TWO FACTOR EXPERIMENTS

 

A common problem in research is investigating the effect of each of a number of variables, or factors, on some response ‘Y’. In earlier times factors were studied one at a time, with separate experiments devoted to each factor. Later, R. A. Fisher pointed out that important advantages are gained by combining the study of several factors in the same factorial experiment. In the factorial approach, the investigator compares all treatments that can be formed by combining the levels of the different factors. Factorial experimentation is highly efficient, because every observation supplies information about all the factors included in the experiment. Also factorial experimentation is a systematic method of investigating the relationships between the effects of different factors.

The individual treatments are called factors.

The treatment levels within a factor are called levels.

A 2 x 2 factor experiment with two factors and two levels for each factor is denoted as a 22 factorial experiment. An experiment with 'f ' factors at 't' levels is denoted as a 'ft'  factorial experiment. If the number of levels in each treatments is different then the notation is tA x tB. For example, if factor A has 3 levels and factor B has 5 then it is a 3 x 5 factorial experiment. OPSTAT provides the analysis of most commonly used two factor experiments such as two factor CRD, Two factor RBD and Split Plot designs.The analysis of two factor experiments will be explained using the following data set:

Example of ANOVA for a 2x2 Factorial (CRD)

 

 Data for the RCBD analysis of a 2 x 2 factorial design

 

 

 

Replicates

 Character 1

1

2

3

4

Treatments combinations

a0b0

12

15

14

13

a0b1

19

22

23

21

a1b0

29

27

33

30

a1b1

32

35

38

37

Character2

Treatments combinations

 

a0b0

12.5 15.7 13.4 14.2

a0b1

16.5 14.5 16.3 17.2

a1b0

14.6 15.8 13.6 11.6

a1b1

12.8 13.5 13.2 15.1

 

In this example we have two factor say A and B. Both A and B have two levels each i.e. 0 and 1.We have 2 x  2 = 4 treatment combinations. For analysis we have to arrange the data of these treatment combination as follows:

    Data are arranged in data file or in text area of web page in such a way that all the replications of 1st level of first factor and 1st level of second factor (i.e. a0b0) should be entered in one line. The observations of replications must be space or tab delimited. Similarly for all other levels of 2nd factor corresponding to 1st level of 1st factor (i.e. a0b1)are entered. Now take the 2nd level of 1st factor (a1) and repeat all the levels of 2nd factor (b0 and b1) in similar manner. Note that each treatment combination must be entered in separate line. Moreover, if you want to analyse the data of many characters having same treatments then enter the data for second character just after the fist character without any line gap. The data file for above mentioned example will be looks likes

 

12 15 14 13

19 22 23 21

29 27 33 30

32 35 38 37

12.5 15.7 13.4 14.2

16.5 14.5 16.3 17.2

14.6 15.8 13.6 11.6

12.8 13.5 13.2 15.1

 

Procedure of Analysis