Stat 405 Lab # 4

Randomized completely Block design(RCBD)

•In this design we are interested in comparing t treatment by using b blocks.

The interested model :

bj

ti

Y ijjiij

,...,1

,...,1

Hypothesis:

truenotHH

OR

truenotHH

H

truenotHH

H

HH

H

B

b

t

t

:

0...:H

:

...:

:

0...:

OR

not true :

...:

01

10

01

210

01

210

01

210

To analyze the above model we must to do the following steps:

1) Enter data2) Describe the data3) Check on the assumptions:Normality ( plot, kolomogorav sermanove) Constant variance (plot , leven’s test) Note: if the above assumptions are satisfied then we will

go to the following steps:4) Construct the ANOVA table by  Analyze > General Linear Model > Univariate >

 

 Analysis using spss:

 5 -Decide if the hypothesis reject or accept based on:

F-test (if , then we reject)

F-test (if then we reject)

 

Decision

)1)(1( ),1( , bttFMSE

MStrF

)1)(1( ),1( , btbFMSE

MSbF

OR Based on P-value if P-value < 0.05, reject null hypothesis.

Comment: we conclude that the treatments means are differs, or the treatments affect On the dependent variable at significance level =0.05.

  Note: We can covert RCBD to RCD where (SSE+SSB) in

RCBD=SSE in RCD

 Consider the following the data?

An industrial engineer is conducting an experiment on eye focus time. He is interested in the effect of t he distance of the object from the eye on the focus time. Four different distances are of interest. He has five subjects available for the experiment. Because there may be differences between individuals, he decides to conduct the experiment in a randomized block design. The data obtained are shown below?

Example:

Subject

Distances (Treatments)

6 6 6 6 10 4

6 1 6 6 7 6

5 2 3 3 5 8

3 2 4 4 6 10

1) Are there differences in the age focus time for four distances, use State the hypothesis Comment?

2) Does RCBD appear to be appropriate? Why??01.0

Response

Treatment

Block

Enter data

SolutionLevene's Test of Equality of Error Variancesa

Dependent Variable:focus

F df1 df2 Sig.

. 19 0 .

Tests the null hypothesis that the error variance of the

dependent variable is equal across groups.

a. Design: Intercept + Distances + Subject

Tests of Normality

Kolmogorov-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

focus .207 20 .024 .921 20 .104

a. Lilliefors Significance Correction

Between-Subjects Factors

N

Distances 4 5

6 5

8 5

10 5

Subject 1 4

2 4

3 4

4 4

5 4

Tests of Between-Subjects Effects

Dependent Variable:focus

Source

Type III Sum of

Squares df Mean Square F Sig.

Corrected Model 69.250a 7 9.893 7.759 .001

Intercept 470.450 1 470.450 368.980 .000

Distances 32.950 3 10.983 8.614 .003

Subject 36.300 4 9.075 7.118 .004

Error 15.300 12 1.275

Total 555.000 20

Corrected Total 84.550 19

a. R Squared = .819 (Adjusted R Squared = .713)