## Hypothesis testing. Null vs alternative

Hi, and welcome back.

This is the main section of this course.

It is based on the knowledge that you acquired previously, so if you haven’t been through

it, you may have a hard time keeping up.

Make sure you have seen all the videos about confidence intervals, distributions, z-tables

and t-tables, and have done all the exercises.

If you’ve completed them already, you are good to go.

Confidence intervals provide us with an estimation of where the parameters are located.

However, when you are making a decision, you need a yes/no answer.

The correct approach in this case is to use a test.

In this section, we will learn how to perform one of the fundamental tasks in statistics

- hypothesis testing!

Okay.

There are four steps in data-driven decision-making.

First, you must formulate a hypothesis.

Second, once you have formulated a hypothesis, you will have to find the right test for your

hypothesis.

Third, you execute the test.

And fourth, you make a decision based on the result.

Let’s start from the beginning.

What is a hypothesis?

Though there are many ways to define it, the most intuitive I’ve seen is:

“A hypothesis is an idea that can be tested.”

This is not the formal definition, but it explains the point very well.

So, if I tell you that apples in New York are expensive, this is an idea, or a statement,

but is not testable, until I have something to compare it with.

For instance, if I define expensive as: any price higher than \$1.75 dollars per pound,

then it immediately becomes a hypothesis.

Alright, what’s something that cannot be a hypothesis?

An example may be: would the USA do better or worse under a Clinton administration, compared

Statistically speaking, this is an idea, but there is no data to test it, therefore it

cannot be a hypothesis of a statistical test.

Actually, it is more likely to be a topic of another discipline.

Conversely, in statistics, we may compare different US presidencies that have already

been completed, such as the Obama administration and the Bush administration, as we have data

on both.

Alright, let’s get out of politics and get into hypotheses.

Here’s a simple topic that can be tested.

According to Glassdoor (the popular salary information website), the mean data scientist

salary in the US is 113,000 dollars.

So, we want to test if their estimate is correct.

There are two hypotheses that are made: the null hypothesis, denoted H zero, and the alternative

hypothesis, denoted H one or H A. The null hypothesis is the one to be tested and the

alternative is everything else.

In our example, The null hypothesis would be: The mean data

scientist salary is 113,000 dollars, While the alternative: The mean data scientist

salary is not 113,000 dollars.

Now, you would want to check if 113,000 is close enough to the true mean, predicted by

our sample.

In case it is, you would accept the null hypothesis.

Otherwise, you would reject the null hypothesis.

The concept of the null hypothesis is similar to: innocent until proven guilty.

We assume that the mean salary is 113,000 dollars and we try to prove otherwise.

Alright.

This was an example of a two-sided or а two-tailed test.

You can also form one sided or one-tailed tests.

Say your friend, Paul, told you that he thinks data scientists earn more than 125,000 dollars

per year.

You doubt him so you design a test to see who’s right.

The null hypothesis of this test would be: The mean data scientist salary is more than

125,000 dollars.

The alternative will cover everything else, thus: The mean data scientist salary is less

than or equal to 125,000 dollars.

It is important to note that outcomes of tests refer to the population parameter rather than

the sample statistic!

As such, the result that we get is for the population.

Another crucial consideration is that, generally, the researcher is trying to reject the null

hypothesis.

Think about the null hypothesis as the status quo and the alternative as the change or innovation

that challenges that status quo.

In our example, Paul was representing the status quo, which we were challenging.

Alright.

That’s all for now.

In the next lectures, we will see some examples and learn how to make data-driven decisions.