Getting to the Bottom of P-value: The Intuitive Explanation

Getting to the Bottom of P-value: The Intuitive Explanation

Understand, visualizing, and calculating p-value. Welcome to this lesson on calculating p-values. Before we jump into how to calculate a p-value, it’s important to think about what the p-value is really for.

Introduction

Welcome to this lesson on calculating p-values.

Before we jump into how to calculate a p-value, it’s important to think about what the p-value is really for.

Hypothesis Testing Refresher

Without going into too much detail for this post, when establishing a hypothesis test, you will determine a null hypothesis. Your null hypothesis represents the world in which the two variables your assessing don’t have any given relationship. Conversely the alternative hypothesis represents the world where there is a statistically significant relationship such that you’re able to reject the null hypothesis in favor of the alternative hypothesis.

Diving Deeper

Before we move on from the idea of hypothesis testing… think about what we just said. You effectively need to prove that with little room for error, what we’re seeing in the real world could not be taking place in a world where these variables are not related or in a world where the relationship is independent.

Sometimes when learning concepts in statistics, you hear the definition, but take little time to conceptualize. There is often a lot of memorization of rule sets… I find that understanding the intuitive foundation of these principles will serve you far better when finding their practical applications.

Continuing on this vein of thought. If you want to compare your real world stat with the fake world, that’s exactly what you should do.

As you’d guess we can calculate our observed statistic by creating a linear regression model where we explain our response variable as a function of our explanatory variable. Once we’ve done this we can quantify the relationship between these two variables using the slope or coefficient identified through our ols regression.

But now we need to come up with a this idea of the _null world_… or the world where these variables are independent. This is something we don’t have, so we’ll need to simulate it. For our convenience, we’re going to leverage the infer package.

et’s Calculate our Observed Statistic

First things first, let’s get our observed statistic!

The dataset we’re working with is a Seattle home prices dataset. I’ve used this dataset many times before and find it particularly flexible for demonstration. The record level of the dataset is by home and details price, square footage, ## of beds, ## of baths, and so forth.

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