ANOVA in Data Analysis Python - Time & Space Complexity

Time Complexity: ANOVA

O(n)

Understanding Time Complexity

We want to understand how the time needed to run ANOVA changes when we have more groups or more data points.

How does the work grow as the data size grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd
from scipy import stats

data = pd.DataFrame({
    'group': ['A']*50 + ['B']*50 + ['C']*50,
    'value': list(range(50)) + list(range(50, 100)) + list(range(100, 150))
})

f_val, p_val = stats.f_oneway(
    data[data['group'] == 'A']['value'],
    data[data['group'] == 'B']['value'],
    data[data['group'] == 'C']['value']
)

This code runs ANOVA to compare means of three groups, each with 50 data points.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Calculating group means and variances by scanning each data point.
• How many times: Each data point is visited once to compute sums and variances.

How Execution Grows With Input

As the number of data points grows, the time to compute group statistics grows roughly in direct proportion.

Input Size (n)	Approx. Operations
10	About 10 operations to sum and calculate variance
100	About 100 operations
1000	About 1000 operations

Pattern observation: Doubling data roughly doubles the work needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to run ANOVA grows linearly with the total number of data points.

Common Mistake

[X] Wrong: "ANOVA time grows with the square of data size because it compares all pairs of points."

[OK] Correct: ANOVA calculates group statistics by scanning data once, not by comparing every pair.

Interview Connect

Understanding how ANOVA scales helps you explain performance when working with bigger datasets in real projects.

Self-Check

"What if we increased the number of groups instead of data points? How would the time complexity change?"