Hypothesis Testing

Hypothesis Testing

Why is this Important?

Hypothesis testing is one of the most important concepts in Statistics.

This is how we decide if:

Effects actually occurred
Treatments have effects
Groups different from each other
One variable predicts another.

There are complicated definitions and descriptions of the process. They may confuse you. The logic will seem backward.
The idea if written in plain English is simple. We will talk it out before introducing complex terms.

A A The Big Idea A A

You have an idea that something happened è Your Hypothesis

Something Happened Might Be:

Groups Are different From each other
Some treatment has an effect on an outcome measure
One variable predicts another variable.

There are two possibilities

1. Nothing Happened è the Null Hypothesis - H_o
2. Something Happened è the Alternative Hypothesis - H₁

That's it! When you test a statistical hypothesis, you are trying to see if something happened and comparing against the possibility that nothing happened.

Let's give fancy names to these simple ideas!

Nothing Happened = The Null Hypothesis.

Null = Nothing = Zero = Nada = Bupkus = Zilch

You didn't find an effect
You didn't find the groups to be different
Your treatment doesn't seem to help anybody
Your variables are not related

Statistical Nuances:
You test your sample statistic against the value based on the Null Hypothesis sampling distribution and they are close. It is not different.

Something Happened = The Alternative Hypothesis

There was an effect of your treatment
Your groups are different
One variable predicts another.

Statistical Nuances:
You test your sample statistic against the value based on the Null Hypothesis sampling distribution and they are not close. It is different.

How do we test hypotheses?

This is the counterintuitive part.

We try to disprove the Null Hypothesis.

We try to disprove that nothing happened.

If we disprove that nothing happened - then SOMETHING HAPPENED

Isn't that counterintuitive? To prove that we have an effect, that our treatment works, that our groups differ - we try to disprove that our treatment didn't work or that our groups don't differ.

But - you have to learn this logic!