This slide contains B.Pharm 4th year (8th sem), Biostatistics and Research Methodology subject topic from Unit- 4 "Blocking and Confounding system at two level factorials.

1. BLOCKING AND CONFOUNDING
SYSTEM FOR TWO-LEVEL
FACTORIALS
Mr. HIMANSHU SHARMA (ASST. PROF.)
SHRI RAM COLLEGE OF PHARMACY
BIOSTATISTICS AND RESEARCH METHODOLOGY
B.PHARM 4th YEAR (8th SEM)

2. Research Studies
Observational
Analytical
Cohort
Case-control
Cross-
sectional
Descriptive
Case Report
Case Series
Surveys
Experimental
Randomised
Controlled
Parallel
Cross-over
Uncontrolled
Others
Latin Square
Factorial
Randomized
Cluster
Randomised
Non-
randomised
Controlled
Uncontrolled

3. Blocking System for 2k Factorial
 In the statistical theory of the design of experiments, blocking is the
arranging of experimental units in groups (blocks) that are similar to one
another.
 Blocking is a technique used in design of experiments methodology to deal
with the systematic differences to ensure that all the factors of interest and
interactions between the factors can be assessed in the design.
 The blocking technique is used to make the treatments are equally effective
across many situations.
 Blocking technique is used for dealing with controllable nuisance (hindrance)
variable.
 Sometime it is impossible to perform all 2K factorial experiment under
homogeneous condition.
 If there are N replicates of the design then each replicate is a block Each
replicate is run in one of the blocks (time periods, batches of raw material
etc.)

4. Blocking System for 2k Factorial
 Example:
Data for Tablet production for old and new machine in different shifts by different no.
of operators.
Solution:
Old(-) Less(8)= -
New(+) More(10)= +
Factor- A
(Machine)
Factor- B (Operators)
Less (8) More (16)
Old 65 75
New 85 95
Standard Order Factor A Factor B Treatment Combination
1 -1 -1 (1)
2 +1 -1 a
3 -1 +1 b
4 +1 +1 ab

5. Confounding System for 2k Factorial
 A confounding design is one where some treatment effects (main or
interactions) are estimated by the same linear combination of the
experimental observations as some blocking effects. In this case, the
treatment effect and the blocking effect are said to be confounded.
 Confounding is a design technique for arranging a complete factorial
experiment blocks, where the block size is smaller than the number of
treatment combination in one replicate.
 Confounding these are design techniques for arranging experiments to make
high order interaction to be indistinguishable from (or confound with) blocks.
 In many case it is impossible to perform a complete replicate of factorial
design in one block
 Block size smaller than the number of treatment combination in one
replicate.

6. Confounding System for 2k Factorial
 Example:
Factor- A
(Machine)
Factor- B (Operators)
Less (8) More (16)
Old 65 75
New 85 95
Treatment
Combination
Factorial Effect
A B AB Block
(1) - - + 1
a + - - 2
b - + - 2
ab + + + 1
Block 1
Block 2
(1)
ab
a
b

7. Confounding System for Two level Factorial
 Example: 2k Factorial Design Experiments (i.e., 23 = 8)
Standard Order Factor A Factor B Factor C
Treatment
Combination
1 -1 -1 -1 (1)
2 +1 -1 -1 a
3 -1 +1 -1 b
4 +1 +1 -1 ab
5 -1 -1 +1 c
6 +1 -1 +1 ac
7 -1 +1 +1 bc
8 +1 +1 +1 abc

8. Confounding System for Two level Factorial
 Example: 2k Factorial Design Experiments (i.e., 23 = 8)
Treatment
Combination
Factorial Effect
A B AB C AC BC ABC Block
(1) - - + - + + - 1
a + - - - - + + 2
b - + - - + - + 2
ab + + + - - - - 1
c + - - + - - + 2
ac + - - + + - - 1
bc - + - + - + - 1
abc + + + + + + + 2
Block 1
Block 2
(1)
ab
ac
bc
a
b
c
abc

9. THANK YOU