A Field Guide to Experimental 
Designs

Regression--treatments from an otherwise continuous range of values applied to a CRD.

Note: this is a simple arrangement of treatments that could be found in almost any other experimental design. See arrangements versus design.

Field marks:

  • Treatments are specific quantities from an otherwise continuous range of values. For example 0, 2, 5, 10 kg of fertilizer per experimental subject.
  • Replications of treatments are assigned completely at random to independent experimental subjects.
  • Adjacent subjects could potentially have the same treatment.

Sample layout:
Different colors represent the range of treatments. There are 4 (0, 1, 2, 5) treatments with 4 replications (a-d) each.
Regression sample layout

     5a  2a  0a  5b
     1a  5c  1b  0b
     2b  1c  0c  2c
     0d  5d  2d  1d

 

ANOVA table format:

Source of
variation
Degrees of
freedoma
Sums of
squares (SSQ)
Mean
square (MS)
F
Regression (R) 1 SSQR SSQR MSR/MSE
Error (E) t*r-2 SSQE SSQE/(t*r-2)  
Total (Tot) t*r-1 SSQTot    
awhere t=number of treatments and r=number of replications per treatment.

Sample ANOVA table:

Source of
variation
Degrees of
freedom
Sums of
squares (SSQ)
Mean
square (MS)
F
Regressiona 1 935.39 935.39 1513.75b
Error 14 8.65 0.62  
Total 15 944.04    
aThe calculated regression line is Y=9.99+4.09X
bF test with 1.14 degrees of freedom at P=0.05 is 4.60

Sample SAS GLM statements:

PROC GLM;
  MODEL Y = X / SOLUTION;
RUN;

Note: the SOLUTION option returns the regression line parameters.

Compare with:

 

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Thursday, August 17, 2000