Details

Input Data Set

Four numeric SAS variables , Group , Block , Treatmnt , and Rep , are used in the input data set to define the lattice design. The Group , Block ,and Treatmnt variables are required in the data set to which PROC LATTICE is applied. The Rep variable must be present when the design involves repetition of the entire basic plan.

Group	specifies which orthogonal replication in the basic plan includes the experimental unit. Values of Group must be 1, 2, , n , where n is the number of replicates in the basic plan.
Block	specifies the block in which the experimental unit is present. Values of Block must be 1, 2, , m , where m is the number of blocks in a replication.
Treatmnt	specifies which treatment was applied to the experimental unit. Values of Treatmnt must be 1, 2, , i , where i is the number of treatments in a replication.
Rep	specifies which repetition of the basic plan includes the experimental unit. Values of Rep must be 1, 2, , p , where p is the number of replications of the entire basic plan. Thus, the experiment has a total of np replicates.

Missing Values

If a value of Group , Block , Treatmnt , or Rep is missing, the analysis is not performed and an appropriate error message is displayed.

If a value of a response variable is missing, this entire variable is dropped from the analysis. If other response variables exist that do not have missing values, they are analyzed .

Displayed Output

For each response variable, PROC LATTICE displays

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

  • Replications

  • Blocks within Replications (adjusted for treatments)

  • Treatments (unadjusted)

  • 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); refer to Cochran and Cox (1957).

• the Least Significant Differences (LSDs) at the .01 and .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; refer to Cochran and Cox (1957).

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

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.

ODS Table Names

PROC LATTICE assigns a name to each table it creates. You can use these names to reference the table when using the Output Delivery System (ODS) to select tables and create output data sets. These names are listed in the following table. For more information on ODS, see Chapter 14, Using the Output Delivery System.

Table 38.1: ODS Tables Produced in PROC LATTICE

ODS Table Name	Description	PROC LATTICE Option
ANOVA	Analysis of variance	default
AdjTreatmentMeans	Adjusted treatment means	default
Statistics	Additional statistics	default