Balanced Incomplete Block Design (BIBD) Notation
Description: Balanced Incomplete Block Design (BIBD) Notation a-number of treatments m-number of treatmentsblock r-number of treatment reps b-number of blocks Narbm r(m-1)l(a-1) BIBD Example Block 1 2 3 4 A A A B B B C C C D D D Verify that l2 One
Related Topics
Download Presentation
"Balanced Incomplete Block Design (BIBD) Notation" is the property of its rightful owner. Permission is granted to download and print the materials on this website for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Presentation Transcript
slide1. Balanced Incomplete Block Design (BIBD) Notation
a-number of treatments
m-number of treatments/block
r-number of treatment reps
b-number of blocks
N=ar=bm
r(m-1)=l(a-1)<br>
slide2. BIBD Example
Block
1 2 3 4
A A A B
B B C C
C D D D
Verify that l=2<br>
slide3. One way to generate BIBD’s (assuming a and m have been selected) is to choose
This worked well in the previous example
It can be inefficient for large a or m≈a/2 Generating BIBD’s<br>
slide4. These are the adjusted means that one obtains from LSMEANS in SAS Least Squares critetion for a<br>
slide5. The solution for ai: Least Squares estimator of a<br>
slide6. These estimators are called intrablock estimators because they can be expressed as contrasts of within block observations. Intrablock estimator for a<br>
slide7. Properties of LS estimators<br>
slide8. The variance estimate is not the square of the standard error for the LSMEANS that one obtains in SAS (it’s not corrected for the overall mean). Variance of LS estimators<br>
slide9. Example Region II Science Fair Winner
Treatment is organic chemical repellent
Block is Day
Response is average number of flies on underside of lid (smaller is better)
Originally presented as a Latin Square (additional block was Fly Group)<br>
slide10. A=Ascorbic Acid B=Citric Acid C=Control D=Hesperidin
E=Lemon Juice F=Black Pepper G=Piperine Data Table<br>
slide11. When Block is a random effect, alternative estimators of treatment effects can be found Interblock Model<br>
slide12. Interblock Estimators<br>
slide13. Some properties: Interblock Estimator Properties<br>
slide14. For the random block model,
Source df SS EMS
Trt a-1 SSTrt
Blockadj b-1 SSBlock(adj)
Error N-a-b+1
Total N-1 Interblock EMS<br>
slide15. Variance Compoents<br>
slide16. Suppose we want to minimize the variance of estimators of the form:
The best weighted estimator is: BIBD Estimators<br>
slide17. The noncentrality parameters look similar to all other one factor designs we have so far seen Power Analysis<br>
a-number of treatments
m-number of treatments/block
r-number of treatment reps
b-number of blocks
N=ar=bm
r(m-1)=l(a-1)<br>
slide2. BIBD Example
Block
1 2 3 4
A A A B
B B C C
C D D D
Verify that l=2<br>
slide3. One way to generate BIBD’s (assuming a and m have been selected) is to choose
This worked well in the previous example
It can be inefficient for large a or m≈a/2 Generating BIBD’s<br>
slide4. These are the adjusted means that one obtains from LSMEANS in SAS Least Squares critetion for a<br>
slide5. The solution for ai: Least Squares estimator of a<br>
slide6. These estimators are called intrablock estimators because they can be expressed as contrasts of within block observations. Intrablock estimator for a<br>
slide7. Properties of LS estimators<br>
slide8. The variance estimate is not the square of the standard error for the LSMEANS that one obtains in SAS (it’s not corrected for the overall mean). Variance of LS estimators<br>
slide9. Example Region II Science Fair Winner
Treatment is organic chemical repellent
Block is Day
Response is average number of flies on underside of lid (smaller is better)
Originally presented as a Latin Square (additional block was Fly Group)<br>
slide10. A=Ascorbic Acid B=Citric Acid C=Control D=Hesperidin
E=Lemon Juice F=Black Pepper G=Piperine Data Table<br>
slide11. When Block is a random effect, alternative estimators of treatment effects can be found Interblock Model<br>
slide12. Interblock Estimators<br>
slide13. Some properties: Interblock Estimator Properties<br>
slide14. For the random block model,
Source df SS EMS
Trt a-1 SSTrt
Blockadj b-1 SSBlock(adj)
Error N-a-b+1
Total N-1 Interblock EMS<br>
slide15. Variance Compoents<br>
slide16. Suppose we want to minimize the variance of estimators of the form:
The best weighted estimator is: BIBD Estimators<br>
slide17. The noncentrality parameters look similar to all other one factor designs we have so far seen Power Analysis<br>