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Analysis of Data from Designed Experiments

 Incomplete Block Design

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Analysis Using SAS 

Analysis Using SPSS 

 Main Procedure is:

 Start® All Programs ® SPSS for Windows® SPSS 15.0/ SPSS13.0/ SPSS10.0 (based on the version available on your machine)   ® Enter data in Data Editor ® Analyze ® GLM ® Univariate  ® calories ® [puts Calories  under Dependent list: ] ® blk® [put blk under Fixed Factor(s): ]   trt ® [put trt under Fixed Factor(s):]  Continue ® Model... [Opens Model dialogue box] ® Custom ® Build Term(s) ® Main effects  ®   [puts blk, trt under Model: ] ® Continue ® OK

 

For performing analysis, input the data in the following format.  Here we call the block as BLK and treatment as TRT.  

 

Following are the brief description of the steps along with screen shots.

· Open Data editor: Start® All Programs® SPSS for Windows® SPSS 15.0/ SPSS13.0/ SPSS10.0.

· Enter data in SPSS Data editor. There are two views in SPSS Data Editor. In variable view, one can define the name of variables and variable types string or numeric and data view gives the spreadsheet in which data pertaining to variables may be entered in respective columns. In the present case, we enter data in numeric format.  

 

 

 

 ·Once the data entry is complete, Choose Analyze from the Menu Bar. Now select Analyze → General linear Model  → Univariate.

 

 

     

 

      · This selection displays the following screen

 

       

 · Select calories and send it to the Dependent Variable box; blk and trt may be selected for  Fixed
        Factor(s) box. After doing these the dialog box should be like this.

 

       

 

·  Now define model as per design adopted to analyze the data. A Click on the model displays Univariate:
           Model
dialog box. Click on custom then change the Build Terms as Main effects and send trt(F) and
           blk(F) to the
Model box. One gets the following screen. 

 

              

 

     ·  Click Continue to return back to the Univariate dialog box, then click paste to get the commands in
              syntax editor.

 

To test whether there is any significant difference between the average effect of 1st two treatments and the average effect of the 

remaining 5 treatments. We have to write the treatment contrast in the syntax editor as follows.
             /Lmatrix 'treatment 1,2 vs treatment 3,4,5,6,7' trt -5 -5 2 2 2 2 2;

 

To compare the treatment 3,4,5,6,7 among themselves we have to write the treatment contrast in the syntax editor as follows.
             /Lmatrix 'within treatment 3,4,5,6,7' trt 0 0 1 -1 0 0 0;
                                                                    trt 0 0 1 1 -2 0 0;
                                                                    trt 0 0 1 1 1 -3 0;
                                                                    trt 0 0 1 1 1 1 -4;
For making all possible pairwise comparisons, we have to write 21 elementary treatment contrasts in the syntax editor.
All these
contrast should be defined in the syntax editor as follows.


/Lmatrix '1 vs 2' trt 1 -1 0 0 0 0 0;
/Lmatrix '1 vs 3' trt 1 0 -1  0 0 0 0;
/Lmatrix '1 vs 4' trt 1 0 0 -1  0 0 0;
/Lmatrix '1 vs 5' trt 1 0 0 0 -1  0 0;
/Lmatrix '1 vs 6' trt 1 0 0 0 0 -1  0;
/Lmatrix '1 vs 7' trt 1 0 0 0 0 0  -1;
/Lmatrix '2 vs 3' trt  0 1 -1 0 0 0 0;
/Lmatrix '2 vs 4' trt  0 1 0 -1 0 0 0;
/Lmatrix '2 vs 5' trt  0 1 0 0 -1 0 0;
/Lmatrix '2 vs 6' trt  0 1 0 0 0 -1 0;
/Lmatrix '2 vs 7' trt  0 1 0 0 0 0 -1;
/Lmatrix '3 vs 4' trt  0 0 1 -1 0 0 0;
/Lmatrix '3 vs 5' trt  0 0 1 0 -1 0 0;
/Lmatrix '3 vs 6' trt  0 0 1 0 0 -1 0;
/Lmatrix '3 vs 7' trt  0 0 1 0 0 0 -1;
/Lmatrix '4 vs 5' trt  0 0 0 1 -1 0 0;
/Lmatrix '4 vs 6' trt  0 0 0 1 0 -1 0;
/Lmatrix '4 vs 7' trt  0 0 0 1 0 0 -1;
/Lmatrix '5 vs 6' trt  0 0 0 0 1 -1 0;
/Lmatrix '5 vs 7' trt  0 0 0 0 1 0 -1;
/Lmatrix '6 vs 7' trt  0 0 0 0 0 1 -1;

The following window will come.

              

Click  Run → All 

 

 

 To answer the questions from 1 to 5  one can use the following syntax after creating the data file.

 

UNIANOVA

calories BY blk trt

/METHOD = SSTYPE(3)

/INTERCEPT = INCLUDE

/CRITERIA = ALPHA(.05)

/Lmatrix 'treatment 1,2 vs treatment 3,4,5,6,7' trt -5 -5 2 2 2 2 2;

/Lmatrix 'within treatment 3,4,5,6,7' trt 0 0 1 -1 0 0 0;

                                                       trt 0 0 1 1 -2 0 0;

                                                       trt 0 0 1 1 1 -3 0;

                                                       trt 0 0 1 1 1 1 -4;

/Lmatrix '1 vs 2' trt 1 -1 0 0 0 0 0;

/Lmatrix '1 vs 3' trt 1 0 -1 0 0 0 0;

/Lmatrix '1 vs 4' trt 1 0 0 -1 0 0 0;

/Lmatrix '1 vs 5' trt 1 0 0 0 -1 0 0;

/Lmatrix '1 vs 6' trt 1 0 0 0 0 -1 0;

/Lmatrix '1 vs 7' trt 1 0 0 0 0 0 -1;

/Lmatrix '2 vs 3' trt 0 1 -1 0 0 0 0;

/Lmatrix '2 vs 4' trt 0 1 0 -1 0 0 0;

/Lmatrix '2 vs 5' trt 0 1 0 0 -1 0 0;

/Lmatrix '2 vs 6' trt 0 1 0 0 0 -1 0;

/Lmatrix '2 vs 7' trt 0 1 0 0 0 0 -1;

/Lmatrix '3 vs 4' trt 0 0 1 -1 0 0 0;

/Lmatrix '3 vs 5' trt 0 0 1 0 -1 0 0;

/Lmatrix '3 vs 6' trt 0 0 1 0 0 -1 0;

/Lmatrix '3 vs 7' trt 0 0 1 0 0 0 -1;

/Lmatrix '4 vs 5' trt 0 0 0 1 -1 0 0;

/Lmatrix '4 vs 6' trt 0 0 0 1 0 -1 0;

/Lmatrix '4 vs 7' trt 0 0 0 1 0 0 -1;

/Lmatrix '5 vs 6' trt 0 0 0 0 1 -1 0;

/Lmatrix '5 vs 7' trt 0 0 0 0 1 0 -1;

/Lmatrix '6 vs 7' trt 0 0 0 0 0 1 -1;

/DESIGN = trt blk .

 

 

Alternatively, all possible pair wise treatment comparisons can be performed using the Button Options on the dialogue box. 

A click on Button Options, gives the option for estimated marginal means and display means for. From the left hand box, take 

the effect treatment in the Display means  for. Then check the box Compare main effects and then there are 3 options for confidence

 interval adjustment viz. LSD(none), Bonferrnoni and Sidak. Any one of these 3 options can be selected. Default option is LSD(None). 

A screen shot for these options is 

 

 

  • Click continue to return to the Univariate dialog box and click OK to get the output.

 

 Alternatively to answer the questions from 1 to 5  one can use the following syntax after creating the data file.

 

UNIANOVA

calories BY blk trt

/METHOD = SSTYPE(3)

/INTERCEPT = INCLUDE

/EMMEANS = TABLES(trt) COMPARE ADJ(LSD)

/CRITERIA = ALPHA(.05)

/Lmatrix 'treatment 1,2 vs treatment 3,4,5,6,7' trt -5 -5 2 2 2 2 2;

/Lmatrix 'within treatment 3,4,5,6,7' trt 0 0 1 -1 0 0 0;

                                                       trt 0 0 1 1 -2 0 0;

                                                       trt 0 0 1 1 1 -3 0;

                                                       trt 0 0 1 1 1 1 -4;

 

/DESIGN = trt blk .

 

Data File

Syntax File1  File2

Result File1  File2

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Descriptive Statistics
Tests of Significance
Correlation and Regression
Completely Randomised Design
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Incomplete Block Design
Resolvable Block Design
Augmented Design
Factorial RCB Design
Partially Confounded Design
Factorial Experiment with Extra Treatments
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Principal Component Analysis
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Groups of Experiments
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Other Designed Experiments
   
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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)