Understanding the p-Value: A Key Concept in Statistical Hypothesis Testing

 The p-value is a vital notion in statistics that aids researchers in assessing the relevance of their findings. However, what is a p-value exactly, and why is it so significant?

A p-value: what is it?
In a statistical test, the p-value, also known as the probability value, is a metric that indicates how strong the evidence is against the null hypothesis. Generally speaking, the null hypothesis states that there is no impact or difference. In a clinical trial, for instance, the null hypothesis can claim that a novel medication has no effect when compared to a placebo.

How Does One Use the p-Value?
A p-value is computed during a hypothesis test to determine whether the null hypothesis should be rejected or not. This is a streamlined procedure:

• Construct Hypotheses: Describe your alternative hypothesis (H₁) and null hypothesis (H₀).
• Select the Level of Significance (α): The standard options are 0.05 and 0.01.
• Determine the p-Value. Conduct the examination and determine the p-value.
• P-Value in relation to α
• Reject the null hypothesis if the p-value is less than or equal to α.
• Do not reject the null hypothesis if the p-value is greater than α.  

How to Interpret the p-Value

• A low p-value (≤ α) suggests that there is an inconsistency between the observed data and the null hypothesis. This shows that there is a statistically significant influence in your data.
• Elevated p-value (more than α): Indicates that the observed data aligns with the null hypothesis. This indicates that the alternative hypothesis is not well supported by the available data.

Example: t-Test Calculation

Consider a simple example using Python's scipy library to perform a t-test:

from scipy import stats

import numpy as np

data1 = np.array([5, 6, 7, 5, 6])

data2 = np.array([8, 9, 10, 8, 9])

t_stat, p_value = stats.ttest_ind(data1, data2)

print("p-Value:", p_value)