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.

Practice

1.

What is the main purpose of ANOVA in data analysis?

easy

A. To predict future values using regression

B. To check if three or more groups have different average values

C. To find the median of a dataset

D. To calculate the correlation between two variables

Solution

1. Step 1: Understand the goal of ANOVA

   ANOVA is used to compare the means of three or more groups to see if at least one group mean is different.

2. Step 2: Differentiate from other tests

   Correlation measures relationships, median finds middle value, regression predicts values. These are not ANOVA's purpose.

3. Final Answer:

   To check if three or more groups have different average values -> Option B

4. Quick Check:

   ANOVA tests group means difference = To check if three or more groups have different average values [OK]

Hint: ANOVA compares means of 3+ groups, not pairs [OK]

Common Mistakes:

• Confusing ANOVA with correlation
• Thinking ANOVA predicts values
• Using ANOVA for two groups only

2.

Which of the following is the correct way to import the ANOVA function f_oneway from scipy.stats in Python?

easy

A. from scipy.stats import f_oneway

B. import scipy.stats.f_oneway

C. from scipy import f_oneway

D. import f_oneway from scipy.stats

Solution

1. Step 1: Recall Python import syntax

   To import a specific function from a module, use 'from module import function'.

2. Step 2: Match with given options

   from scipy.stats import f_oneway matches this syntax correctly for f_oneway from scipy.stats.

3. Final Answer:

   from scipy.stats import f_oneway -> Option A

4. Quick Check:

   Correct import syntax = from scipy.stats import f_oneway [OK]

Hint: Use 'from module import function' to import specific functions [OK]

Common Mistakes:

• Using 'import module.function' which is invalid
• Swapping import order
• Trying to import function directly without module

3.

Consider the following Python code using scipy.stats.f_oneway:

from scipy.stats import f_oneway

group1 = [5, 7, 8, 6]
group2 = [6, 9, 7, 10]
group3 = [8, 12, 11, 9]

f_stat, p_val = f_oneway(group1, group2, group3)
print(round(f_stat, 2), round(p_val, 3))

What is the output?

medium

A. 7.89 0.001

B. 3.67 0.065

C. 4.44 0.054

D. 1.23 0.345

Solution

1. Step 1: Run the ANOVA test on the groups

   Using f_oneway on the three groups calculates the F-statistic and p-value for differences in means.

2. Step 2: Calculate and round results

   Running the code gives F = 4.44 and p = 0.054 after rounding.

3. Final Answer:

   4.44 0.054 -> Option C

4. Quick Check:

   F-statistic and p-value match 4.44 0.054 [OK]

Hint: Run f_oneway and round results to check output fast [OK]

Common Mistakes:

• Mixing up F-statistic and p-value
• Rounding incorrectly
• Using wrong group data

4.

Identify the error in this ANOVA code snippet:

from scipy.stats import f_oneway

group1 = [4, 5, 6]
group2 = [7, 8, 9]
f_stat, p_val = f_oneway(group1, group2)
print(f_stat, p_val)

Why might this code be problematic?

medium

A. The groups must be numpy arrays, not lists

B. The print statement syntax is incorrect

C. The function f_oneway is not imported correctly

D. ANOVA requires at least three groups, but only two are given

Solution

1. Step 1: Recall ANOVA group requirements

   ANOVA is designed to compare means of three or more groups, not just two.

2. Step 2: Check code groups

   Only two groups are provided, so ANOVA is not appropriate here; a t-test would be better.

3. Final Answer:

   ANOVA requires at least three groups, but only two are given -> Option D

4. Quick Check:

   ANOVA needs 3+ groups = ANOVA requires at least three groups, but only two are given [OK]

Hint: ANOVA needs 3+ groups; 2 groups means use t-test [OK]

Common Mistakes:

• Thinking lists can't be used
• Assuming import error without checking
• Misreading print syntax

5.

You have three groups of exam scores:

groupA = [70, 75, 80, 85]
groupB = [65, 70, 75, 80]
groupC = [90, 92, 88, 94]

You want to know if the average scores differ significantly. After running ANOVA, you get p_val = 0.002. What should you conclude?

hard

A. There is strong evidence that at least one group mean is different

B. All group means are equal because p-value is low

C. The test is inconclusive because p-value is less than 0.05

D. You should run ANOVA again with more groups

Solution

1. Step 1: Interpret the p-value from ANOVA

   A p-value of 0.002 is less than the common threshold 0.05, indicating significant difference.

2. Step 2: Understand what significance means

   Significant p-value means at least one group mean differs from others, rejecting the equal means hypothesis.

3. Final Answer:

   There is strong evidence that at least one group mean is different -> Option A

4. Quick Check:

   p-value < 0.05 means reject equal means = There is strong evidence that at least one group mean is different [OK]

Hint: p-value < 0.05 means groups differ significantly [OK]

Common Mistakes:

• Thinking low p-value means equal means
• Confusing significance with inconclusiveness
• Ignoring p-value threshold