Mathematical Expectation of the Complete Randomized Design Model - 05

  Mathematical Expectation of the Complete Randomized Design 

Model

In lecture, we learnt that 

The partition of total variation into its two components parts is given by:

SSTotal = SST + SSE

Sampling Distribution

Consider the model:

Yij= μ + τj + ϵij

The error term “ ϵij” following normal distribution with mean = 0 and fixed variance “σ2”.  Using the property of normal distribution that  is a linear function of . So, Yij is also follow normal distribution

Example:  

An agricultural experiment station wishes to determine the yields of five varieties of corn. Each type of corn is planted to four plots of land with equal fertility, and the yields, in units of 100 bushels, are shown below. In view of these results, can we conclude that the mean yields of the five varieties of corn are the same using the 5% level of significance? (F=4.14)

Varieties
A	B	C	D	E
4	7	5	11	4
6	13	4	10	8
4	10	4	9	6
10	12	9	14	10

If, you are given that 1 = 7, 2 = 11, 3 = 6, 4 = 12, and 5 = 7, specifically identify the estimate of the following errors, ε11, ε23, ε44, and ε52. (-3, -2, 2, 1).

Solution: 

Varieties
	A	B	C	D	E
	4	7	5	11	4
	6	13	4	10	8
	4	10	4	9	6
	10	12	9	14	10
T.j	24	42	22	44	28	160
Sqr T.j						5544

ANOVA Table:

SV	df	SS	MS	F	F(4, 13)
b/w Treatments	4	106	26.50	4.14	3.06
Error	15	96	6.40
Total	19	202

• Read More: CRD Subsampling