Understanding the different methods of hypothesis testing is crucial for accurate data interpretation. Among these methods, onetailed and twotailed tests stand out due to their specific applications and implications.
This article discusses onetailed vs twotailed tests, their examples, scenarios where each test is applicable, and the pros and cons associated with onetailed and twotailed tests.
What is a OneTailed Test?
Onetailed tests are used when a hypothesis predicts a specific direction of effect. They are ideal for scenarios where the interest lies in determining whether a parameter is significantly greater or less than a specific value.
This type of test evaluates whether the observed data deviates significantly from the null hypothesis (the hypothesis of no effect or no difference) but only in the specified direction.
In the context of A/B testing, a onetailed test is used to determine if there is a significant difference in a specific direction between two webpage versions, products, or strategies.
For example, if you conduct an A/B test to see if a new website design leads to higher user engagement compared to the current design, a onetailed test would be used to assess if the new design increases engagement specifically, ignoring the possibility of a decrease.
This focused approach makes onetailed tests suitable for scenarios where you expect a directional and clearly defined outcome.
Example of a OneTailed Test in A/B Testing:
Suppose an ecommerce company wants to increase its website’s conversion rate. The CRO team they hired hypothesizes that changing the color of the “Add to Cart” button from blue to red will lead to more clicks and, consequently, more purchases. To test this hypothesis, they set up an A/B test:
Version A (Control): The original webpage with the blue “Add to Cart” button.
Version B (Variant): The same webpage but with the red “Add to Cart” button.
The hypothesis predicts the red button will increase conversions. The null hypothesis (H0) states there will be no increase, or possibly a decrease, in conversions with the red button.
A onetailed test checks for increased conversions with the red button. If the test shows statistical significance, it supports the hypothesis that the red button performs better. If not, there’s insufficient evidence to reject the null hypothesis, meaning the increase isn’t statistically significant.
Pros of onetailed tests

Increased Power
Onetailed tests have more statistical power compared to twotailed tests when testing the same hypothesis. They focus all statistical power in one direction of the distribution (the direction of interest), making it more likely to detect an effect in that direction.

Lower Sample Size Requirement
Due to its increased power, a onetailed test often requires a smaller sample size to achieve the same level of statistical significance as a twotailed test. This is a significant advantage in practical scenarios where collecting large samples can be timeconsuming or expensive.

Specific Hypothesis Testing
Onetailed tests are tailored for specific, directional hypotheses. This means they are ideal when the hypothesis makes a specific prediction about the direction of the effect. For example, if a hypothesis states that a new marketing strategy will increase sales, a onetailed test is appropriate because it specifically looks for an increase in sales.
Cons of onetailed tests

Risk of Missing Opposite Effect
One of the main drawbacks of a onetailed test is the risk of missing a significant effect in the opposite direction of the hypothesis. Since the test is designed to detect an effect in one specific direction, it may overlook meaningful changes that occur in the other direction.

Bias Risk
Choosing a onetailed test, especially after data collection, poses a risk of bias. Decisions should be based on strong theoretical grounds or prior evidence, not on a desire to achieve significant results.

Limited Insight
Onetailed tests provide less comprehensive insight compared to twotailed tests. By focusing only on one direction, they may miss out on understanding the full spectrum of the effect being studied.
What is a TwoTailed Test?
A twotailed test is a statistical method used when the direction of the effect is not specified in the hypothesis; unlike a onetailed test that looks for a significant effect in one specific direction, a twotailed test checks for significance in both directions.
This type of test is useful when you are interested in detecting any significant difference, regardless of whether it is positive or negative.
A/B testing uses a twotailed test to determine whether a statistically significant difference exists between two versions (A and B) without a predetermined direction of the expected outcome.
This approach is crucial when the goal is to ascertain any significant change, whether an increase or a decrease, in a key metric due to variations in the test.
For instance, a twotailed test is appropriate if you test two different website layouts to see which one performs better in terms of user engagement without a specific hypothesis about which layout will be superior.
Example of a TwoTailed Test in A/B Testing:
The same ecommerce company wants to evaluate the impact of a new product description format on its website. The company is unsure whether the new format will increase or decrease customer engagement, so they conducted an A/B test again.
Version A (Control): The original product page with the standard description format.
Version B (Variant): The same product page but with the new description format.
The hypothesis is: “The new format will significantly impact engagement,” without specifying the direction of this impact.
A twotailed test is chosen to detect any significant change in engagement, whether an increase or decrease. It assesses if the new format leads to a statistically significant difference in engagement compared to the control.
If the test shows significance, it confirms the new format notably affects engagement, but further analysis is required to determine if the effect is positive or negative.
Pros of twotailed tests

Detects Effects in Both Directions
The primary advantage of a twotailed test is its ability to detect statistically significant effects in both directions. This means it can identify whether the tested variable has a positive or negative impact compared to the control.

More Conservative
A twotailed test is considered more conservative than a onetailed test because it divides the significance level across both ends of the distribution. This means that for a result to be considered statistically significant, it must meet a stricter criterion compared to a onetailed test.
Cons of twotailed tests

Reduced Power
One of the main drawbacks of a twotailed test is its reduced statistical power compared to a onetailed test. The power of a statistical test is its ability to detect an effect when there is one. In a twotailed test, because the significance level is split between both tails of the distribution, it requires a stronger effect to reach statistical significance.

Larger Sample Size Needed
Due to its reduced power, a twotailed test often requires a larger sample size to achieve the same level of statistical significance as a onetailed test. This can be a significant challenge in research scenarios where gathering a large amount of data is difficult, timeconsuming, or expensive.

Overly General
In A/B testing, a twotailed test can be overly general when there’s already a strong theory predicting the direction of an effect. It checks for changes in both directions, which may not be necessary if you only expect an increase or decrease.
OneTailed vs TwoTailed Tests: Which Should You Choose?
When deciding between a onetailed and a twotailed test in A/B testing, the choice hinges on your hypothesis and what you aim to discover or prove. Both tests have their place, but their applicability depends on the specific context of your research question.
Understanding the differences between these tests, their applications, and their implications is vital for accurate data interpretation and effective decisionmaking in various testing scenarios.