Getting Started | SAS/STAT 9.1, Users Guide, Volume 3 (volume 3 ONLY)

A One-Way Design

A one-way analysis of variance considers one treatment factor with two or more treatment levels. This example employs PROC GLMMOD together with PROC REG to perform a one-way analysis of variance to study the effect of bacteria on the nitrogen content of red clover plants. The treatment factor is bacteria strain, and it has six levels. Red clover plants are inoculated with the treatments , and nitrogen content is later measured in milligrams. The data are derived from an experiment by Erdman (1946) and are analyzed in Chapters 7 and 8 of Steel and Torrie (1980). PROC GLMMOD is used to create the design matrix. The following DATA step creates the SAS data set Clover .

  title 'Nitrogen Content of Red Clover Plants';   data Clover;   input Strain $ Nitrogen @@;   datalines;   3DOK1  19.4 3DOK1  32.6 3DOK1  27.0 3DOK1  32.1 3DOK1  33.0   3DOK5  17.7 3DOK5  24.8 3DOK5  27.9 3DOK5  25.2 3DOK5  24.3   3DOK4  17.0 3DOK4  19.4 3DOK4   9.1 3DOK4  11.9 3DOK4  15.8   3DOK7  20.7 3DOK7  21.0 3DOK7  20.5 3DOK7  18.8 3DOK7  18.6   3DOK13 14.3 3DOK13 14.4 3DOK13 11.8 3DOK13 11.6 3DOK13 14.2   COMPOS 17.3 COMPOS 19.4 COMPOS 19.1 COMPOS 16.9 COMPOS 20.8   ;

The variable Strain contains the treatment levels, and the variable Nitrogen contains the response. The following statements produce the design matrix:

  proc glmmod data=Clover;   class Strain;   model Nitrogen = Strain;   run;

The classification variable, or treatment factor, is specified in the CLASS statement. The MODEL statement defines the response and independent variables . The design matrix produced corresponds to the model

where i = 1 , , 6, and j = 1 , , 5.

Figure 33.1 and Figure 33.2 display the output produced by these statements. Figure 33.1 displays information about the data set, which is useful for checking your data.

  Nitrogen Content of Red Clover Plants   The GLMMOD Procedure   Class Level Information   Class         Levels    Values   Strain             6    3DOK1 3DOK13 3DOK4 3DOK5 3DOK7 COMPOS   Number of Observations Read          30   Number of Observations Used          30   Nitrogen Content of Red Clover Plants   The GLMMOD Procedure   Parameter Definitions   Name of   Column    Associated    CLASS Variable Values   Number      Effect      Strain   1     Intercept   2     Strain        3DOK1   3     Strain        3DOK13   4     Strain        3DOK4   5     Strain        3DOK5   6     Strain        3DOK7   7     Strain        COMPOS

Figure 33.1: Class Level Information and Parameter Definitions

  Nitrogen Content of Red Clover Plants   The GLMMOD Procedure   Design Points   Observation                         Column Number   Number       Nitrogen    1    2    3    4    5    6    7   1         19.4      1    1    0    0    0    0    0   2         32.6      1    1    0    0    0    0    0   3         27.0      1    1    0    0    0    0    0   4         32.1      1    1    0    0    0    0    0   5         33.0      1    1    0    0    0    0    0   6         17.7      1    0    0    0    1    0    0   7         24.8      1    0    0    0    1    0    0   8         27.9      1    0    0    0    1    0    0   9         25.2      1    0    0    0    1    0    0   10         24.3      1    0    0    0    1    0    0   11         17.0      1    0    0    1    0    0    0   12         19.4      1    0    0    1    0    0    0   13          9.1      1    0    0    1    0    0    0   14         11.9      1    0    0    1    0    0    0   15         15.8      1    0    0    1    0    0    0   16         20.7      1    0    0    0    0    1    0   17         21.0      1    0    0    0    0    1    0   18         20.5      1    0    0    0    0    1    0   19         18.8      1    0    0    0    0    1    0   20         18.6      1    0    0    0    0    1    0   21         14.3      1    0    1    0    0    0    0   22         14.4      1    0    1    0    0    0    0   23         11.8      1    0    1    0    0    0    0   24         11.6      1    0    1    0    0    0    0   25         14.2      1    0    1    0    0    0    0   26         17.3      1    0    0    0    0    0    1   27         19.4      1    0    0    0    0    0    1   28         19.1      1    0    0    0    0    0    1   29         16.9      1    0    0    0    0    0    1   30         20.8      1    0    0    0    0    0    1

Figure 33.2: Design Matrix

The design matrix, shown in Figure 33.2, consists of seven columns : one for the mean and six for the treatment levels. The vector of responses, Nitrogen , is also displayed.

Usually, you will find PROC GLMMOD most useful for the data sets it can create rather than for its displayed output. For example, the following statements use PROC GLMMOD to save the design matrix for the clover study to the data set CloverDesign instead of displaying it.

  proc glmmod data=Clover outdesign=CloverDesign noprint;   class Strain;   model Nitrogen = Strain;   run;

Now you can use the REG procedure to analyze the data, as the following statements demonstrate :

  proc reg data=CloverDesign;   model Nitrogen = Col2-Col7;   run;

The results are shown in Figure 33.3.

  Nitrogen Content of Red Clover Plants   The REG Procedure   Model: MODEL1   Dependent Variable: Nitrogen   Analysis of Variance   Sum of           Mean   Source                   DF        Squares         Square    F Value    Pr > F   Model                     5      847.04667      169.40933      14.37    <.0001   Error                    24      282.92800       11.78867   Corrected Total          29     1129.97467   Root MSE              3.43346    R-Square     0.7496   Dependent Mean       19.88667    Adj R-Sq     0.6975   Coeff Var            17.26515   NOTE: Model is not full rank. Least-squares solutions for the parameters are   not unique. Some statistics will be misleading. A reported DF of 0 or B   means that the estimate is biased.   NOTE: The following parameters have been set to 0, since the variables are a   linear combination of other variables as shown.   Col7 = Intercept   Col2   Col3   Col4   Col5   Col6   Parameter Estimates   Parameter      Standard   Variable    Label          DF      Estimate         Error   t Value   Pr > t   Intercept   Intercept       B      18.70000       1.53549     12.18     <.0001   Col2        Strain 3DOK1    B      10.12000       2.17151      4.66     <.0001   Col3        Strain 3DOK13   B   5.44000       2.17151   2.51     0.0194   Col4        Strain 3DOK4    B   4.06000       2.17151   1.87     0.0738   Col5        Strain 3DOK5    B       5.28000       2.17151      2.43     0.0229   Col6        Strain 3DOK7    B       1.22000       2.17151      0.56     0.5794   Col7        Strain COMPOS   0             0             .       .        .

Figure 33.3: Regression Analysis