Question

Some of the green thumbs were talking one day and determined that there were about 4 factors that had a significant impact on the growth of a plant during any one phase.

These factors are: 1) Temperature 2) Water 3) Fertilizer 4) Carbon Dioxide Level.

The green thumbs thought that at least two of these factors interacted with each other, so they wanted to design an experiment to test the effects of these factors on the growth of the azaleas. They asked you to create a two-level experiment so they could determine the optimum levels for each factor. They told you that the high and low for temperature should be 75 and 90 degrees F. Water should be 1 and 4 oz. per day per container.

Fertilizer should be at 2 and 4 tablespoons per container, and the carbon dioxide content should be between .03% and .04%.

Create an experimental design such that there are 2 replications for each treatment.

Discuss the importance of randomization. Also, discuss the importance of identifying interaction, and what impact it has on your decision-making. That is, in the presence of significant main effects and significant interaction, how do you determine the optimal settings of the factors?

Answer 1

In the Experiment we have four factors 1.Temperature with two levels high 90⁰ and Low 75⁰ F

2. Water with two levels 1 oz and 2 oz per day per container

3. fertilizer with two levels 2 and 4 teaspoons per container

4. carbondioxide with two levels 0.03% and 0.04%

Each treatment is replicated 2 times completely at random

Experimental design Experimental design is 4 factor factorial experiment each with 2 levels and 2 replications

  

Temperature T	Water W	Fertilizer F	corbondioxide C	REP 1	REP 2
T1	W1	F1	C1	T1W1F1C1R1	T1W1F1C1R2
T1	W1	F1	C2	T1W1F1C2R1	T1W1F1C2R2
T1	W1	F2	C1	T1W1F2C1R1	T1W1F2C1R2
T1	W1	F2	C2	T1W1F2C2R1	T1W1F2C2R2
T1	W2	F1	C1	T1W2F1C1R1	T1W2F1C1R2
T1	W2	F1	C2	T1W2F1C2R1	T1W2F1C2R2
T1	W2	F2	C1	T1W2F2C1R1	T1W2F2C1R2
T1	W2	F2	C2	T1W2F2C2R1	T1W2F2C2R2
T2	W1	F1	C1	T2W1F1C1R1	T2W1F1C1R2
T2	W1	F1	C2	T2W1F1C2R1	T2W1F1C2R2
T2	W1	F2	C1	T2W1F2C1R1	T2W1F2C1R2
T2	W1	F2	C2	T2W1F2C2R1	T2W1F2C2R2
T2	W2	F1	C1	T2W2F1C1	T2W2F1C1R2
T2	W2	F1	C2	T2W2F1C2R1	T2W2F1C2R2
T2	W2	F2	C1	T2W2F2C1R1	T2W2F2C1R2
T2	W2	F2	C2	T2W2F2C2R1	T2W2F2C2R2

Total no.of experimental units = 2x2x2x2x2 =32

i have given each treatment combination in the above table but at the time of conducting the experiment you have to apply each treatment combination completely at random to each plot and replicate each combination two times

Importance of randomization Randomization is the process of applying each treatment combination to each experimental plot in such a way that probability of applying any treatment combination to any experimental plot is constant, It is useful for minimizing the experimental error.

Objective of conducting the Experiment The main objective of conducting this experiment is to find the significant effect of each of the factor seperately and their interactions on the growth of plants

Anova table for the design

treatment	d.f	s.s	m.s.s = s.s/ d.f	variance ratioo F
replication	1
T	1
W	1
F	1
C	1
TW ( INTERACTION)	1
TF	1
TC	1
WF	1
WC	1
FC	1
TWF	1
TWC	1
TFC	1
WFC	1
TWFC	1
Error	15
Total	31

compare Fcal value with the corresponding F critical value for (1,19) degrees of freedom at the given level of significance for testing the significant effect of each of the factor and their interactions