# The LATTICE Procedure

### Displayed Output

For each response variable, PROC LATTICE displays the following

• an Analysis of Variance table and related statistics, including the following as separate sources of variations:

• Replications

• Blocks within Replications (adjusted for treatments)

• Intra-block Error

• Randomized Complete Block Error

The Blocks within Replications sum of squares is further broken down into Component A and Component B. If there is no repetition of the basic plan, the Component B sum of squares is the same as the Blocks within Replications sum of squares. If there is repetition of the basic plan, the Component A sum of squares reflects the variation among blocks that contain the same treatments.

The source of variation called Randomized Complete Block Error is the sum of the Blocks within Replications sum of squares and the Intra-block Error sum of squares. It is the appropriate error term if the experimental design is a randomized complete block design, with the replications filling the roles of complete blocks.

• two values for the Variance of Means. For some lattice designs, these are only approximations. The first value is applicable when the two treatments appear in the same block; the other (when it appears) applies when the two treatments never appear in the same block (a possibility in partially balanced and rectangular designs).

• an Average of Variance. Except with small designs, it is sufficient to use this average variance of means for tests between treatments (whether the two treatments appear in the same block or not); see Cochran and Cox (1957).

• the Least Significant Differences (LSDs) at the 0.01 and 0.05 levels of significance, based on the Average of Variance

• Efficiency Relative to RCBD, the efficiency of the lattice design relative to a randomized complete block design. The efficiency is the ratio of the randomized complete block mean squared error to the effective error variance; see Cochran and Cox (1957).

• the Adjusted Treatment Means. These are adjusted for blocks if the relative precision is greater than 105%.

When you specify the COVARIANCE option, PROC LATTICE produces sums of products and the mean product for each source of variation in the analysis of variance table.