ANOVA (f_oneway) in SciPy

Introduction

ANOVA helps us check if different groups have different average values. It tells us if the differences we see are real or just by chance.

Comparing test scores of students from three different schools.

Checking if three types of diets lead to different average weight loss.

Seeing if different machines produce parts with different average sizes.

Comparing average customer ratings for three different products.

Syntax

SciPy

scipy.stats.f_oneway(group1, group2, ...)

Each group is a list or array of numbers.

The function returns two values: the F-statistic and the p-value.

Examples

Compare two groups with simple numbers.

SciPy

from scipy.stats import f_oneway

f_oneway([1, 2, 3], [4, 5, 6])

Compare three groups to see if their averages differ.

SciPy

f_oneway([10, 12, 14], [10, 11, 13], [9, 12, 15])

Sample Program

This code compares the average scores of three classes to see if they differ significantly.

SciPy

from scipy.stats import f_oneway

# Scores of students from three classes
class1 = [85, 90, 88, 75, 95]
class2 = [80, 85, 84, 70, 90]
class3 = [78, 82, 85, 72, 88]

f_stat, p_val = f_oneway(class1, class2, class3)

print(f"F-statistic: {f_stat:.3f}")
print(f"p-value: {p_val:.3f}")

Important Notes

A small p-value (usually less than 0.05) means the groups are different.

ANOVA assumes the groups have similar spread (variance) and are independent.

If p-value is large, it means no strong evidence that groups differ.

Summary

ANOVA tests if multiple groups have different averages.

Use scipy.stats.f_oneway with groups as inputs.

Look at the p-value to decide if differences are significant.

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