ANOVA (f_oneway) in SciPy - Mini Project: Build & Apply

Comparing Group Means Using ANOVA with f_oneway

📖 Scenario: You are a data analyst at a company that wants to understand if three different training programs lead to different average test scores among employees.

🎯 Goal: Build a simple Python program that uses the scipy.stats.f_oneway function to perform a one-way ANOVA test on the test scores from the three training groups.

📋 What You'll Learn

Create three lists named group1, group2, and group3 with exact test score values

Create a variable alpha to set the significance level

Use scipy.stats.f_oneway with the three groups to perform ANOVA

Print the F-statistic and p-value clearly

💡 Why This Matters

🌍 Real World

ANOVA helps compare multiple groups to see if their averages differ, useful in business, medicine, and social sciences.

💼 Career

Data analysts and scientists use ANOVA to test hypotheses about group differences in experiments and surveys.

1

Create the test score data for three groups

Create three lists called group1, group2, and group3 with these exact test scores: group1 = [85, 88, 90, 85, 87], group2 = [78, 75, 80, 79, 77], group3 = [92, 95, 94, 96, 93].

SciPy

# Your code here

Hint

Use square brackets to create lists with the exact numbers given.

2

Set the significance level for the ANOVA test

Create a variable called alpha and set it to 0.05 to represent the significance level.

SciPy

group1 = [85, 88, 90, 85, 87]
group2 = [78, 75, 80, 79, 77]
group3 = [92, 95, 94, 96, 93]
# Your code here

Hint

Use a simple assignment to create alpha with the value 0.05.

3

Perform the ANOVA test using scipy.stats.f_oneway

Import f_oneway from scipy.stats and use it with group1, group2, and group3 to get the F-statistic and p-value. Store the results in variables f_statistic and p_value.

SciPy

group1 = [85, 88, 90, 85, 87]
group2 = [78, 75, 80, 79, 77]
group3 = [92, 95, 94, 96, 93]
alpha = 0.05
# Your code here

Hint

Use from scipy.stats import f_oneway and then call f_oneway(group1, group2, group3).

4

Print the ANOVA test results

Print the F-statistic and p-value using print statements with clear labels.

SciPy

from scipy.stats import f_oneway

group1 = [85, 88, 90, 85, 87]
group2 = [78, 75, 80, 79, 77]
group3 = [92, 95, 94, 96, 93]
alpha = 0.05

f_statistic, p_value = f_oneway(group1, group2, group3)
# Your code here

Hint

Use print(f"F-statistic: {f_statistic}") and print(f"p-value: {p_value}").

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