<p>You seem to have <span class="math-container">$H_0: \beta_1 \le 0$</span> and <span class="math-container">$H_1: \beta_1 &gt; 0$</span>. In this case, you reject <span class="math-container">$H_0$</span> in favor of <span class="math-container">$H_1$</span> if your t-value (not the <strong>absolute</strong> t-value, but the t-value itself) is bigger than the one-tailed critical value. In your case, <span class="math-container">$\hat\beta_1 &lt; 0$</span> so your t-value is negative and so you do <strong>not</strong> reject <span class="math-container">$H_0$</span> in favor of <span class="math-container">$H_1$</span>.</p>

<p><strong>Edit</strong></p>

<p>Regarding significant* variables with the wrong signs (negative when expecting positive in your case), Jeffrey Wooldridge (<em>Introductory Econometrics: A Modern Approach</em>, 7e, end of Section 4-2f, p. 134) writes:</p>

<p>"A significant variable that has the unexpected sign and a practically large effect is much more troubling and difficult to resolve. One must usually think more about the model and the nature of the data to solve such problems. Often, a counterintuitive, significant estimate results from the omission of a key variable or from one of the important problems we will discuss in Chapters 9 and 15."</p>

<p>Note *: "Significance" means rejection of the null in favor of the <em>two-sided</em> alternative. "Significance" does not necessary imply the rejection  of the null in favor of a one-sided alternative.</p>

CC BY-SA 4.0
2019-09-24T06:51:49.177Z
This does not answer the question, rather just formats what OP has stated already. What is OP missing? This does not answer this
Brennan
CC BY-SA 4.0
2019-09-24T12:04:42.710Z
@Brennan There is nothing is missing. And my answer does not just format what OP has stated already. The null is not rejected in the given situation. OP wrote "I can reject the null hypothesis" but that's not correct. I thought one would understand it if one read the question and my answer carefully. If not, well, that's fine too.
chan1142
CC BY-SA 4.0
2019-09-24T16:42:08.500Z
Ah I re-read it all and this makes perfect sense, sorry
Brennan
CC BY-SA 4.0
2019-09-26T15:07:28.043Z
This is the kind of answer I was looking for. I though we looked at the absolute T-value as per the decision rule. Could you intuitively explain what a negative t-value means?
Rumi
CC BY-SA 4.0
2019-09-27T16:07:49.830Z
@Rumi Please see if the edit is relevant to your question.
chan1142
CC BY-SA 4.0
2019-09-24T00:34:04.680Z
2019-09-27T17:11:10.233Z
2019-09-27T17:11:10.233Z
chan1142
<p>My absolute t-value is greater than t-critical value. This means that I can reject my null hypothesis which was that <span class="math-container">$\beta_1\leq 0$</span>. Therefore, <span class="math-container">$\beta_1\gt 0$</span> and my alternative hypothesis is correct. However, my data has a negative slope. which tells me that <span class="math-container">$\beta_1\lt 0$</span>. What am I missing here? </p>

CC BY-SA 4.0
2019-09-23T05:47:17.413Z
Can you show your regression output? If you want to provide your data as well that would excellent. What do you mean the data has a negative slope—like the scatterplot of Y on X?
Brennan
CC BY-SA 4.0
2019-09-28T09:19:22.183Z
Also, when one is using doing conventional (Neyman-Pearson) hypothesis tests, one should specify the null hypothesis as an equality, otherwise the "statistics" aren't meaningful as random variables.
Student
<econometrics><hypothesis-testing>
Econometrics - Need help interpreting results
Rumi
# Econometrics - Need help interpreting results

(Asked by: username_0 on 2019-09-23)

My absolute t-value is greater than t-critical value. This means that I can reject my null hypothesis which was that $\beta\_1\leq 0$. Therefore, $\beta\_1\gt 0$ and my alternative hypothesis is correct. However, my data has a negative slope. which tells me that $\beta\_1\lt 0$. What am I missing here?

**Tags:** econometrics, hypothesis-testing

> **Comments:**
> **username_1**: Can you show your regression output? If you want to provide your data as well that would excellent. What do you mean the data has a negative slope—like the scatterplot of Y on X?  
> **username_2**: Also, when one is using doing conventional (Neyman-Pearson) hypothesis tests, one should specify the null hypothesis as an equality, otherwise the "statistics" aren't meaningful as random variables.  

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## 1 answers

### Answer by username_3 on 2019-09-24. Score: 0 | Accepted answer

You seem to have $H\_0: \beta\_1 \le 0$ and $H\_1: \beta\_1 > 0$. In this case, you reject $H\_0$ in favor of $H\_1$ if your t-value (not the **absolute** t-value, but the t-value itself) is bigger than the one-tailed critical value. In your case, $\hat\beta\_1 < 0$ so your t-value is negative and so you do **not** reject $H\_0$ in favor of $H\_1$.

**Edit**

Regarding significant\* variables with the wrong signs (negative when expecting positive in your case), Jeffrey Wooldridge (*Introductory Econometrics: A Modern Approach*, 7e, end of Section 4-2f, p. 134) writes:

"A significant variable that has the unexpected sign and a practically large effect is much more troubling and difficult to resolve. One must usually think more about the model and the nature of the data to solve such problems. Often, a counterintuitive, significant estimate results from the omission of a key variable or from one of the important problems we will discuss in Chapters 9 and 15."

Note \*: "Significance" means rejection of the null in favor of the *two-sided* alternative. "Significance" does not necessary imply the rejection of the null in favor of a one-sided alternative.

> **Comments:**
> **username_1**: This does not answer the question, rather just formats what OP has stated already. What is OP missing? This does not answer this  
> **username_3**: @username_1 There is nothing is missing. And my answer does not just format what OP has stated already. The null is not rejected in the given situation. OP wrote "I can reject the null hypothesis" but that's not correct. I thought one would understand it if one read the question and my answer carefully. If not, well, that's fine too.  
> **username_1**: Ah I re-read it all and this makes perfect sense, sorry  
> **username_0**: This is the kind of answer I was looking for. I though we looked at the absolute T-value as per the decision rule. Could you intuitively explain what a negative t-value means?  
> **username_3**: @username_0 Please see if the edit is relevant to your question.  

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