Elementary Statistics and Computer Application

Analysis of RBD

• The results of RBD can be arranged in a two way table according to the replications (blocks) and treatments
• There will be r x t observations in total where r stands for number of replications and t for number of treatments
• The data are arranged in a two way table form by representing treatments in rows and replications in columns

 

Treatment	Replication					Total
	1	2	3	…………	r
1	y11	y12	y13	…………	y1r	T1
2	y21	y22	y23	…………	y2r	T2
3	y31	y32	y33	…………	y3r	T3
t	yt1	yt2	yt3	………….	ytr	Tt
Total	R1	R2	R3		Rr	G.T

• In this design the total variance is divided into three sources of variation viz., between replications, between treatments and error

• Total SS=TSS= y ij 2 – CF
• Replication SS=RSS= = Rj2 – CF
• Treatments SS=TrSS = Ti2 - CF

• Error SS=ESS = Total SS – Replication SS – Treatment SS
• The skeleton ANOVA table for RBD with t treatments and r replications

Sources of variation	d.f.	SS	MS	F Value
Replication	r-1	RSS	RMS	RM S/ EM S
Treatment	t-1	TrSS	TrMS	TrMS/EMS
Error	(r-1) (t-1)	ESS	EMS
Total	rt –1	TSS

• CD = SE(d) . t where S.E(d)=
• t = critical value of t for a specified level of significance and error degrees of freedom
• Based on the CD value the bar chart can be drawn.
• From the bar chart conclusion can be written.