) for Order and Sequence effects, the researcher decides to use a 3x3 Latin Square design (withinsubjects). In a pilot study, five kids are given several problems of each type to practice (and then tested on three problems), in one of the three Sequences: DRT, TDR, OR RTD.
The data are given below, organized by Order (i.e., the first number for every subject is the score for the first problem experienced, and so forth):
group DRT:

subj 01

3 5 2


subj 02

4 3 5


subj 03

3 5 2


subj 04

4 3 5


subj 05

4 6 2

group TDR:

subj 06

3 6 6


subj 07

2 6 4


subj 08

3 5 2


subj 09

0 4 5


subj 10

4 5 6

group RTD:

subj 11

2 3 5


subj 12

4 3 6


subj 13

3 5 6


subj 14

3 1 4


subj 15

3 3 6
