P-values and significance in Data Analysis Python - Time & Space Complexity

Time Complexity: P-values and significance

O(n)

Understanding Time Complexity

We want to understand how the time to calculate p-values changes as the amount of data grows.

How does the work needed grow when we have more data points?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np
from scipy import stats

def calculate_p_value(data1, data2):
    t_stat, p_val = stats.ttest_ind(data1, data2)
    return p_val

# data1 and data2 are lists or arrays of numbers

This code calculates the p-value from two groups of data using a t-test.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The t-test function internally processes each data point in both groups.
• How many times: Each data point in both data1 and data2 is visited once to compute means and variances.

How Execution Grows With Input

As the number of data points increases, the time to compute the p-value grows roughly in direct proportion.

Input Size (n)	Approx. Operations
10	About 20 (10 in each group)
100	About 200
1000	About 2000

Pattern observation: Doubling the data roughly doubles the work needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to calculate the p-value grows linearly with the total number of data points.

Common Mistake

[X] Wrong: "Calculating a p-value takes the same time no matter how much data there is."

[OK] Correct: The calculation must look at each data point to find averages and variances, so more data means more work.

Interview Connect

Understanding how data size affects calculation time helps you explain your approach clearly and shows you know what happens behind the scenes.

Self-Check

"What if we used a bootstrap method with 1000 resamples to estimate the p-value? How would the time complexity change?"