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.