Question

06, (2096) A group of students have performed an experiment where they investigate how the factors: amount of water (factor A) and amount of light (factor B) influence the growth of a certain plant. Two amounts of water and two amounts of light are used, and four replicates for each treatment combination are run. The results are as follows: Amount of Water Amount of Light Amount of Water Amount of Light 15 12 15 12 10 2 a) Determine the effects for factor A, factor B and the interaction of A and B b) Obtain a main effects plot for factors A and B c) Obtain an interaction plot d) On the basis of the results obtained in a)-c), what conclusions can you reach concerning the importance of factor A, factor B, and the interaction of A and B on the growth of the plant?

Answer 1

a) Let's do a two-way ANOVA to measure the effects of both factors and their interaction on our dependent variable.

Here, we have two factors, A and B. The dependent variable is Number of inches of fabric burned.

Enter the data into SPSS and use Analyse -> Univariate to run the two-way ANOVA test. The output is as follows:

Type lll Sum of Squares df Mean Square Sig Source Corrected Model Intercept Fabric Factor Fabric * Factor Error Tota Corrected Total a. R Squared .876 (Adjusted R Squared844) 847.500a 21904.000 49.000 756.250 42.250 120.500 22872.000 968.000 28.133 21904.000 2181.311 4.880 75.311 4.207 282.500 49.000 756.250 42.250 10.042 047 063 12 16

Here, Fabric is Factor A and 'Factor' is Fabric B.

As the p-value is significant for Fabric and Factor B (p<0.05 for both), we can say that fabric and treatments have a significant effect on the fabric burned. However as the interaction effect has p-value>0.05, there is no effect of interaction on the fabric burned.

b) Main effects plot of Factor A is:

Main effects plot of Factor B:

Estimated aginal reavg of Dota 0 actos

c) Main effects plot of interaction:

factos 2-00 24

Here, under Fabric:

1 = Cotton

2 = Polyester

Under 'Factor' variable which is Treatments or Factor B,

1 = X

2 = Y

d) We can say that both factors A and B are important. However, the interaction of A and B didn't come out to be significant. From the graphs, we can say that Fabric 1 (Cotton) and Treatment Y has a lesser mean of no. of inches of fabric burned than their corresponding fabric and treatment.