ANOVA (f_oneway) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of One-Way ANOVA Test

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

SciPy

from scipy.stats import f_oneway

group1 = [5, 7, 8, 6, 9]
group2 = [10, 12, 11, 13, 12]
group3 = [7, 8, 7, 6, 7]

stat, p = f_oneway(group1, group2, group3)
print(round(stat, 3), round(p, 3))

A 12.5 0.002

B 10.8 0.001

C 15.0 0.000

D 8.3 0.005

💡 Hint

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

The F-statistic is approximately 10.8 and the p-value is very small (close to 0), indicating significant differences between groups.

❓ data_output

intermediate

Number of Groups in ANOVA Test

How many groups are being compared in this ANOVA test?

SciPy

from scipy.stats import f_oneway

# Data groups
A = [4, 5, 6]
B = [7, 8, 9]
C = [10, 11, 12]
D = [13, 14, 15]

stat, p = f_oneway(A, B, C, D)
print(len([A, B, C, D]))

A 4

B 3

C 2

D 5

💡 Hint

Count the number of lists passed to the function.

There are 4 groups: A, B, C, and D.

🔧 Debug

advanced

Identify the Error in ANOVA Code

What error does the following code produce?

SciPy

from scipy.stats import f_oneway

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

stat, p = f_oneway(group1, group2)
print(stat, p)

A TypeError: f_oneway() argument 2 must be a sequence

B ValueError: operands could not be broadcast together

C No error, outputs F-statistic and p-value

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

💡 Hint

Check the data types of the groups passed to f_oneway.

group2 is a tuple, which is a sequence, so f_oneway accepts it without error.

🚀 Application

advanced

Interpreting ANOVA Results

You run an ANOVA test and get F-statistic = 2.5 and p-value = 0.12. What does this mean about the groups?

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

B All group means are exactly equal.

C The test is invalid because p-value is greater than 0.05.

D There is no strong evidence to say the group means differ.

💡 Hint

Remember the p-value threshold for significance is usually 0.05.

A p-value of 0.12 is greater than 0.05, so we do not reject the null hypothesis that group means are equal.

🧠 Conceptual

expert

Assumptions of One-Way ANOVA

Which of the following is NOT an assumption required for a valid one-way ANOVA test?

A The dependent variable is categorical.

B The groups have equal variances (homogeneity of variance).

C The samples are independent of each other.

D The data in each group are approximately normally distributed.

💡 Hint

Think about the type of data ANOVA analyzes.

ANOVA requires the dependent variable to be continuous, not categorical.

Practice

1.

What does the scipy.stats.f_oneway function test in data science?

easy

A. If a dataset follows a normal distribution

B. If two variables are correlated

C. If the means of multiple groups are significantly different

D. If the variance within a single group is zero

Solution

1. Step 1: Understand the purpose of ANOVA

   ANOVA (Analysis of Variance) tests if the means of multiple groups differ significantly.

2. Step 2: Identify what f_oneway does

   The f_oneway function in scipy performs this ANOVA test on given groups.

3. Final Answer:

   If the means of multiple groups are significantly different -> Option C

4. Quick Check:

   ANOVA tests group means difference = A [OK]

Hint: ANOVA checks if group averages differ significantly [OK]

Common Mistakes:

• Confusing ANOVA with correlation tests
• Thinking it tests variance within one group
• Assuming it checks normality of data

2.

Which of the following is the correct way to call scipy.stats.f_oneway for three groups a, b, and c?

import scipy.stats as stats

# Choose the correct call

easy

A. stats.f_oneway(a + b + c)

B. stats.f_oneway(a, b, c)

C. stats.f_oneway([a, b, c])

D. stats.f_oneway(a, [b, c])

Solution

1. Step 1: Check function signature

   f_oneway takes each group as a separate argument, not a list of groups.

2. Step 2: Match correct call

   Passing groups as separate arguments like a, b, c is correct.

3. Final Answer:

   stats.f_oneway(a, b, c) -> Option B

4. Quick Check:

   Separate groups as arguments = C [OK]

Hint: Pass each group as separate arguments, not a list [OK]

Common Mistakes:

• Passing a list of groups instead of separate arguments
• Concatenating groups instead of passing separately
• Mixing list and individual arguments

3.

What will be the output of the following code?

import scipy.stats as stats

a = [5, 7, 8, 6]
b = [6, 9, 7, 10]
c = [15, 18, 20, 17]

result = stats.f_oneway(a, b, c)
print("{:.3f}".format(result.pvalue))

medium

A. 0.000

B. 0.500

C. 0.050

D. 0.100

Solution

1. Step 1: Understand the data groups

   Groups a and b have similar means (~6.5-8), group c has much higher values (~17.5).

2. Step 2: Interpret ANOVA result

   Because group c differs strongly, the p-value will be very low, indicating significant difference.

3. Final Answer:

   0.000 -> Option A

4. Quick Check:

   Big group mean difference -> low p-value = 0.000 [OK]

Hint: Big mean differences give very low p-values [OK]

Common Mistakes:

• Assuming p-value is high when groups differ
• Confusing p-value with F-statistic
• Rounding errors in p-value

4.

Identify the error in this code snippet that uses scipy.stats.f_oneway:

import scipy.stats as stats

a = [1, 2, 3]
b = [4, 5, 6]

result = stats.f_oneway(a, b)
print(result.pvalue)

medium

A. Missing import statement for scipy

B. Using pvalue instead of p_value

C. Passing lists instead of numpy arrays

D. No error; code runs correctly

Solution

1. Step 1: Check imports and function usage

   The code imports scipy.stats as stats correctly and calls f_oneway with two lists.

2. Step 2: Verify output attribute

   The result object has attribute pvalue (not p_value), so accessing result.pvalue is correct.

3. Final Answer:

   No error; code runs correctly -> Option D

4. Quick Check:

   Lists accepted and pvalue attribute correct = B [OK]

Hint: Lists work; attribute is 'pvalue', not 'p_value' [OK]

Common Mistakes:

• Thinking lists must be numpy arrays
• Using wrong attribute name for p-value
• Missing import statement

5.

You have three groups of exam scores:

group1 = [70, 75, 80, 85]
group2 = [72, 78, 79, 83]
group3 = [90, 92, 88, 91]

You want to test if the average scores differ significantly. After running scipy.stats.f_oneway(group1, group2, group3), you get a p-value of 0.04.

What is the correct conclusion at a 5% significance level?

hard

A. At least one group mean is significantly different

B. The test is invalid because p-value is less than 0.05

C. All group means are exactly equal

D. There is no significant difference between group means

Solution

1. Step 1: Understand p-value meaning

   A p-value of 0.04 means there is a 4% chance the observed differences happened by random chance.

2. Step 2: Compare p-value to significance level

   Since 0.04 < 0.05, we reject the null hypothesis that all group means are equal.

3. Final Answer:

   At least one group mean is significantly different -> Option A

4. Quick Check:

   p-value < 0.05 means significant difference = D [OK]

Hint: p-value below 0.05 means significant difference [OK]

Common Mistakes:

• Thinking p-value < 0.05 means no difference
• Assuming all means are equal if p-value is low
• Misinterpreting significance level