Statistical Model & Analysis of Split Plot Design Lecture - 47

 Statistical Model

 & 

Analysis  of  Split Plot Design

Lecture - 47

Statistical Model in CRD

Let A and B are two factors. Factor A with “a” levels that’s A1, A2, ....,Aj, ...., Aa and factor B with “b” levels that’s B1, B2, ...., Bk,..., Bb. and factor A is assign to main plot The linear model for the split-plot, with main plots arranged as a CRD is:

Yijk= μ + αj + δij + βk + (αβ)jk + ϵijk  

i =1, 2, ... ,r

j=1, 2, ... ,a

k = 1, 2, ..., b

Analysis of Split Design

Let Yijk be the yield of ith replication jth level of factor A (assign to whole plot) and kth level factor B (assign to sub plot).

The factor A total is given by;

The factor B total is given by;

ANOVA Table:

The standard error for the mean of factor A is:

The difference of standard error is:

The standard error for the mean of factor B is:

The standard error for the mean of factor AB is:

Difference between two A means at same or different level of B:

Example: 

An agriculture researcher desires to compare two varieties of wheat seeds  and 4 levels of nitrogen percentage . The experiment is performed in RCBD split plot design and data obtained given below:

Solution:

a = 2 , b = 4, r = 3

 

Now consider factor A & B:

ANOVA Table:

 Remarks: The factor A is significant, factor B and AB interaction is insignificant.

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