Elementary Statistics and Computer Application

Layout of a CRD

• Completely randomized Design is the one in which all the experimental units are taken in a single group which are homogeneous as far as possible.
The randomization procedure for allotting the treatments to various units will be as follows.

• Ste p 1: Determine the total number of experimental units.
• Step 2: Assign a plot number to each of the experimental units starting from left to right for all rows.
• Step 3: Assign the treatments to the experimental units by using random numbers.
The statistical model for CRD with one observation per unit

• Yij =µ + ti + eij
• µ = overall mean effect
• ti = true effect of the ith treatment
• eij = error term of the jth unit receiving ith treatment
The arrangement of data in CRD is as follows

	Treatments
	T1	T2	Ti	TK
	y11	y21	yi1	YK1
	y12	y22	yi2	YK2
	y1r1	y2r2	yiri	Yk rk
Total	Y1	Y2	Yi	Tk	GT


(GT – Grand total)

The null hypothesis will be

• Ho : µ1 = µ2=………….=µk or There is no significant difference between the treatments
• And the alternative hypothesis is
• H1: µ1 ≠ µ2≠ ………….≠ µk. There is significant difference between the treatments
The different steps in forming the analysis of variance table for a CRD are
1.
n= Total number of observations
2.
3.



4.

= TSS – TrSS

5. Form the following ANOVA table and calculate F value
6. Compare the calculated F with the critical value of F corresponding to treatment degrees of freedom and error degrees of freedom so that acceptance or rejection of the null hypothesis can be determined.
7. If null hypothesis is rejected that indicates there is significant differences between the different treatments.
8. Calculate C D value.
C.D. = SE(d). t

ri = number of replications for treatment i
rj = number of replications for treatment j and
t is the critical t value for error degrees of freedom at specified level of significance, either 5% or 1%.