How to find P-value from a t-Score using Python

In Python, p-value can be calculated using the scipy.stats module. Scipy is a python library used for scientific computation. It provides us scipy.stats.t.sf() function to compute the p-value.

Syntax to install scipy library in python:

pip3 install scipy

Syntax for scipy.stats.t.sf() function:

scipy.stats.t.sf(abs(t_score), df=degree_of_freedom

Parameters:

t_score: It signifies the t-score
degree_of_freedom: It signifies the degrees of freedom

P-value for a One-sample T-test

Let’s consider a scenario where we have a sample of exam scores from a group of students, and we want to test whether the average exam score is significantly different from a population mean. The average exam score for a population of students is known to be 75 in a sample of 250 students.

Python3

import numpy as np
from scipy.stats import t
 
 
def one_sample_t_test(sample, population_mean, alpha=0.05, tail="two"):
    # Step 1: Calculate T-score
    sample_mean = np.mean(sample)
    sample_std = np.std(sample, ddof=1)
    sample_size = len(sample)
 
    t_score = (sample_mean - population_mean) / \
        (sample_std / np.sqrt(sample_size))
 
    # Step 2: Determine degrees of freedom
    df = sample_size - 1
 
    # Step 3: Identify the appropriate t-distribution
    # No need to explicitly specify degrees of freedom for one-sample t-test in scipy.stats.t
 
    # Step 4: Find the p-value
    if tail == "two":
        p_value = t.sf(np.abs(t_score), df) * 2  # for two-tailed test
    elif tail == "left":
        p_value = t.sf(t_score, df)  # for left-tailed test
    elif tail == "right":
        p_value = t.sf(-t_score, df)  # for right-tailed test
    else:
        raise ValueError(
            "Invalid tail argument. Use 'two', 'left', or 'right'.")
 
    # Step 5: Interpret the p-value
    print("P-value:", p_value)
 
    if p_value < alpha:
        print(
            "Reject the null hypothesis. There is a statistically significant difference.")
    else:
        print("Fail to reject the null hypothesis. There is no statistically significant difference.")
 
 
# Let's generate a sample for experiment
np.random.seed(42)
# Generating a sample
sample_data = np.random.normal(loc=77, scale=10, size=250)
population_mean = 75
 
# Example for a two-tailed test
one_sample_t_test(sample_data, population_mean, tail="two")

Output:

P-value: 0.0013870092433008773
Reject the null hypothesis. There is a statistically significant difference.

P-value for a Two-sample T-test Independence

Suppose you are a data analyst working for a company that has two different methods for manufacturing a certain type of product. You want to investigate whether there is a significant difference in the average quality of the product produced by the two methods. To do this, you collect samples from each manufacturing method and perform a two-sample t-test.

Sample 1: Quality scores from 100 products manufactured using Method 1.
Sample 2: Quality scores from 120 products manufactured using Method 2.

Python3

import numpy as np
from scipy.stats import t
 
# Step 1: Calculate the T-score
def calculate_t_score(sample1, sample2):
    mean1 = np.mean(sample1)
    mean2 = np.mean(sample2)
    std1 = np.std(sample1, ddof=1) 
    std2 = np.std(sample2, ddof=1)
    n1 = len(sample1)
    n2 = len(sample2)
 
    t_score = (mean1 - mean2) / np.sqrt((std1**2 / n1) + (std2**2 / n2))
    return t_score
 
# Step 2: Determine the degrees of freedom (df)
def calculate_degrees_of_freedom(sample1, sample2):
    n1 = len(sample1)
    n2 = len(sample2)
    df = n1 + n2 - 2  # For a two-sample t-test
    return df
 
# Step 3: Identify the appropriate t-distribution
# (The scipy.stats.t distribution is used, which automatically considers the degrees of freedom)
 
# Step 4: Find the p-value
def calculate_p_value(t_score, df):
    p_value = 2 * (1 - t.cdf(np.abs(t_score), df))
    return p_value
 
# Step 5: Interpret the p-value
def interpret_p_value(p_value, alpha=0.05):
    if p_value < alpha:
        return "Reject the null hypothesis. There is a statistically significant difference."
    else:
        return "Fail to reject the null hypothesis. There is no statistically significant difference."
 
# Generate two independent samples for Example
np.random.seed(42)
sample1 = np.random.normal(loc=50, scale=10, size=100)
sample2 = np.random.normal(loc=45, scale=12, size=120)
 
t_score = calculate_t_score(sample1, sample2)
df = calculate_degrees_of_freedom(sample1, sample2)
p_value = calculate_p_value(t_score, df)
result = interpret_p_value(p_value)
 
print("p-value:", p_value)
print(result)

Output:

p-value: 0.04126391962537701
Reject the null hypothesis. There is a statistically significant difference.

How to Find a P-Value from a t-Score in Python?

In the realm of statistical analysis, the p-value stands as a pivotal metric, guiding researchers in drawing meaningful conclusions from their data. This article delves into the significance and computation of p-values in Python, focusing on the t-test, a fundamental statistical tool.

Table of Content

What is the P-value?
How to find a P-value from a t-Score?
How to find P-value from a t-Score using Python
Frequently Based Questions(FAQs) on P-Value

Tags:

#Geeks-Premier-League-2022 #python #Python-scipy #AI-ML-DS #Geeks Premier League #Machine Learning #Statistics #Machine Learning #python

How to find a P-value from a t-Score?

Conclusion

How to find P-value from a t-Score using Python

P-value for a One-sample T-test

Python3

P-value for a Two-sample T-test Independence

Python3

How to Find a P-Value from a t-Score in Python?

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