Hypothesis Testing - Null and Alternate

# HStatistics.com

### Null and Alternate Hypothesis

Before we understand Null and Alternate Hypothesis, let’s clear a few things.
Firstly, What is Hypothesis?
It is defined as “a supposition or claim on the basis of limited evidence as a starting point for further investigation”

Now, any claim can be divided into two parts.

Example 1: You claim that the temperature tomorrow would be 28 degree centigrade, then
Part 1 would be Temp = 28 and
Part 2 would be Temp NOT = 28.

Example 2:
You claim that the temperature tomorrow would be more than 28 degree centigrade, then
Part 1 would be Temp > 28 and
Part 2 would be Temp <= 28

So, any claim can be divided into two parts.
Now, one of these parts would be your Null Hypothesis and the other would be the Alternate Hypothesis.
But, which one should be chosen as the Null Hypothesis and which one as the Alternate?

By convention, we choose the part having the Equal To sign as the Null Hypothesis and the other part as the Alternate Hypothesis.
So, in example 1 (above) Part 1 would be our Null Hypothesis and Part 2 would be the Alternate Hypothesis.
However, in example 2 (above) Part 2 would be chosen as our Null Hypothesis and Part 1 as the Alternate Hypothesis.
This is because Part 2 has the equal to sign and hence it is chosen as the Null Hypothesis.
This is just a convention to select the part having the ‘equal to’ sign as the Null Hypothesis.
So, whatever your claim may be, you select that part as the Null Hypothesis which contains the equal to sign.

In essence,
The null hypothesis always has the following signs:
=  OR   ≤   OR    ≥

The alternate hypothesis always has the following signs:
≠   OR  >   OR    <

One Tailed and Two Tailed Tests:

In example 1 (above), we had claimed that the temperature tomorrow would be = 28 degree centigrade. This is our claim (based on our analysis) for tomorrow.

But, we could go wrong in two ways.

First, we might have under estimated the temperature. Meaning, we claimed 28 degree whereas in reality it turns out to be 35 degree.
Second, we might have over estimated the temparature. Meaning, we claimed 28 degree whereas in reality it turns out to be 22 degree.

Since we could go wrong in two directions (both under estimating and over estimating) this would be a Two Tailed test.

However, in example 2 (above), we had claimed the temperature to be > 28.
So our Null Hypothesis was Temp <= 28.
Here, we could go wrong only in 1 one direction. Ie. underestimating it.
Meaning, in reality the temperature turned out to be 35.
In the other direction (of overestimating it) we cannot go wrong here.

Why?

Because even if in reality the temperature turns out to be 10 degree. Our Null Hypothesis was not wrong. Since it already said that temp <= 28, and 10 satisfies that condition.

Thus we could go wrong only in one direction and this is why it is called a One tailed test.

In this next post we would discuss about critical value method of Hypothesis testing.