Analysis of Variance and
Design of Experiments-II
MODULE IV
LECTURE - 20
PARTIAL CONFOUNDING
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
Similarly, when B is estimated from the replicates 1 and 3 separately,
Analysis of Variance and
Design of Experiments-II
MODULE I
LECTURE - 5
INCOMPLETE BLOCK DESIGNS
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
Theorem E ( P ) D , Var ( P ) 2 D
= =
Proof
=
D K NR 1 N '
=
P B NR
Analysis of Variance and
Design of Experiments-II
MODULE - II
LECTURE - 12
BALANCED INCOMPLETE BLOCK
DESIGN (BIBD)
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
The variance of an elementary contrast ( j j ' ,
Analysis of Variance and
Design of Experiments-II
MODULE - III
LECTURE - 15
PARTIALLY BALANCED
INCOMPLETE BLOCK DESIGN
(PBIBD)
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
The balanced incomplete block designs
Analysis of Variance and
Design of Experiments-II
MODULE - II
LECTURE - 14
BALANCED INCOMPLETE BLOCK
DESIGN (BIBD)
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
The effective variance can be approximately estim
Analysis of Variance and
Design of Experiments-II
MODULE I
LECTURE - 8
INCOMPLETE BLOCK DESIGNS
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
Generally, we are not interested merely in the interblock analysis o
Analysis of Variance and
Design of Experiments-II
MODULE IV
LECTURE - 19
PARTIAL CONFOUNDING
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
The objective of confounding is to mix the less important treatment com
Analysis of Variance and
Design of Experiments-II
MODULE - III
LECTURE - 18
PARTIALLY BALANCED
INCOMPLETE BLOCK DESIGN
(PBIBD)
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
Intrablock analysis of PBIBD with two
Analysis of Variance and
Design of Experiments-II
MODULE - III
LECTURE - 17
PARTIALLY BALANCED
INCOMPLETE BLOCK DESIGN
(PBIBD)
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
Group divisible association scheme
Le
Analysis of Variance and
Design of Experiments-II
MODULE - II
LECTURE - 13
BALANCED INCOMPLETE BLOCK
DESIGN (BIBD)
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
The variance of
l ' is obtained as
k
Var (l ')
Analysis of Variance and
Design of Experiments-II
MODULE I
LECTURE - 3
INCOMPLETE BLOCK DESIGNS
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
Analysis of variance table
Under the null hypothesis H 0 : = 0, the
Analysis of Variance and
Design of Experiments-II
MODULE I
LECTURE - 2
INCOMPLETE BLOCK DESIGNS
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
In order to obtain the estimates of the parameters, there are two op
Analysis of Variance and
Design of Experiments-II
MODULE I
LECTURE - 7
INCOMPLETE BLOCK DESIGNS
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
Interblock analysis of incomplete block design
The purpose of block
Analysis of Variance and
Design of Experiments-II
MODULE I
LECTURE - 1
INCOMPLETE BLOCK DESIGNS
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
If the number of treatments to be compared is large, then we need a
Analysis of Variance and
Design of Experiments-II
MODULE I
LECTURE - 6
INCOMPLETE BLOCK DESIGNS
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
Contrast
v
A linear function
c j j = C ' where c1 , c2 ,., cv are g
Analysis of Variance and
Design of Experiments-II
MODULE I
LECTURE - 4
INCOMPLETE BLOCK DESIGNS
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
Theorem:
E (Q) = C
Var (Q) = 2C
Proof:
n B
n1 j B1
+ . + bj b
Qj
Analysis of Variance and
Design of Experiments-II
MODULE - II
LECTURE - 9
BALANCED INCOMPLETE BLOCK
DESIGN (BIBD)
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
The designs like CRD and RBD are the complete bloc
Analysis of Variance and
Design of Experiments-II
MODULE - II
LECTURE - 10
BALANCED INCOMPLETE BLOCK
DESIGN (BIBD)
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
Interpretation of conditions of BIBD
Interpretati
Analysis of Variance and
Design of Experiments-II
MODULE - II
LECTURE - 11
BALANCED INCOMPLETE BLOCK
DESIGN (BIBD)
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
Intrablock analysis of BIBD
Consider the model
yi
Analysis of Variance and
Design of Experiments-II
MODULE - III
LECTURE - 16
PARTIALLY BALANCED
INCOMPLETE BLOCK DESIGN
(PBIBD)
Dr. Shalabh
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
2
In order to learn how to write these