One vs Two-Tailed Test: Difference and Comparison

There are two types of hypothesis testing- one and two-tailed tests. But how do we know when to do a one-tailed test and a two-tailed test.

The key differences between these two tests can help to do research and experiments properly as both of them are very common processes used for testing.

Key Takeaways

1. One-tailed tests detect an effect in one specific direction, while two-tailed tests consider effects in both directions.
2. One-tailed tests require a priori knowledge about the direction of the effect, whereas two-tailed tests do not.
3. Two-tailed tests are more conservative, reducing the likelihood of false positives, while one-tailed tests have increased power to detect effects in a single direction.

One-Tailed Test vs Two-Tailed Test

The hypothesis being evaluated in a one-tailed test is directional, which means it predicts the direction of the difference or relationship between variables. The hypothesis in a two-tailed test is non-directional, which means it predicts the presence of a difference or link between variables without defining its direction.

A one-tailed test is only for testing one side of the hypothesis. It means that you have to select the direction of the test earlier and can use this test to confirm whether the mean you have selected is either greater or lesser than the other one.

On the other hand, a two-tailed test allows you to test both against each other. You don’t have to pick your direction beforehand.

Thus, there is a possibility of both a positive and a negative effect of this test.

However, since this test involves both directions, it becomes time-consuming.

Comparison Table

Parameters of Comparison	One-Tailed Test	Two-Tailed Test
What is it	In a one-tailed test, only one side of the hypothesis is tested.	In a two-tailed test, both sides of the hypothesis are tested.
Direction	In this test, there is only one direction.	But in a two-tailed test, there is no direction.
Identification	If any of these signs, >, < are used, it means that a one-tailed test has been carried out.	If this sign ‘#’ is used, it indicates that a two-tailed test is used.
Purpose	In a one-tailed test, it is determined that the variables share a relationship in which direction, left or right.	In a two-tailed test, it is determined if there is any relationship between the variables.
Classification	In a one-tailed test, it is determined that the variables share a relationship in which direction, left or right.	In a two-tailed test, it is determined if there is any relationship between the variables.

What is One-Tailed Test?

A one-tailed test is used for hypothesis testing. When you are using this test, it means that you are taking it for the determination of whether the relationship between the variables is in one specified direction.

So you have to select the direction previously and confirm whether the selected variable is greater or lesser than the other one.

For example, a company produces soaps, and the mass in each soap is equal to 200 grams. Then, Ho: µ = 200. This is the null hypothesis.

Now, if someone disagrees and believes that the mass of each soap is not equal to 200 grams, then it would be, Ho: µ ≠ 200. This is called the alternative hypothesis.

In the one-tailed test, there is the only possibility for the relationship in the direction you have chosen and not the other direction.

Thus when you are doing a one-tailed test, you should not be worried about note using the other direction that you have not selected for the test.

Only in such situations you should opt for a one-tailed test.

However, there are many advantages and disadvantages to a one-tailed test. The biggest advantage that it has is it reaches the significance level in less time.

But it has the potential to completely miss out on another direction.

Moreover, there are two types of one-tailed tests- left-tailed tests and right-tailed tests.

What is Two-Tailed Test?

A two-tailed test is also called a non-directional test.

In this test, you can examine both the means against each other, and you also do not need to pick the direction beforehand, unlike a one-tailed test terror two possibilities in this test, both positive and negative.

One example of this test can be the way new teaching techniques have effects on the marks of students.

Now here, the hypothesis that we can work on is that there is no significant effect of new teaching techniques on marks of students.

But new teaching techniques can affect both ways. It may increase or decrease a student’s marks.

So this test is not giving any kind of direction. In a two-tailed test, there is distribution on both sides. Unlike a one-tailed test, there is less chance of the rejection of the null hypothesis.

In a two-tailed test, a researcher can test the effect or difference in both directions.

In a two-tailed test, differences in both directions are discovered but not the direction of the difference.

For example, if you have to study the effect of two different teaching methods on marks of students through a two-tailed test, you can reach a conclusion that there is a significant difference between both the teaching methods in relation to marks of students.

But you would not be able to decide which method is more effective than the other.

Main Differences Between One and Two-Tailed Test

1. One tail test is only related to or specified direction. But a two-tailed test works in both directions of the hypothesis.
2. There are two types of one-tailed tests- left tailed test and the right-tailed test. Since both directions are involved in a two-tailed test, there is no such classification.
3. In a one-tailed test, the chances of the rejection of the null hypothesis are higher than a two-tailed test.
4. The purpose of a one-tailed test is to determine the relationship between the two variables is in which direction. But two-tailed tests were conducted to know whether there is any relationship between the two variables.
5. A one-tailed test does not take much time. But a two-tailed test is time-consuming.

References

1. https://psycnet.apa.org/record/1959-03845-001
2. https://www.igi-global.com/article/one-tailed-or-two-tailed-p-values-in-pls-sem/121988