high

Check this out --

http://www2.chass.ncsu.edu/garson/PA765/anova.htm

Latin Square (or Graeco Latin Square?)

Latin square designs extend the logic of block designs to control for two categorical variables.

Latin square designs also reduce the number of observations necessary to compute ANOVA.

This design requires that the researcher assume all interaction effects are zero.

Normally, if one had three variables, each of which could assume four values, then one would need 43 = 64 observations just to have one observation for every possible combination.

Under Latin square design, however, the number of necessary observations is reduced to 42 = 16 because the third variable is nested.

For instance, suppose there are 4 teachers, 4 classes, and 4 textbooks. The 16 groups in the design would be the 16 different teacher-class pairs.

Each teacher would teach in each of the four classes, using a different text each time. Each class would be taughty by each of the four different teachers, using a different text each time.

However, only 16 of the 64 possible teacher-class-textbook combinations would be represented in the design because textbooks are a nested factor, with each class and each teacher being exposed to a given textbook only once.

Eliminating all but 16 cells from the complete (crossed) design requires the researcher to assume there are no significant teacher-textbook or class-textbook interaction effects, only the main effects for teacher, class, and textbook For a discussion of how to select the necessary observations under Latin square, see Iverson and Norpoth (1987: 80-84).

Nested designs. In nested designs, there are two (or more) factors, but the levels of one factor are never repeated as levels of the other factor. This happens in hierarchical designs, for instance, when a forester samples trees, then samples seedlings of each sampled trees for survival rates.. The seedlings are unique to each tree and are a random factor. Likewise, we could sample drug companies and within sampled companies, we could sample drug products for quality. This contrasts with crossed designs of ordinary two-way (or higher) ANOVA, in which the levels of one factor appear as levels in another factor (ex., tests may appear as levels across schools). We can get the mean of different tests by averaging across schools, but we cannot get the mean survival rate of different seedlings across trees because each tree has its own unique seedlings. Likewise, we cannot compute the mean quality rating for a drug product across companies because each company has its own unique set of products.

Latin square and Graeco-Latin square designs (see above) are also nested designs.

SPSS procedure:

In SPSS, Analyze, General Linear Model, Univariate; specify the main factor as fixed or random, then specify the nested factor as random;click the Model button and enter the main effects of the main (not nested) factor(s); click the Paste button and modify the /DESIGN statement to a format such as /DESIGN = mainfactor nestedfactor(mainfactor), signifying the model is the main effect of the fixed factor plus the effects of the random nested factor at each value of the main fixed factor. In the syntax window, Run All. In the resulting ANOVA table, a significant nestedfactor(mainfactor) effect means that the dependent variable varies by the nested factor even within the same level of (controlling for) the main factor. So my syntax looks like:

UNIANOVA
mean_percent_recall BY order direction text
/RANDOM = text
/METHOD = SSTYPE(3)
/INTERCEPT = INCLUDE
/PLOT = PROFILE( direction*order )
/EMMEANS = TABLES(OVERALL)
/PRINT = DESCRIPTIVE ETASQ HOMOGENEITY
/PLOT = SPREADLEVEL
/CRITERIA = ALPHA(.05)
/DESIGN = order direction order*direction text(order).