Design of Experiments
2. Levels X Treatments Design
This design is a direct improvement over simple random design in the sense that in this design ‘S’error is minimized and we guarantee that sampling error has been controlled. It provides a direct control for intra subjects variations. The main focus of design is to control ‘S’ error. It does not consider ‘G’ and
‘R’ errors. In this design stratified sampling technique is used. It means the population is classified on the basis of some relevant criterion. Thus, the strata are formed on the basis of criterion subjects from each stratum is assigned to each treatment and each treatment is assigned to every level of subject;
these treatments should be assigned independently. The purpose of assigning treatment to each level of subjects is to eliminate the ‘S’error.
Layout of the Design
In this design levels are introduced only to equate the groups for studying in main effects. The ‘N’ size of sample is selected from the population. It is stratified into three levels. An equal number of subjects are taken from each level. The subjects of each level are assigned to each treatment as shown below:
Treatments
Levels A1 A2 A3
L1 n n n
Criterion
L2 n n n
Intelligence
L3 n n n
Experimental Variables is administered.
Criterion Test X1 Y1 Z1
Scores
X2 Y2 Z2
X3 Y3 Z3
– – –
– – –
Xn Yn Zn
Total å x å y å z = åi
Analysis of Data
Simple one way analysis of variance technique may be used for analysis. The main effect of treatment is analyzed as follows:
Analysis Variance Table
Source df. S S MS F
Between (K–1) SSb MSb
MSw F= MSb
Within N–K SSw MSw df ® (K–1), (N–K)
Total N–1 SSt
The significance of F value with (K–1), (N–K) degrees of freedom is ascertained with the help of Table and interpretation of the result is done. The conclusions are drawn about effectiveness of treatments.
There are three treatments, which therefore, ‘t’, must be followed if ‘F’ is significant.
Advantages
The following are the advantages of this design:
1. It is the direct improvement over simple randomised design.
2. It eliminates ‘S’ error by selecting subjects from each level.
3. This design yields relatively more dependable and accurate results than earlier one.
Disadvantages
The following are the limitations of this design:
1. This design has less difference than the simple randomized design because type ‘G’ and ‘R’
errors are not considered in this design.
2. The levels are formed only on the basis of one criterion. Thus, the groups are equated quantitatively but not qualitatively. So the intra subjects variation is not controlled.
3. It is a difficult job to consider the criterion for stratifying the sample. In an investigation a number of criterion seem to be equally relevant in that situation, it is difficult for investigator to choose the most relevant criterion for stratification.
4. This design generally confused with the factorial design.
5. The design is not practicable in teaching-learning situation.
Suggestions
The following precautions should be taken in using the design:
1. Other improved designs may be used.
2. Pre-test and post -test should be administered and we should prefer analysis of covariance technique.
3. The levels and treatments effect may be considered for obtaining accurate results 3. Treatments X Subjects Design
Treatment X Subjects designs are those in which all treatments are successively given to the same subjects. The choice of this design is conditioned by the fact that treatments are such that all can be administered in a sequence to the same subjects and the effects of each treatment are influenced by the fact that other treatments have previously been administered to the same subjects. Thus, it is possible to eliminate entirely the influence of inter-subjects differences upon the treatments effect. Since exactly the same subjects are assigned in all the treatments, no part of the difference in the treatment means can be attributed to differences among subjects. This design eliminates entirely the ‘S’error. Although the chance error of measurement might still favour one treatment or the other inter subjects differences are usually a major source of error in educational and psychological experiments. This design is more precise then simple randomized design and treatments X Levels design.
Model or Layout of Design
The same subjects are assigned to each treatment successively as shown below:
Treatments
T1 T2 T3
Subjects A B C
C A B
B C A
– – –
Treatment M1 M2 M3 Main effects
Analysis of Data
The analysis of variance technique is used to analyze the main effects of treatment.
Analysis Variance Table
Source df. S S MS F
Treatment a–1 SSA MSA
AS A
MS F= MS
Subjects S s–a SSS MSA
Treatment & (a–1)(s–1) SSAS MSAS df(a–1), (S–1)
Subject As
Total N–1 SSr
The significance of F is examined for the result.
Advantages
The following are the main advantages of this design:
1. The treatments X Subjects design is usually for more precise than the simple randomized or treatments X levels design, granting that a fairly reliable criterion measure is employed.
2. This design is a useful design so far concerned with the sampling error. It eliminates entirely the ‘S’ error.
Disadvantages
The following are the limitations of this design:
1. The effect of given treatment is usually not independent or unaffected by the previous administration of another treatment to the same subjects.
2. The use of this design usually requires that equivalent forms of a criterion test be available, so as to eliminate or render negligible the practice effect of taking the same test more than once.
3. The design does not take into consideration type ‘G’ and type ‘R’ errors.
4. The same subjects are assigned to the same treatments, it causes, ‘R’ errors because the subjects are the replicates. It means that intervening variables may influence the treatment effect.