ANOVA in Data Analysis Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of One-Way ANOVA F-statistic Calculation

What is the output of the following Python code that performs a one-way ANOVA test on three groups of data?

Data Analysis Python

import scipy.stats as stats

group1 = [23, 21, 19, 24, 30]
group2 = [30, 29, 31, 28, 35]
group3 = [22, 20, 19, 18, 21]

f_stat, p_value = stats.f_oneway(group1, group2, group3)
print(round(f_stat, 2))

A 15.34

B 16.22

C 5.12

D 0.87

💡 Hint

Recall that the F-statistic measures variance between groups relative to variance within groups.

The F-statistic calculated by scipy.stats.f_oneway for these groups is approximately 16.22, indicating significant differences between group means.

❓ data_output

intermediate

Number of Significant Differences in Post-Hoc Test

After performing a one-way ANOVA test that showed significance, a Tukey HSD post-hoc test was run on four groups. How many pairs show a significant difference at alpha=0.05?

Data Analysis Python

import pandas as pd
from statsmodels.stats.multicomp import pairwise_tukeyhsd

data = pd.DataFrame({
    'value': [5,6,7,8,5,6,7,8,10,11,12,13,10,11,12,13],
    'group': ['A','A','A','A','B','B','B','B','C','C','C','C','D','D','D','D']
})

result = pairwise_tukeyhsd(data['value'], data['group'], alpha=0.05)
significant_pairs = sum(result.reject)
print(significant_pairs)

A 1

B 6

C 3

D 4

💡 Hint

Check how many pairs have reject=True in the Tukey HSD result.

The Tukey HSD test shows significant differences between 4 pairs at alpha=0.05, so the count is 4.

🔧 Debug

advanced

Identify the Error in ANOVA Code

What error will this code raise when trying to perform a one-way ANOVA test?

Data Analysis Python

import scipy.stats as stats

# Groups with unequal lengths
group1 = [10, 12, 14]
group2 = [15, 16]
group3 = [20, 22, 23]

f_stat, p_value = stats.f_oneway(group1, group2, group3)
print(f_stat)

A ValueError: all input arrays must have the same length

B TypeError: unsupported operand type(s) for +: 'int' and 'list'

C No error, prints F-statistic

D IndexError: list index out of range

💡 Hint

Check if scipy.stats.f_oneway requires equal length groups.

scipy.stats.f_oneway can handle groups of unequal length, so no error occurs and the F-statistic is printed.

🧠 Conceptual

advanced

Interpretation of ANOVA p-value

If a one-way ANOVA test returns a p-value of 0.03, what is the correct interpretation at a 0.05 significance level?

A There is evidence to reject the null hypothesis; at least one group mean differs.

B There is strong evidence that all group means are equal.

C There is insufficient evidence to reject the null hypothesis.

D The test is inconclusive; more data is needed.

💡 Hint

Recall that p-value less than alpha means rejecting the null hypothesis.

A p-value of 0.03 is less than 0.05, so we reject the null hypothesis that all group means are equal, meaning at least one differs.

🚀 Application

expert

Choosing the Correct ANOVA Type for Data

You have data from three different diets tested on the same group of 10 people measured over three weeks. Which ANOVA test is most appropriate to analyze if diet affects weight loss?

A Repeated measures ANOVA

B Two-way ANOVA without replication

C One-way ANOVA

D Chi-square test

💡 Hint

Consider that the same people are measured multiple times under different diets.

Repeated measures ANOVA is used when the same subjects are measured multiple times under different conditions, accounting for within-subject variability.