ANOVA Analysis for Sugar Beet

The objective of this script is to analyze the effects of different factors on the yield (Y) of sugar beets. The data is structured according to a latin square split-plot design, with factors 'Harvest', 'Rep' (repetition), 'Column', and 'Variety'. The DATA STEP block generates observations from 'datalines' to construct the 'Beets' dataset. Then, PROC ANOVA is used to model the yield based on these factors and to perform specific tests on the effects of the factors Harvest, Rep, Column, and Variety, using appropriate error terms for the experimental design.

Data Analysis

Type : CREATION_INTERNE

The data for the 'Beets' dataset is directly created and populated within the SAS script via a DATALINES block. It represents the results of an experiment with a latin square split-plot design, measuring the yield of different sugar beet varieties over two harvests.

1 Code Block

DATA STEP Data

Explanation :
This DATA STEP block is responsible for creating the 'Beets' dataset. It uses nested 'do' loops to generate the variables 'Harvest' (1 to 2), 'Rep' (1 to 6), and 'Column' (1 to 6). The 'Variety' variable and the dependent variable 'Y' (yield) are read sequentially from the DATALINES block. The ' @code_sas/16.4'.sas instruction at the end of 'input' keeps the pointer on the same data line until all observations for a combination of Harvest, Rep, and Column are read, which is typical for experimental designs where multiple measurements are on the same physical data line. The 'title1' and 'title3' statements define the SAS output titles.

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1	title1 'Sugar Beet Varieties';
2	title3 'Latin Square Split-Plot Design';
3	DATA Beets;
4	DO Harvest=1 to 2;
5	DO Rep=1 to 6;
6	DO Column=1 to 6;
7	INPUT Variety Y @;
8	OUTPUT;
9	END;
10	END;
11	END;
12	DATALINES;
13	3 19.1 6 18.3 5 19.6 1 18.6 2 18.2 4 18.5
14	6 18.1 2 19.5 4 17.6 3 18.7 1 18.7 5 19.9
15	1 18.1 5 20.2 6 18.5 4 20.1 3 18.6 2 19.2
16	2 19.1 3 18.8 1 18.7 5 20.2 4 18.6 6 18.5
17	4 17.5 1 18.1 2 18.7 6 18.2 5 20.4 3 18.5
18	5 17.7 4 17.8 3 17.4 2 17.0 6 17.6 1 17.6
19	3 16.2 6 17.0 5 18.1 1 16.6 2 17.7 4 16.3
20	6 16.0 2 15.3 4 16.0 3 17.1 1 16.5 5 17.6
21	1 16.5 5 18.1 6 16.7 4 16.2 3 16.7 2 17.3
22	2 17.5 3 16.0 1 16.4 5 18.0 4 16.6 6 16.1
23	4 15.7 1 16.1 2 16.7 6 16.3 5 17.8 3 16.2
24	5 18.3 4 16.6 3 16.4 2 17.6 6 17.1 1 16.5
25	;

2 Code Block

PROC ANOVA

Explanation :
This block uses the PROC ANOVA procedure to perform the analysis of variance on the 'Beets' dataset. The 'class' statement declares the categorical variables (factors) 'Column', 'Rep', 'Variety', and 'Harvest'. The 'model' statement specifies the linear model, where 'Y' is the dependent variable and the other variables are the factors and their interactions. The 'test' statements are used to specify the appropriate error terms for hypothesis testing. For example, 'test h=Rep Column Variety e=Rep*Column*Variety' indicates that the effect of 'Rep', 'Column', and 'Variety' should be tested against the 'Rep*Column*Variety' error, which is common in split-plot and latin square designs for whole-plot effects. Similarly, 'test h=Harvest e=Harvest*Rep' tests the effect of 'Harvest' against its interaction with 'Rep'.

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1	PROC ANOVA DATA=Beets;
2	class Column Rep Variety Harvest;
3	model Y=Rep Column Variety RepColumnVariety
4	Harvest Harvest*Rep
5	Harvest*Variety;
6	test h=Rep Column Variety e=RepColumnVariety;
7	test h=Harvest e=Harvest*Rep;
8	RUN;

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