Question

A research laboratory was developing a new compound for the relief of severe cases of hay fever. In an experiment with 36 volunteers, the amounts of the two active ingredients (A & B) in the compound were varied at three levels each. Randomization was used in assigning four volunteers to each of the nine treatments. The data on hours of relief can be found in the following .csv file: Fever.csv

State the Null and Alternate Hypothesis for conducting one-way ANOVA for both the variables ‘A’ and ‘B’ individually.

1.2) Perform one-way ANOVA for variable ‘A’ with respect to the variable ‘Relief’. State whether the Null Hypothesis is accepted or rejected based on the ANOVA results.

1.3) Perform one-way ANOVA for variable ‘B’ with respect to the variable ‘Relief’. State whether the Null Hypothesis is accepted or rejected based on the ANOVA results.

1.4) Analyse the effects of one variable on another with the help of an interaction plot.
What is an interaction between two treatments?
[hint: use the ‘pointplot’ function from the ‘seaborn’ function]

1.5) Perform a two-way ANOVA based on the different ingredients (variable ‘A’ & ‘B’) with the variable 'Relief' and state your results.

1.6) Mention the business implications of performing ANOVA for this particular case study.

A	B	Volunteer	Relief
1	1	1	2.4
1	1	2	2.7
1	1	3	2.3
1	1	4	2.5
1	2	1	4.6
1	2	2	4.2
1	2	3	4.9
1	2	4	4.7
1	3	1	4.8
1	3	2	4.5
1	3	3	4.4
1	3	4	4.6
2	1	1	5.8
2	1	2	5.2
2	1	3	5.5
2	1	4	5.3
2	2	1	8.9
2	2	2	9.1
2	2	3	8.7
2	2	4	9
2	3	1	9.1
2	3	2	9.3
2	3	3	8.7
2	3	4	9.4
3	1	1	6.1
3	1	2	5.7
3	1	3	5.9
3	1	4	6.2
3	2	1	9.9
3	2	2	10.5
3	2	3	10.6
3	2	4	10.1
3	3	1	13.5
3	3	2	13
3	3	3	13.3
3	3	4	13.2

Answer 1

1.2)

By using MINITAB software, we analysis one-way ANOVA test for the variable A with respect to the variable Relief.

The output of the MINITAB software is given below:

________________________________________________________________

1.3)

By using MINITAB software, we analysis one-way ANOVA test for the variable B with respect to the variable Relief.

The output of the MINITAB software is given below:

_______________________________________________________________

1.4)

The Interaction Plot between the Variable A and Variable B based on the response variable Relief:

By using MINITAB software, the output of the Interaction plot is shown below:

By observing the interaction plot between Variable A and Variable B, we can say that there is an interaction between Variable A and Variable B based on the response variable Relief.

________________________________________________________________

1.5)

By using MINITAB software, we analysis Two-way ANOVA test between the variable A and the variable B with respect to the variable Relief.

The output of the MINITAB software is given below: