t-test with scipy.stats in Data Analysis Python - Time & Space Complexity

Time Complexity: t-test with scipy.stats

O(n)

Understanding Time Complexity

We want to understand how the time needed to run a t-test changes as the data size grows.

How does the number of data points affect the work done by the t-test function?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

from scipy import stats

data1 = [1, 2, 3, 4, 5]
data2 = [2, 3, 4, 5, 6]

result = stats.ttest_ind(data1, data2)
print(result)

This code runs an independent t-test to compare two lists of numbers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The function calculates means and variances by going through each list of numbers.
• How many times: Each list is scanned once to compute summary statistics.

How Execution Grows With Input

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

Input Size (n)	Approx. Operations
10	About 20 (two lists scanned)
100	About 200
1000	About 2000

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

Final Time Complexity

Time Complexity: O(n)

This means the time to run the t-test grows linearly with the number of data points.

Common Mistake

[X] Wrong: "The t-test time grows with the square of the data size because it compares every pair of points."

[OK] Correct: The t-test only needs summary statistics like means and variances, so it scans each list once, not every pair.

Interview Connect

Understanding how statistical tests scale helps you write efficient data analysis code and explain your choices clearly.

Self-Check

"What if we used a bootstrap method with many resamples instead of a t-test? How would the time complexity change?"

Practice

1.

What does a t-test help you find out in data analysis?

easy

A. If two groups have different average values

B. The total number of data points in a dataset

C. The exact values of all data points

D. How to sort data in ascending order

Solution

1. Step 1: Understand the purpose of a t-test

   A t-test compares the means (averages) of two groups to see if they are different.

2. Step 2: Identify what the t-test does not do

   It does not count data points, show exact values, or sort data.

3. Final Answer:

   If two groups have different average values -> Option A

4. Quick Check:

   T-test checks mean difference = A [OK]

Hint: T-test compares averages between groups [OK]

Common Mistakes:

• Thinking t-test counts data points
• Confusing t-test with sorting methods
• Assuming t-test shows exact data values

2.

Which of the following is the correct way to import the t-test function for independent samples from scipy.stats?

?

easy

A. from scipy.stats import ttest_ind

B. import scipy.stats.ttest_ind

C. from scipy import ttest_ind

D. import ttest_ind from scipy.stats

Solution

1. Step 1: Recall Python import syntax

   To import a specific function, use 'from module import function'.

2. Step 2: Match the correct import statement

   'from scipy.stats import ttest_ind' correctly imports the independent t-test function.

3. Final Answer:

   from scipy.stats import ttest_ind -> Option A

4. Quick Check:

   Correct import syntax = A [OK]

Hint: Use 'from module import function' to import specific functions [OK]

Common Mistakes:

• Using 'import scipy.stats.ttest_ind' which is invalid
• Trying 'from scipy import ttest_ind' missing 'stats'
• Writing 'import ttest_ind from scipy.stats' which is wrong syntax

3.

What will be the output of this code snippet?

import numpy as np
from scipy.stats import ttest_1samp

data = np.array([5, 7, 8, 6, 9])
test_stat, p_value = ttest_1samp(data, popmean=6)
print(round(p_value, 3))

medium

A. 0.045

B. 0.100

C. 0.500

D. 0.317

Solution

1. Step 1: Understand the t-test 1 sample function

   ttest_1samp tests if the sample mean differs from the population mean (6 here).

2. Step 2: Calculate the p-value for the data

   Using the data, the p-value is approximately 0.317, meaning no strong evidence against mean=6.

3. Final Answer:

   0.317 -> Option D

4. Quick Check:

   p-value from ttest_1samp = 0.317 [OK]

Hint: Round p-value to 3 decimals to compare easily [OK]

Common Mistakes:

• Confusing test statistic with p-value
• Using wrong population mean in function
• Not rounding p-value before comparing

4.

Identify the error in this code that tries to perform a paired t-test:

from scipy.stats import ttest_rel

data1 = [10, 12, 14, 16]
data2 = [11, 13, 15]

result = ttest_rel(data1, data2)
print(result.pvalue)

medium

A. Missing import for numpy

B. ttest_rel is not the correct function for paired tests

C. The two data lists have different lengths

D. print statement syntax is incorrect

Solution

1. Step 1: Check input data lengths for paired t-test

   Paired t-test requires both data arrays to have the same length because it compares pairs.

2. Step 2: Identify the mismatch in data lengths

   data1 has 4 elements, data2 has 3 elements, causing an error.

3. Final Answer:

   The two data lists have different lengths -> Option C

4. Quick Check:

   Paired t-test needs equal length arrays = C [OK]

Hint: Paired t-test needs equal length data arrays [OK]

Common Mistakes:

• Using different length arrays for paired test
• Confusing ttest_rel with independent t-test
• Assuming print syntax error without checking data

5.

You have two groups of exam scores:

group1 = [78, 85, 90, 88, 76]
group2 = [82, 79, 88, 91, 77]

You want to check if their average scores differ significantly. Which code correctly performs this test and interprets the result?

hard

A. from scipy.stats import ttest_ind
stat, p = ttest_ind(group1, group2)
if p > 0.05:
print('Different averages')
else:
print('No difference')

B. from scipy.stats import ttest_ind
stat, p = ttest_ind(group1, group2)
if p < 0.05:
print('Different averages')
else:
print('No difference')

C. from scipy.stats import ttest_rel
stat, p = ttest_rel(group1, group2)
if p < 0.01:
print('Different averages')
else:
print('No difference')

D. from scipy.stats import ttest_1samp
stat, p = ttest_1samp(group1, group2)
if p < 0.05:
print('Different averages')
else:
print('No difference')

Solution

1. Step 1: Choose the correct t-test for two independent groups

   ttest_ind is used for comparing two independent samples like group1 and group2.

2. Step 2: Interpret the p-value correctly

   If p-value is less than 0.05, we say averages differ; otherwise, no difference.

3. Final Answer:

   Use ttest_ind and check if p < 0.05 to decide difference -> Option B

4. Quick Check:

   Independent t-test + p < 0.05 means difference [OK]

Hint: Use ttest_ind for independent groups and p < 0.05 for difference [OK]

Common Mistakes:

• Using ttest_1samp for two groups
• Using ttest_rel for independent groups
• Reversing p-value condition for significance