<blockquote>
  <p><em>We'd like to test if an variable $x_j$ is relevant in the respect of the model</em></p>
</blockquote>

<p>means that we want to test its "statistical significance", so the null hypothesis is  $$\text{H}_0 : \beta = 0$$</p>

<p>(by the way, historically, that's why it is called the "null" hypothesis: a hypothesis of "null"-zero- effect).</p>

<p>The $t$-statistic for this test is</p>

<p>$$t=\frac{\hat{\beta_j}}{SE(\hat{\beta_j})}$$</p>

<p>Using a two-tailed test does not constrain us as regards the sign of the coefficient (the direction of the effect, if it exists). It may be positive or negative. If it is positive, the null if it is rejected, will be because the $t$-statistic takes a large positive value. But if the effect is negative, then the $t$-statistic will take a high negative value. So we want to test against either case, and this is why we use a "two-tailed" test.</p>

CC BY-SA 3.0
2016-01-18T13:22:16.460Z
@ÜbelYildmar You're welcome.
Alecos Papadopoulos
CC BY-SA 3.0
2016-01-18T12:38:09.430Z
2016-01-18T13:22:27.883Z
2016-01-18T13:22:27.883Z
Alecos Papadopoulos
<p>Let's assume a standard regression model:
$$y=\beta x+u$$
We'd like to test if an variable $x_j$ is relevant in the respect of the model.</p>

<p>t-statistics: $$t=\frac{\hat{\beta_j}-b}{SE(\hat{\beta_j})}$$</p>

<p>Most of the time, we assume the following two-tailed hypothesis:
$$H_0: \beta_j=b, \ H_1: \beta_j \neq b$$</p>

<p>My question is, why don't we use more often the one-tailed hypothesis to test the significance of a variable $x_j$? When I read papers and write assignments I hardly ever come across one-tailed t-tests in the respect to regression models. Why?</p>

<econometrics><statistics>
Why do we use mostly two-tailed Student's t-statistics to find if an explanatory variable is significant in a regression?
Übel Yildmar
# Why do we use mostly two-tailed Student's t-statistics to find if an explanatory variable is significant in a regression?

(Asked by: username_0 on 2016-01-18)

Let's assume a standard regression model:
$$y=\beta x+u$$
We'd like to test if an variable $x\_j$ is relevant in the respect of the model.

t-statistics: $$t=\frac{\hat{\beta\_j}-b}{SE(\hat{\beta\_j})}$$

Most of the time, we assume the following two-tailed hypothesis:
$$H\_0: \beta\_j=b, \ H\_1: \beta\_j \neq b$$

My question is, why don't we use more often the one-tailed hypothesis to test the significance of a variable $x\_j$? When I read papers and write assignments I hardly ever come across one-tailed t-tests in the respect to regression models. Why?

**Tags:** econometrics, statistics

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## 1 answers

### Answer by username_1 on 2016-01-18. Score: 4 | Accepted answer

> *We'd like to test if an variable $x\_j$ is relevant in the respect of the model*

means that we want to test its "statistical significance", so the null hypothesis is $$\text{H}\_0 : \beta = 0$$

(by the way, historically, that's why it is called the "null" hypothesis: a hypothesis of "null"-zero- effect).

The $t$-statistic for this test is

$$t=\frac{\hat{\beta\_j}}{SE(\hat{\beta\_j})}$$

Using a two-tailed test does not constrain us as regards the sign of the coefficient (the direction of the effect, if it exists). It may be positive or negative. If it is positive, the null if it is rejected, will be because the $t$-statistic takes a large positive value. But if the effect is negative, then the $t$-statistic will take a high negative value. So we want to test against either case, and this is why we use a "two-tailed" test.

> **Comments:**
> **username_1**: @ÜbelYildmar You're welcome.  

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