Difference Between One-tailed and Two-tailed Test

A one-tailed test and a two-tailed test are the two methods for conducting a statistical significance test of a characteristic obtained from the population with regard to the test statistic.

You are given a p-value somewhere in the output when you conduct a test of statistical significance, regardless of whether it is from a correlation, an ANOVA, a regression, or some other kind of test. You can choose from one of three alternate hypotheses if your test statistic has a symmetric distribution. One of these corresponds to a two-tailed test, while the other two correspond to one-tailed tests.
The relationship between the statistical variables can be determined using one- and two-tailed tests.

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Two-tailed Test

The critical area or region of rejection for the two-tailed test, which is referred to as a hypothesis test, is located on both ends of the normal distribution. It establishes whether the sample under test is inside or outside of a given range of values. Hence, if the calculated value lies in either of the two tails of the probability distribution, an alternative hypothesis is accepted in place of the null hypothesis.

This test divides into two equal parts and places one-half on each side, taking the possibility of both positive and negative effects into consideration. Extreme values serve as evidence against the null hypothesis since it is checked to determine if the estimated parameter is above or below the assumed parameter.

A two-tailed test allocates half of your alpha to testing the statistical significance in one direction and half of your alpha to testing the statistical significance in the other direction if you are using a significance level of 0.05. This indicates that.025 is present in each tail of the distribution of your test statistic. Regardless of the direction of the relationship you hypothesize, by performing a two-tailed test, you are testing for the probability of the relationship in both directions.

Example of Two-tailed Test

A t-test, for instance, could be used to compare a sample’s mean to a given value x. The mean being equal to x is our null hypothesis. A two-tail test will determine whether the mean is considerably higher or significantly lower than x. If the test statistic falls within the top 2.5% or bottom 2.5% of its probability distribution and has a p-value less than 0.05, the mean is considered statistically different from x.

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One-tailed test

One-tailed test refers to a significance test in which the area of rejection is found at one extreme of the sample distribution. It indicates if the crucial value for the estimated test parameter is higher or lower. The alternative hypothesis is accepted instead of the null hypothesis when the sample under test falls within the region of rejection, that is, either on the left or right side, depending on the situation. It is mostly used to determine the goodness of fit in chi-square distribution.

In this statistical hypothesis test, all the critical region, related to α, is placed in any one of the two tails. One-tailed tests include

Left-tailed test: The hypothesis test used is the left-tailed test when the population parameter is thought to be lower than the assumed one.
Right-tailed test: A right-tailed test is one in which the population parameter is expected to be bigger than the assumed parameter.

A one-tailed test allocates all of your alpha to testing the statistical significance in the one direction of interest if you are employing a significance level of.05. This indicates that your test statistic’s distribution has.05 in one tail. A one-tailed test fully ignores the potential of a relationship in the opposite direction while testing for the possibility of a relationship in one direction.

Example of One-tailed Test

Let’s go back to the t-test example where we compared the sample mean to a given value x. The mean being equal to x is our null hypothesis. A one-tail test will determine whether the mean is significantly more than x or significantly less than x, but not both. Then, depending on the selected tail, the mean is significantly greater than or less than x if the test statistic is in the top 5% or bottom 5% of its probability distribution, resulting a p-value less than 0.05.

The one-tailed test gives more power to detect an effect in one direction by not testing the effect in the other direction.

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Difference Between One-tailed and Two-tailed Test

1- One-tail test is a statistical hypothesis test in which the alternative hypothesis only has one end. On the other hand, a two-tail test indicates a test of the alternative hypothesis, which has two ends.

2- The alternative hypothesis is represented directionally in the one-tail test. The two-tail test, on the other hand, is a non-directional hypothesis test.

3- The region of rejection in a one-tail test is either on the left or right of the sample distribution. The region of rejection, on the other hand, is on both sides of the sampling distribution.

4- To determine whether there is any relationship between variables in a single direction, such as left or right, a one-tail test is employed. In contrast, the two-tail test is used to determine whether there is a relationship between variables in either direction.
5- The test parameter calculated for a one-tail test is greater or less than the critical value. In contrast to a two-tail test, the outcome is either within or outside the critical range.
6- A two-tail test is used when an alternate hypothesis has ‘≠’ sign. In contrast, a one-tail test is used when the alternative hypothesis has a  ‘> or <‘ sign.

One-tailed Test	Two-tailed Test
One tail test is a statistical hypothesis test in which the alternative hypothesis only has one end	Two-tail test refers to a significance test in which the alternative hypothesis has two ends
Region of rejection is either left or right	Region of rejection is both left and right
Determines relationship between variables in single direction	Determines relationship between variables in either direction
Results are greater or less than certain value	Results are greater or less than certain range of values
Directional	Non-directional
> or <	≠

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Example of One-tailed and Two-tailed Test

Case 1:

A manufacturer of light bulbs claims that the average lifespan of its energy-saving bulbs is 60 days. Create a hypothesis test to verify this claim and provide suggestions on the type of test we should employ.

As a result, we have:

H 0: An energy-saving light bulb typically lasts 60 days.
H 1: The average lifespan of an energy-saving light bulb is not 60 days.

We must take into account both the chance that the energy-saving light bulb’s lifetime is greater than 60 and the probability that it is less than 60 due to the “is not” in the alternative hypothesis. This necessitates the use of a two-tail test.

Case 2:

The manufacturer has now decided that it only concerned if an energy-saving light bulb has a mean lifespan of less than 60 days. What changes would you make to Case 1?

As a result, we have

H 0: An energy-saving lightbulb has an average lifespan of 60 days.
H 1: The average lifespan of an energy-saving light bulb is less than 60 days.

We now have a “less than” in the alternative hypothesis. This indicates that we will do a left-sided one-tail test rather than a two-tail test.

When should a one-tail test be used?

You might be tempted to perform a one-tail test whenever you have a hypothesis about the direction of an effect because it gives you more power to detect an effect. Before doing so, think about the implications of missing an effect in the other direction.

Consider that you have created a new medication that you feel is better to one that is already on the market. You decide on a one-tail test to enhance your chances of spotting the improvement. By doing this, you disregard the likelihood that the new medication will be less effective than the current medication. Although the consequences in this case are severe, they serve to highlight the risk associated with improper one tail test use.

When is a one-tail test appropriate?

You can proceed with a one-tailed test if you consider the consequences of missing an effect in the untested direction and determine that they are negligible and in no way unethical or improper. Consider once more that you have created a brand-new medication.

You think it is just as effective as the current medication and is less expensive. You are solely interested in testing whether this drug is less effective than the one currently on the market. You don’t care whether it’s much more efficient. You simply want to demonstrate that it is still effective. A one-tail test would be suitable in this situation.

When is a one-tail test NOT appropriate?

It is inappropriate to use a one tail test solely to achieve significance. No matter how “near” to significant the two-tailed test was, choosing a one-tailed test after running a two-tailed test that failed to reject the null hypothesis is not suitable. Inappropriate use of statistical tests might result in unreliable and very dubious results, which is a high price to pay for a significance star in your results table.

Conclusion

To conclude, we can state that the basic difference between a one-tailed test and a two-tailed test is one of direction; if the research hypothesis indicates the direction of an interaction or difference, a one-tailed test is used; otherwise, a two-tailed test is used.

Other articles

Please read through some of our other articles with examples and explanations if you’d like to learn more about research methodology.