A tail vs. TWO TAPES | TOWARDS DATA SCIENCE

Introduction

If you have ever analyzed data using built -in T test functions, such as R or Scipy, here is a question for you: Have you ever adjusted the default configuration for the alternative hypothesis? If your answer is no, or if you are not even sure what this means, this blog post is for you!

The alternative hypothesis parameter, commonly known as “a” versus “two queues” tail in statistics, defines the expected direction of the difference between control and treatment groups. In a two -tailed test, we evaluate if there is any difference in the average values ​​between the groups, without specifying an address. A proof of a tail, on the other hand, raises a specific address, whether the average control group is less or greater than that of the treatment group.

Choosing between one and two tails hypothesis may seem a minor detail, but it affects each stage of the A/B tests: from test planning to data analysis and the interpretation of results. This article builds a theoretical basis on why the hypothesis address matters and explores the pros and cons of each approach.

Hypothesis test versus two tails: understand the difference

To understand the importance of choosing between a tail hypothesis and two tails, we briefly review the basic concepts of the T test, the common use method in A/B tests. Like other hypothesis test methods, the T test begins with a conservative assumption: there is no difference between the two groups (the null hypothesis). Only if we find strong evidence against this assumption, we can reject the null hypothesis and conclude that the treatment has had an effect.

But what qualifies as “strong evidence”? To that end, a rejection region is determined under the null hypothesis and all the results that fall within this region are considered so unlikely that we take them as evidence against the viability of the null hypothesis. The size of this rejection region is based on a default probability, known as Alfa (α), which represents the probability of incorrectly rejecting the null hypothesis.

What does this have with the direction of the alternative hypothesis? A lot of really. While the alpha level determines the size of the rejection region, the alternative hypothesis dictates its placement. In a tail proof, where we propose the hypothesis of a specific direction of difference, the rejection region is located in a single tail of the distribution. For a positive hypothetical effect (e .. g., That the average of the treatment group is higher than the average of the control group), the rejection region is in the right tail, creating a right tail test. On the contrary, if we propose the hypothesis of a negative effect (for example, that the average of the treatment group is less than the average of the control group), the rejection region would be placed in the left tail, resulting in a left tail test.

In contrast, a two -tailed test allows the detection of a difference in any direction, so the rejection region is divided between both tails of the distribution. This adapts to the possibility of observing extreme values ​​in any direction, if the effect is positive or negative.

To build intuition, let's visualize how rejection regions appear under the different hypotheses. Remember that according to the null hypothesis, the difference between the two groups should focus around zero. Thanks to the central limit theorem, we also know that this distribution is close to a normal distribution. Consequently, the rejection areas corresponding to the different alternative hypotheses are seen:

Why does the difference?

The choice of address for the alternative hypothesis affects the entire A/B test process, starting with the planning phase, specifically, to determine the sample size. The sample size is calculated based on the desired power of the test, which is the probability of detecting a true difference between the two groups when it exists. To calculate power, we examine the area under the alternative hypothesis that corresponds to the rejection region (since power reflects the ability to reject the null hypothesis when the alternative hypothesis is true).

Since the address of the hypothesis affects the size of this rejection region, the power is generally lower for a two -tailed hypothesis. This is because the rejection region is divided into both queues, which makes it more difficult to detect an effect in any direction. The following graph illustrates the comparison between the two types of hypotheses. Keep in mind that the purple area is larger for the hypothesis of a tail, compared to the two -tailed hypothesis:

In practice, to maintain the desired power level, we compensate for the reduced power of a two -tailed hypothesis by increasing the sample size (the increase in the size of the sample increases the power, although the mechanics of this can be a topic for a separate article). Therefore, the choice between one and two tails hypothesis directly influences the size of the sample required for its test.

Beyond the planning phase, the choice of alternative hypothesis directly affects the analysis and interpretation of the results. There are cases in which a test can reach an importance with an approach to a tail, but not with one of two tails, and vice versa. Reviewing the previous graph can help illustrate this: for example, a result in the left tail could be significant under a two -tailed hypothesis, but not under a hypothesis of a right tail. On the contrary, certain results may fall within the rejection region of a right test of a tail, but are outside the rejection area in a two -tailed test.

How to decide between a hypothesis of a tail and two tails

Let's start with the final result: there is no absolute or incorrect choice here. Both approaches are valid, and the main consideration must be their specific commercial needs. To help you decide which option best suits your company, we will describe the pros and key cons of each.

At first glance, an alternative of a tail may seem the clear option, since it is often aligned with commercial objectives. In industry applications, the approach is usually to improve specific metrics instead of exploring the impact of a treatment on both directions. This is especially relevant in A/B tests, where the goal is to optimize conversion rates or improve income. If the treatment does not lead to a significant improvement, the change examined will not be implemented.

Beyond this conceptual advantage, we have already mentioned a key benefit of a tail hypothesis: it requires a smaller sample size. Therefore, choosing a tail alternative can save time and resources. To illustrate this advantage, the following graphics show the sample sizes required for one and two tails with different power levels (ALPHA is set at 5%).

In this context, the decision between one and two tails hypothesis becomes particularly important in sequential tests, a method that allows continuous data analysis without inflating the alpha level. Here, selecting a tail test can significantly reduce the duration of the test, allowing faster decision making, which is especially valuable in dynamic business environments where rapid responses are essential.

However, do not take over discarding the two -tailed hypothesis! It has its own advantages. In some commercial contexts, the ability to detect “significant negative results” is an important benefit. As a client once shared, he preferred significant negative results about non -conclusive because they offer valuable learning opportunities. Even if the result was not expected, it could conclude that the treatment had a negative effect and obtain information about the product.

Another benefit of two tails tests is its direct interpretation using trust intervals (IC). In two tails tests, a IC that does not include zero indicates directly importance, which facilitates professionals to interpret the results of a look. This clarity is particularly attractive since CIS is widely used in A/B test platforms. On the contrary, with the tests of a tail, a significant result could still include zero in the IC, which can lead to confusion or distrust of the findings. Although unilateral confidence intervals can be used with tests of a tail, this practice is less common.

Conclusions

By adjusting a single parameter, you can significantly affect your A/B tests: specifically, the sample size you need to collect and the interpretation of the results. When deciding between one and two tails hypothesis, consider factors such as the size of the available sample, the advantages of detecting negative effects and the convenience of aligning trust intervals (IC) with hypothesis tests. Ultimately, this decision must be made thoughtfully, taking into account what best fits your commercial needs.

(Note: All images in this publication were created by the author)