P-values are one of the most widely misunderstood and misused concepts in statistics and data science. Despite their frequent appearance in research papers, A/B tests, and machine learning evaluations, many practitioners aren't entirely confident about what p-values really represent.

In this blog, we’ll demystify p-values by covering their conceptual motivation, technical definition, common thresholds, and limitations. Whether you’re a beginner in statistics or brushing up your concepts, this post will help you make better data-driven decisions.

🔍 Introduction

Every time we run an experiment — whether testing a new drug, launching a marketing campaign, or improving a machine learning model — we need to decide whether the observed results are meaningful or just a result of chance.

That’s where p-values come into play.

💡 Conceptual Motivation for P-Values

Imagine you're testing a new treatment to see if it works better than the current standard. You observe some improvement — but could this improvement have happened just by random luck?

The p-value helps you answer:

“If there was really no difference*, how likely is it that I would observe a result as extreme as this one?”*

📏 What is a P-Value?

At its core, a p-value is a number between 0 and 1. It tells you the probability of obtaining results at least as extreme as the observed ones, under the assumption that the null hypothesis is true.

✅ Lower p-value = stronger evidence against the null

A p-value close to 0 means the observed result is very unlikely under the null hypothesis.
A p-value close to 1 means the observed result is quite likely due to random chance.

But how small is small enough to be confident?

🎯 Thresholds for Statistical Significance

In practice, we often set a threshold (called α or alpha) to decide what we consider statistically significant.

Common thresholds:

Threshold (α)	Interpretation
0.05	Standard threshold (5% chance of false positive)
0.01	More strict; stronger evidence required
0.0001	Very strict; used in highly sensitive experiments
0.2	Very lenient; acceptable in low-risk decisions

A threshold of 0.05 means:
If there were really no difference, only 5% of experiments would show results this extreme purely by chance.

This is widely accepted in most scientific research.

In contrast, a threshold of 0.0001 is used in high-stakes decisions (like approving a new drug) to minimize the risk of false positives.
If the stakes are low (e.g., deciding whether the ice cream truck will arrive on time), a larger threshold like 0.2 might be acceptable.

🧪 P-Values and Hypothesis Testing

P-values play a key role in hypothesis testing.

Null Hypothesis (H₀): Assumes there is no effect or difference.
Alternative Hypothesis (H₁): Assumes there is an effect or difference.

We calculate the p-value under the null hypothesis. If the p-value is less than our chosen threshold, we reject H₀ in favor of H₁.

Example: Using Fisher’s Exact Test, we might compute a p-value to test whether Drug A works better than Drug B.

⚠️ Terminology Alert

False Positive (Type I Error): When we reject the null hypothesis even though it is actually true.
- For a threshold of 0.05, about 5 out of 100 experiments with no true difference will wrongly indicate a difference.

So choosing the right threshold is a balance between risk of error and cost of being wrong.

🚫 What P-Values Don't Tell You

One of the most common misinterpretations is thinking that a small p-value means a large effect size.

❗ A small p-value does not imply the difference is important or large. It just means the result is unlikely to be due to chance.

For example:

A tiny difference in blood pressure readings across thousands of patients might yield a p-value of 0.00001 — statistically significant, but possibly clinically insignificant.

🧠 Summary

P-values quantify how likely observed results are under the assumption of no true effect.
They help guide decisions in hypothesis testing but are not the final word.
Thresholds like 0.05 are commonly used but should be context-dependent.
P-values do not measure effect size — always pair them with confidence intervals and domain knowledge.
And remember: Statistical significance ≠ Practical significance.

Thanks for reading!
If you're on your own data science journey or just starting out with statistics, understanding p-values is a crucial milestone.

💬 Have questions or examples to share? Drop them in the comments!
🔁 Follow me for more posts like this as I continue my #66DaysOfData learning journey.

Understanding P-Values: What They Are and How to Interpret Them

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