Fever Treatment Analysis:
Problem 1:
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
...
Fever Treatment Analysis:
Problem 1:
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
Sample of the dataset:
1.1) State the Null and Alternate Hypothesis for conducting one-way
ANOVA for both the variables ‘A’ and ‘B’ individually.
?0: The means of A and B treatment variable is equal.
?1: At least one of the means of A treatment with respect to B treatment is
unequal.Pvalue =1.0 is larger than the level of significance 0.05 in both the A and
B treatment individually.
Since the p value in this scenario is greater than (0.05), we can say that we
fail to reject the Null Hypothesis (?0 ) in both the A and B treatment
individually.
Thus the mean difference between the A and B treatment are equal.
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.
?0: The means of 'Relief' variable with respect to A treatment is equal.
?1: At least one of the means of 'Relief' variable with respect to A
treatment is unequal.
Since the p value in this scenario is less than (0.05), we can say that we
reject the Null Hypothesis (?0 ).
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.
?0: The means of 'Relief' variable with respect to B treatment is equal.
?1: At least one of the means of 'Relief' variable with respect to B
treatment is unequal.Since the p value in this scenario is less than ? (0.05), we can say that we
reject the Null Hypothesis (?0).
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’ graphical
subroutine in Python]
As seen from the above two interaction plots, there seems to be very high
interaction between 2nd and 3rd Treatment and 1st treatment is high
interactive with 2nd and 3rd treatment, Overall interaction among the two
treatment variables are high.
As seen from the above two interaction plots, there seems to be very high
interaction between 2nd and 3rd Treatment and 1st treatment is high
interactive with 2nd and 3rd treatment. In the 3rd treatment alone
interaction was less. Overall interaction among the two treatment
variables is moderate.
1.5) Perform a two-way ANOVA based on the different ingredients
(variable ‘A’ & ‘B’) and state your results.
?0: The means of 'Relief' variable with respect to A and B ingredients is equal.
?1: At least one of the means of 'Relief' variable with respect to each A and B
ingredients is unequal.Since the p value in both of the above scenarios are less than ? (0.05), we can
say that we reject the null hypothesis ( ?0 ), and it is conclude that mean is not
same for A and B ingredients with respect to relief.
1.6) Mention the business implications of performing ANOVA for this
particular case study.
1) Annova (Analysis of Variance) is the test of difference in group
means. It is used when two or more group’s means are compared.
2) Randomization (sample) assigned to volunteers with A and B
ingredients to treat Fever and find the relief on volunteer.
3) By using ANOVA, we can determine effectiveness of treating them.
We can compare which ingredients works better for treatment whether A
or B ingredients and hence we can choose the best one ingredients.
hypothesis Testing:
?0: The means of 'Relief' variable with respect to A and B ingredients
is equal.
?1: At least one of the means of 'Relief' variable with respect to each A
and B ingredients is unequal.
4) By performing ANOVA for this case study, mean is not equal for A
and B ingredients with respect to relief.
Education – Post 12th Standard Analysis:
Problem 2:
The dataset Education - Post 12th Standard.csv is a dataset which contains
the names of various colleges. This particular case study is based on
various parameters of various institutions. You are expected to do
Principal Component Analysis for this case study according to the
instructions given in the following rubric. The data dictionary of the
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