RCBD with Sub Sampling lecture - 13

 

RCBD with Sub Sampling

The RCBD with sub sampling is represented by the following statistical model:

$$

Yijk = μ +ρi + τj + ϵij + δijk       i =1, 2, ..., b     j=1, 2, ..., t     k =1, 2, ..., n.

Analysis

Let Yijk represent the response value of j^th treatment in the i^th block and k^th observation. That’s

Add the observation of each cell and represented by Tij.  , arranged as:

The partition of total variation into its component parts are as:

SSTotal = SSB + SST + SSS + SSE

ANOVA Table:

SV	df	SS	MS	F
Treatment	t-1	SST	MST	F1
Block	b-1	SSB	MSB	F2
Sampling Error	(b-1)(t-1)	SSS	MSS	F3
Exp. Error	tb (n-1)	SSE	MSE
Total	n-1	SSTotal

Example: 

The responses of 6 fertilizers used on sugar cane by using RCB design is given below: 

Block	Treatment
	A	B	C	D	E	F
1	16.5 16.4	16.0 16.6	15.1 15.6	15.6 15.5	13.5  14.3	14.2  13.0
2	16.4 15.8	14.4 13.9	15.0 14.3	14.7 15.2	14.2  13.3	12.5  12.6
3	15.7 15.3	15.5 16.6	15.9 16.2	15.6 15.5	14.5  15.1	15.1  14.3
4	16.6 16.3	15.6 16.2	16.1 15.2	15.4 14.6	15.4  15.1	14.0  14.8
5	16.0 16.8	16.4 16.2	15.0 14.5	15.6 15.2	14.9  13.3	14.3  14.6

Test the effect of  six fertilizers at 5 %.

Solution:

Block	Treatment
	A	B	C	D	E	F
1	16.5 16.4	16.0 16.6	15.1 15.6	15.6 15.5	13.5 14.3	14.2 13.0
	32.9	32.6	30.7	31.1	27.8	27.2
2	16.4 15.8	14.4 13.9	15.0 14.3	14.7 15.2	14.2 13.3	12.5 12.6
	32.2	28.3	29.3	29.9	27.5	25.1
3	15.7 15.3	15.5 16.6	15.9 16.2	15.6 15.5	14.5 15.1	15.1 14.3
	31.0	32.1	32.1	31.1	29.6	29.4
4	16.6 16.3	15.6 16.2	16.1 15.2	15.4 14.6	15.4 15.1	14.0 14.8
	32.7	31.8	31.3	30.0	30.5	28.8
5	16.0 16.8	16.4 16.2	15.0 14.5	15.6 15.2	14.9 13.3	14.3 14.6
	32.8	32.6	29.5	30.8	28.2	28.9

ANOVA Table:

SV	df	SS	MS	F	F tab
Treatment	5	34.932	6.9864	12.42	3.21
Block	4	9.53	2.3825	4.236
Sampling Error	30	6.536	0.218	2.57
Exp. Error	20	11.24	0.5624
Total	59	62.246

The effect of 6 treatments is significant.

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