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One-Tailed and Two-Tailed Tests

One-Tailed and Two-Tailed Tests

Author: Katherine Williams
Description:

Determine a left-tailed, right-tailed, or two-tailed test from a given null and alternative hypothesis.

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Tutorial

Source: Video Created by Katherine Williams

Video Transcription

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This tutorial talks about one tailed and two tailed tests. With a one tailed test, we have reason to believe that the population parameter is higher or lower than the assumed parameter value of the null hypothesis. We would be talking either about left tailed tests or about right tailed tests. With a two tailed test, we have reason to believe that the population parameter is different from the assumed value of the null hypothesis. And in this case, we're going to be looking to find the probability of both tails.

Now typically, a one tailed test is more powerful than a two tailed test, and that's why we would prefer it. When we're doing a one tailed test, for a left tailed test, we have reason to believe that the population parameter is lower than the assumed parameter value of the null hypothesis. We're looking at something where we have our-- oops-- we have our distribution. And our assumed [INAUDIBLE] value is there. And for a left tailed test, we are looking at lower and seeing that section there to the left of our value.

On the other hand, with a right tailed test, we have reason to believe that the population parameter is higher than the assumed parameter value for the null hypothesis. So here, we have our distribution. We have our assumed parameter value of the null hypothesis. and then we have reason to believe that our population parameter is somewhere in the zone above that assumed parameter value for the null hypothesis.

One thing to keep in mind is that we typically have a claim in mind test before we start our testing, and before we decide whether or not we're going to do a one tailed or two tailed test. We already have that null hypothesis set up. And we're already deciding and thinking about what we would be testing.

Let's look at some examples and decide whether it's going to be a one tailed test or a two tailed test. Here, we're looking at the question of, will starting a new campaign result in more sales? We're thinking this more here, so we care about whether or not the sales are going to be higher than the assumed value. So that is going to be a one tailed test.

And then our next question is, is the new gold dollar a fair coin? So with a fair coin, you have a 50% chance of coming up heads and a 50% chance of coming up tails. Here, we're just concerned with whether or not the new gold dollar is different from that 50%. We don't care whether it's higher or lower. So this would be a time when we're looking at a two tailed test.

So this has been your tutorial on one tailed and two tailed tests.

Terms to Know
Left-tailed test

A hypothesis test where the alternative hypothesis only states that the parameter is lower than the stated value from the null hypothesis.

One-tailed test

A hypothesis test where the alternative hypothesis only states that the parameter is higher (or lower) than the stated value from the null hypothesis.

Right-tailed test

A hypothesis test where the alternative hypothesis only states that the parameter is higher than the stated value from the null hypothesis.

Two-tailed test

A hypothesis test where the alternative hypothesis states that the parameter is different from the stated value from the null hypothesis; that is, the parameter's value is either higher or lower than the value from the null hypothesis.