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Analysis of Data from Designed Experiments

Randomized Complete Block Design 

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Analysis Using SPSS 

       Analysis Using SAS 

Data Input:
For performing the analysis, input the data in the following format. {Here call the Tree Specie Number as Tree and Replication as Rep.It may, however, be noted that one can retain the same name or can code in any other fashion}.

 Prepare a SAS data file using

    DATA plantheight;  /*one can enter any other name for Data*/;
    Input Tree Rep Height;
    Cards;
    1           1           144.44
    2           1           113.50
    3           1             60.88
    4           1           163.44
    5           1           110.11
    6           1           260.05
    7           1           114.00
    8           1             91.94
    9           1           156.11
    10         1             80.20
    1           2           145.11
    2           2           118.61
    3           2             90.94
    4           2           158.55
    5           2           116.00
    6           2           102.27
    7           2           115.16
    8           2             58.16
    9           2           177.97
    10         2           108.05
    1           3           104.00
    2           3           118.61
    3           3             80.33
    4           3           158.88
    5           3           119.66
    6           3           256.22
    7           3           114.88
    8           3             76.83
    9           3           148.22
    10         3             45.18
    1           4           105.44
    2           4           123.00
    3           4             92.00
    4           4           153.11
    5           4           103.22
    6           4           217.80
    7           4           106.33
    8           4             79.50
    9           4           183.17
    10         4             79.55
     ;

* To test the equality of different species tree with respect to heights , one can perform the analysis of variance of the data using the following steps ;

PROC ANOVA;
Class Rep Tree;
Model    Height = Rep Tree;
Run;

/*One can obtain means of trees and all possible pair wise treatment comparisons using least significant differences and Duncan’s New Multiple range tests by using of the following statements:*/

 PROC ANOVA;
Class Rep Tree;
Model    Height = Rep Tree;
Means Tree/LSD;
Means  Tree/DUNCAN;
Run;

/*One may use a host of multiple comparison procedures under the options in MEANS statement viz.  Least Significant Difference (LSD), Duncan’s New multiple - range test (DUNCAN), Waller - Duncan (WALLER) test, Tukey’s Honest Significant Difference (TUKEY).  The LSD, DUNCAN and TUKEY options takes level of significance ALPHA = 5% unless ALPHA = options is specified.  Only ALPHA = 1%, 5% and 10% are allowed with the Duncan’s test.  95% Confidence intervals about means can be obtained using CLM option under MEANS statement 

One can not perform Contrast analysis by using PROC ANOVA, therefore, one has to use PROC GLM. This can be done using the following steps.
Note: Here we want to test

             i.  The interest of the experimenter is to test a null hypothesis that the average effect of Tree
                 species in group one (1, 2, 3, 4, 10) is equal to the average effect of Tree species in
                 group two (5, 6, 7, 8, 9).
            ii. 
  The effects of tree species within each group.
           iii.  The effect of Tree species 9 is equal to the average effect of Tree species
                 1,2,3,4,5,6,7,8,10.
 
        iv.  The effect of Tree species 9 is equal to the average effect of Tree species 1,2,3,4.
           v.  The effect of Tree species 10 is equal to the average effect of Tree species 1,2,3,4.
           vi.  The effect of Tree species 9 is equal to the average effect of Tree species 5,6,7,8.
          vii. The effect of Tree species 10 is equal to the average effect of Tree species 5,6,7,8.

The following SAS statements can be made use of */

 Proc GLM;
Class Rep Tree;
Model Height = Rep Tree;
Contrast 'group 1 vs group 2' Tree 1 1 1 1 -1 -1 -1 -1 -1 1;
Contrast 'within group 1' Tree 1 -1 0 0 0 0 0 0 0 0,
                                          Tree 1 1 -2 0 0 0 0 0 0 0,
                                          Tree 1 1 1 -3 0 0 0 0 0 0,
                                          Tree 1 1 1 1 0 0 0 0 0 -4;
Contrast 'within group 2' Tree 0 0 0 0 1 -1 0 0 0 0,
                                          Tree  0 0 0 0 1 1 -2 0 0 0,
                                          Tree  0 0 0 0 1 1 1 -3 0 0,
                                          Tree  0 0 0 0 1 1 1 1  -4 0;
Contrast '1 vs 2 3 4 5 6 7 8 9 10' Tree 9 -1 -1 -1 -1 -1 -1 -1 -1 -1;
Contrast '1 2 3 4 vs 9' Tree 1 1 1 1 0 0 0 0 -4 0;
Contrast '1 2 3 4 vs 10' Tree 1 1 1 1 0 0 0 0 0 -4;
Contrast '5 6 7 8 vs 9' Tree 0 0 0 0 1 1 1 1 -4 0;
Contrast '5 6 7 8 vs 10' Tree 0 0 0 0 1 1 1 1 0 -4;
 run;

Data File

Result File

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Analysis Using SAS                                                         Analysis Using SPSS                                     

 

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Partially Confounded Design
Factorial Experiment with Extra Treatments
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For exposure on SAS, SPSS, 
MINITAB, SYSTAT and
 
MS-EXCEL for analysis of data from designed experiments:

 Please see Module I of Electronic Book II: Advances in Data Analytical Techniques

available at Design Resource Server (www.iasri.res.in/design)