Difference between One-tailed and Two-Tailed Test

One-tailed and two-tailed test are statistical hypothesis tests to accept or reject the null hypothesis. In this article, we will briefly discuss the difference between one tail and two tail tests.

While working with the datasets, you fix some assumptions, i.e., called the hypothesis, and the process done to check these assumptions is called hypothesis testing. In hypothesis testing, you have to check whether your claim is correct or not. So, one of the initial steps is to perform test statistics (z-test, t-test, chi-square, ANOVA test), but for that, you need to know if it is one-tailed or two-tailed.

Before the start of the article, let’s discuss two important keywords that we will use further in our article, i.e., Critical Region and alpha level.

Test statistics follow some probability distributions, and in any test, the probability density curve has two divisions – Region of Acceptance and Region of Rejection and the region of rejection is known as a Critical Region.  

Alpha-level: It is the probability of making the wrong decision when the Null Hypothesis is true. It is often called the Significance Level.

Table of Content

• One-Tailed Test vs. Two-Tailed Test
• What is a One-Tailed Test?
  • Definition
  • Example
• What is a Two-tailed Test?
  • Definition
  • Example
• Key Difference Between One-tailed Test and Two-Tailed Test

One-Tailed Test vs. Two-Tailed Test

Parameter	One-Tailed Test	Two-Tailed Test
Definition	Statistical hypothesis test, where the alternate hypothesis is one-side (either right or left side).	Statistical hypothesis test, where the alternate hypothesis is two-tailed.
Hypothesis	Directional	Non-Directional
Level of Significance	Entire level of significance lies on one side.	Splits the level of significance into half.
Region of Rejection	Either on the left side  or right side of the sampling distribution.	The rejection region is from both sides.
Sign in alternate hypothesis	< or >	!= (not equal)
Graphical Representation

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What is a One-tailed Test?

Definition

In hypothesis testing, when we test (check) whether the Sample parameter is Higher or Lower (< or >) than the population parameter, it is known as the One-Tailed Test. 

• To reject the null hypothesis, the sample parameter should be either greater or less than the population parameter.
• The region of rejection (critical region) lies on one side of the sampling distribution.
• It represents whether the estimated test parameter is less or greater than the critical value.
• It has the entire 5% of the significance level on one side.
• Null and Alternate Hypotheses must be established before the test.
• It is often use when you want to test your hypothesis in both the direction

It may be either:

Left-Tail: When the population parameter is lower than the assumed value.

Right-Tail: When the population parameter is greater than the assumed value.

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Example

A mobile manufacturer has launched batteries and is interested to know whether the mean lifetime average of these batteries is greater than 50 days or not. Set up Null and alternate hypotheses to check the claim and suggest which test can be used.

Answer:

H0: The mean lifetime average of batteries is 50 days
H1: The mean lifetime average of batteries is greater than 50 days.

Since we have greater than in H1 (i.e., Alternate Hypothesis), hence we will perform the right-sided one-tailed test.

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What is a Two-Tailed Test?

Definition

In hypothesis testing, when we test whether the sample is greater or less than a certain range of values, it is referred to as a two-tailed test.

• The region of rejection lies on both the side of the probability distribution
• It is used for Null Hypothesis Testing.
• The significant level is split in both directions.

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Example

Now, we will take the same above example, with some modifications:

A mobile manufacturer claims that their newly launched batteries last an average of 50 days. Set up Null and alternate hypotheses to check the claim and suggest which test can be used.

Answer:

H0: The mean lifetime of the battery is 50 days.

H1: The mean lifetime of the battery is not 50 days.

Since an alternate hypothesis we have is not, so, we have to perform the test on both sides (to check the possibility of whether the mean lifetime of the battery is greater or less than 50 days.), i.e., two-tail test.

Key Differences

• In the one-tail, the alternate hypothesis has a single end (either left or right), but in the two-tail, the alternate hypothesis has two ends (both sides).
• The region of Rejection (Critical Region) in the one-tail test lies either on the left or side of the probability distribution curve, while in two tail test, the critical region lies on both sides.
• The test parameter in the one-tail is either more or less than the critical value, while in the two-tail, the results are either within or outside the critical value.
• The one-tail checks the relation between the variables in a single direction, while the two-tail checks in both directions.

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Conclusion

In this article, we have discussed one-tailed and two tailed tests, difference between them and examples.

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