presentation of factorial experiment 3*2

experimental designs for research workers

1. 3 2 FACTORIAL EXPERIMENT Presented by-: Deepak M.Sc. Agriculture(Agronomy) Roll no .- 10006

2. Factorial Factorial experiments involve simultaneously more than one factor each at two or more levels . Several factors affect simultaneously the characteristic under study in factorial experiments and the experimenter is interested in the main effects and the interaction effects among different factors.

3. Main Effect The main effect of a factor is defined to be the change in response produced by a change in the level of a factor. The main effect of A is the difference between the average response at A1 and A2.

4. Interaction Effect In some experiments we may find that the difference in response between the levels of one factor is not the same at all levels of the other factor. When this occurs, there is an interaction between the factors.

5. Types of factorial Based on number of factors: A factorial experiment is two factor factorial experiment, three factor factorial experiment. A factorial experiment with five varieties and three doses of nitrogen is a two factor factorial experiment. An experiment with three irrigation schedule, five varieties and three doses of nitrogen is a three factor factorial experiment.

6. Based on level of factors: A factorial experiment is either symmetrical or asymmetrical depending upon the equality or inequality in levels of factors put under experimentation. A factorial experiment is symmetrical, if the no. of levels for all the factors are same. For example, a two factor factorial experiment with five varieties and five different doses of nitrogen, is a symmetrical factorial experiment. On the other hand a two factor factorial experiment with five varieties and any no. of doses of nitrogen, is an asymmetrical factorial experiment .

7. Advantages Factorial experiments give the opportunity to an experimenter to combine the effects of more than one factor at a time. Compared to single factor experiments factorial experiments are effective because of the fact that the interaction effects can be worked out from these experiments which is not possible in single factor experiments. Factorial experiments are not only time saving but also to some extent cost saving also.

8. Disadvantages If the no. of factors or the levels of the factors or both the no. and levels of factors are more, then the no. of treatment combinations will be more, resulting in requirement of bigger experimental area and bigger block size. As the block size increases, it is very difficult under field condition to maintain homogeneity among the plots within the block. Thus there is a possibility of increasing the experimental error vis-a-vis decrease precision of experiment.

9. Statistical procedure and calculation of factorial experiments are more complicated than single factor experiments. As the no. of factors or the levels of the factor or both increases the no. of effects, including the interaction effects also increases. Sometimes it becomes very difficult to extract the information from interactions particularly the higher order interaction effects. Utmost care is needed to meticulously conduct the experiment because the failure in one experiment may result in loss of information greater compared to single factor experiment.

10. 3 2 factorial experiment This is the three level experiment. It has two factors, each at three levels. Let the levels of A be denoted by a0, a1, a2 and the levels of B be denoted by b0, b1, b2. Since every factor has three levels, 2 d.f. will be attached with each factor.

11. 3 2 Factorial RBD Experiment Variety R1 R2 R3 S1 S2 S3 S1 S2 S3 S1 S2 S3 V1 145 155 148 140 160 150 135 160 152 V2 160 162 155 152 168 152 148 165 158 V3 135 148 145 138 155 143 140 152 148

12. Grand Total= 4069 Correction Factor= GT 2 = 4069 2 = 613213.370 3.3.3 27 TSS = 4069-CF = 615257- 613213.370 = 2043.630 RSS = 1353 2 + 1358 2 +1358 2 - 613213.370 9 = 1.852

13. Yield (q/ha) S1 S2 S3 Total Average V1 V2 V3 420 460 413 475 465 436 450 465 436 1345 1420 1304 149.44 157.78 144.89 Total Average 1293 143.67 1425 158.33 1351 150.11

14. TrSS = 420 2 +475 2 +450 2 +..+455 2 +436 2 – 613213 3 =1808.296 ErSS=TSS-TrSS-RSS=2043-1808-1.852=233.482 SS(variety)=1345 2 +1420 2 +1304 2 -69413.370 9 =768.963 SS(spacing)=1293 2 +1425 2 +1351 2 -69413.370 =972.741 9 SS(VS)= TrSS- SSv -SSs =1808.296-768.963-972.741 =66.593

15. Table of Averages Variety Yield(q/ha) V2 V1 V3 157.78 149.44 144.89 Spacing S2 S3 S1 158.33 150.11 143.67