# Understanding the P-value: A Humorous Approach for Data Scientists

Written on

## Chapter 1: The P-value Explained

Understanding the P-value can be quite challenging at first, particularly when relying on definitions found in statistics textbooks or online resources. In this piece, I aim to simplify this concept using the amusing term "ridiculous." You might wonder why I keep using a word like "ridiculous"—I apologize, but it truly serves a purpose. I believe this term acts as a mnemonic device to help remember the P-value concept. Allow me to elaborate.

**Disclaimer**: Many statisticians and data scientists have previously utilized the term “ridiculous” to explain the P-value. I am not the first or the only one to adopt this approach. This word has aided me and countless others in grasping the P-value more effectively, and it may do the same for you.

### Section 1.1: The Ridiculousness of Assumptions

How often have you made an assumption only to realize you were mistaken? I assume quite frequently. In those moments, you formulate hypotheses based on certain observations and ultimately take action based on those hypotheses. When you discover your error, you may find yourself reflecting and thinking, "How ridiculous I was to believe my hypothesis based on the evidence!"

This sentiment is precisely what the P-value quantifies—it measures the absurdity of your null hypothesis.

#### Subsection 1.1.1: What is the Null Hypothesis?

When you gather data (for instance, after introducing a new feature in your app), you might find a notable difference between your data prior to and following the feature's addition (commonly referred to as population data and sample/test data). This moment can be exhilarating, especially if you anticipated that this feature would enhance user engagement. However, it’s essential to temper that excitement!

You must remind yourself that the data suggesting a significant increase in user engagement could simply be a fluke. You are essentially saying, "I was just fortunate to collect these data points after implementing the new feature. They might just be random results, and my feature did not actually cause this difference."

This perspective embodies your "Null Hypothesis."

### Section 1.2: Moving Forward

If your null hypothesis is proven false, then the Alternative Hypothesis must be true. Typically, this is the hypothesis you wish to validate, which in this case might state, "Introducing the new feature in the app improved user engagement."

Once again, the P-value gauges how ludicrous it was to trust the null hypothesis given the observed data.

## Chapter 2: Should I Feel Ridiculous?

A small P-value indicates that it would be quite foolish to continue believing in the null hypothesis after reviewing the evidence presented by the sample/test data. Conversely, a large P-value suggests there is no reason to feel foolish about accepting the null hypothesis.

Thus, if the P-value is high, it is rational to accept the null hypothesis. I understand that it can be difficult to maintain faith in the null hypothesis when you are eager to reject it in favor of the alternative hypothesis. However, as the P-value decreases, you should start feeling somewhat ridiculous for still holding on to the null hypothesis.

**How Much Ridiculousness is Acceptable?**

This leads to the question: how much absurdity should one tolerate before discarding the null hypothesis? Statisticians suggest a general threshold of 0.05; any null hypothesis with a P-value below this should be rejected (indicating a 5% level of significance). This threshold for accepting ridiculousness is known as the alpha value.

**Rejecting the Ridiculous Null Hypothesis!**

There’s a certain joy that comes from rejecting a ridiculous null hypothesis. Why? Because it frees you from believing in the null hypothesis and allows you to embrace the alternative hypothesis—the one that excites you! Now it’s time to celebrate or at least feel good about your new app feature.

**Summary**

In summary, here’s the recipe for hypothesis testing: First, temper your excitement after making an observation (perhaps by taking a moment to collect your thoughts). Remind yourself that the observed data could just be lucky samples and make this your null hypothesis. Calculate the P-value for your null hypothesis (there are many methods available). If your P-value is lower than the alpha value, confidently reject the null hypothesis and warmly welcome your alternative hypothesis.

## Chapter 3: Video Insights

In the following video titled "They Thought We Were Ridiculous - Episode 3: Children of Unlikely Parents," the complexities surrounding the P-value are humorously explored.