Alternate Hypothesis in Statistics: What is it?

Statistics Definitions > Alternate Hypothesis

What is the Alternate Hypothesis?

In order to understand what an alternate hypothesis (also called an alternative hypothesis) is, you first need to understand what the null hypothesis means. The word hypothesis means a working statement. In statistics, we’re interested in proving whether a working statement (the null hypothesis) is true or false. Usually, these working statements are things that are expected to be true —some kind of known or fact or perhaps a historical value. The word “null” can be thought of as “no change”. With the null hypothesis, you get what you expect, from a historical point of view. In hypothesis-testing, there are always two competing hypotheses under consideration [1]:

1. The status quo (null) hypothesis (H₀),
2. The research (alternate) hypothesis (H_a or H₁).

You can think of the alternate hypothesis as just an alternative to the null. For example, if your null is “I’m going to win up to $1,000” then your alternate is “I’m going to win $1,000 or more.” Basically, you’re looking at whether there’s enough change (with the alternate hypothesis) to be able to reject the null hypothesis. In many cases, the alternate hypothesis will just be the opposite of the null hypothesis. For example, the null hypothesis might be “There was no change in the water level this Spring,” and the alternative hypothesis would be “There was a change in the water level this Spring.” In other cases, there might be a change in the amount of something. For example, let’s say a Gallup poll predicts an election will re-elect a president with a 5 percent majority. However, you, the researcher, has uncovered a secret grassroots campaign composed of hundreds of thousands of minorities who are going to vote the opposite way from expected.

• Null hypothesis: President re-elected with 5 percent majority
• Alternate hypothesis: President re-elected with 1-2 percent majority.

Although the outcome hasn’t changed (the President is still re-elected), the majority percentage has changed—which may be important to an electoral campaign. The alternate hypothesis is usually what you will be testing in hypothesis testing. It’s a statement that you or another researcher) thinks is true and one that can ultimately lead you to reject the null hypothesis and replace it with the alternate hypothesis.

Stating the alternate hypothesis

A general guideline [2]:

• If you want to support a claim, make it the alternative hypothesis.
• If you do not wish to support a claim, make it the null hypothesis.

For example, consider a problem involving the average cost of house repairs. Suppose that a general contractor claims that the average home repair cost is less than $1000. Using the Greek letter μ to represent the mean, we can write (μ < 1000). You wish to support the claim that the repairs are actually much more expensive. This is the alternate hypothesis. Thus, we have:

• H₀: μ < 1000
• H₁: μ ≥ 1000 (your claim)

Now, suppose the repair contractor’s claim was that the mean repair cost for an electrical repair is at least $1200. In this case, we think that this is overinflated and that the repair costs are actually much lower. We can write:

• H₀: μ ≥ 1200
• Ha: u < 1200.

Alternate Hypothesis Examples

Example 1: It’s an accepted fact that ethanol boils at 173.1°F; you have a theory that ethanol actually has a different boiling point, of over 174°F. The accepted fact (“ethanol boils at 173.1°F”) is the null hypothesis; your theory (“ethanol boils at temperatures of 174°F”) is the alternate hypothesis. Example 2: A classroom full of students at a certain elementary school is performing at lower than average levels on standardized tests. The low test scores are thought to be due to poor teacher performance. However, you have a theory that the students are performing poorly because their classroom is not as well ventilated as the other classrooms in the school. The accepted theory (“low test scores are due to poor teacher performance”) is the null hypothesis; your theory (“low test scores are due to inadequate ventilation in the classroom”) is the alternative hypothesis. Check out our YouTube channel for more help and tips!

References

1. 9 Hypothesis Tests
2. Hypothesis Testing Memo