ANOVA - Lab

Introduction

In this lab, you'll get some brief practice generating an ANOVA table (AOV) and interpreting its output. You'll also perform some investigations to compare the method to the t-tests you previously employed to conduct hypothesis testing.

Objectives

In this lab you will:

• Use ANOVA for testing multiple pairwise comparisons
• Interpret results of an ANOVA and compare them to a t-test

Load the data

Start by loading in the data stored in the file 'ToothGrowth.csv':

# Your code here

Generate the ANOVA table

Now generate an ANOVA table in order to analyze the influence of the medication and dosage:

# Your code here

Interpret the output

Make a brief comment regarding the statistics and the effect of supplement and dosage on tooth length:

# Your comment here

Compare to t-tests

Now that you've had a chance to generate an ANOVA table, its interesting to compare the results to those from the t-tests you were working with earlier. With that, start by breaking the data into two samples: those given the OJ supplement, and those given the VC supplement. Afterward, you'll conduct a t-test to compare the tooth length of these two different samples:

# Your code here

Now run a t-test between these two groups and print the associated two-sided p-value:

# Calculate the 2-sided p-value for a t-test comparing the two supplement groups

A 2-Category ANOVA F-test is equivalent to a 2-tailed t-test!

Now, recalculate an ANOVA F-test with only the supplement variable. An ANOVA F-test between two categories is the same as performing a 2-tailed t-test! So, the p-value in the table should be identical to your calculation above.

Note: there may be a small fractional difference (>0.001) between the two values due to a rounding error between implementations.

# Your code here; conduct an ANOVA F-test of the oj and vc supplement groups.
# Compare the p-value to that of the t-test above. 
# They should match (there may be a tiny fractional difference due to rounding errors in varying implementations)

Run multiple t-tests

While the 2-category ANOVA test is identical to a 2-tailed t-test, performing multiple t-tests leads to the multiple comparisons problem. To investigate this, look at the various sample groups you could create from the 2 features:

for group in df.groupby(['supp', 'dose'])['len']:
    group_name = group[0]
    data = group[1]
    print(group_name)

('OJ', 0.5)
('OJ', 1.0)
('OJ', 2.0)
('VC', 0.5)
('VC', 1.0)
('VC', 2.0)

While bad practice, examine the effects of calculating multiple t-tests with the various combinations of these. To do this, generate all combinations of the above groups. For each pairwise combination, calculate the p-value of a 2-sided t-test. Print the group combinations and their associated p-value for the two-sided t-test.

# Your code here; reuse your t-test code above to calculate the p-value for a 2-sided t-test
# for all combinations of the supplement-dose groups listed above. 
# (Since there isn't a control group, compare each group to every other group.)

Summary

In this lesson, you implemented the ANOVA technique to generalize testing methods to multiple groups and factors.