<p>The situation implicitly described in the question assumes that the two sub-samples have equal size (which is not necessary for the test to go through).  </p>

<p>In such a situation, if the ratio $RSS2/RSS1$ equals <strong>unity</strong>, then the null-hypothesis of homoskedasticity won't indeed be rejected <em>for any significance level up to $0.5$</em>, (to be compared to the conventional levels of $0.1,\; 0.05,\; 0.01$)  because the statistic used, under the null hypothesis follows an <a href="https://en.wikipedia.org/wiki/F-distribution" rel="nofollow"><strong>F-distribution</strong></a> (exactly or asymptotically), and more over, one that has equal degrees of freedom for the numerator and the denominator (due to the equal sub-sample sizes). </p>

<p>This also makes intuitive sense: if the obtained estimates for the sub-sample variance are equal, then, in order to reject the null, we should accept that it would be more probable than not, that the rejection will be mistaken.</p>

CC BY-SA 3.0
2015-06-12T16:17:58.767Z
2015-06-12T16:17:58.767Z
Alecos Papadopoulos
<p>I wonder what it means if the statistic (ratio) of <a href="https://en.wikipedia.org/wiki/Goldfeld%E2%80%93Quandt_test" rel="nofollow">this test</a> is one?
The statistic is built from sample splitting. Then you have to calculate the ratio RSS2 / RSS1, which are the Residual Sum Squares of the new subsamples. <br>
I think it means that both subsamples have the same variance but I am not sure at all.<br>
Thank you in advance.</p>

CC BY-SA 3.0
2015-06-12T12:12:03.350Z
Additional information needed: 1) Total number of observations in the sample, 2) number of observation in sub-smaple 2, 3) number of observations in sub-sample 1. Also 4) Number of regressors (including the constant term).
Alecos Papadopoulos
CC BY-SA 3.0
2015-06-12T12:26:20.500Z
And, it would be better to include this information in the question rather than in a comment.
Alecos Papadopoulos
CC BY-SA 3.0
2015-06-12T15:19:39.373Z
It is just a therorical question. Any regression was made in this case.
Pithit
<econometrics><statistics>
Goldfeld - Quandt test statistic equal to 1
Pithit
# Goldfeld - Quandt test statistic equal to 1

(Asked by: username_0 on 2015-06-12)

I wonder what it means if the statistic (ratio) of [this test](https://en.wikipedia.org/wiki/Goldfeld%E2%80%93Quandt_test) is one?
The statistic is built from sample splitting. Then you have to calculate the ratio RSS2 / RSS1, which are the Residual Sum Squares of the new subsamples.   
I think it means that both subsamples have the same variance but I am not sure at all.  
Thank you in advance.

**Tags:** econometrics, statistics

> **Comments:**
> **username_1**: Additional information needed: 1) Total number of observations in the sample, 2) number of observation in sub-smaple 2, 3) number of observations in sub-sample 1. Also 4) Number of regressors (including the constant term).  
> **username_1**: And, it would be better to include this information in the question rather than in a comment.  
> **username_0**: It is just a therorical question. Any regression was made in this case.  

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## 1 answers

### Answer by username_1 on 2015-06-12. Score: 1

The situation implicitly described in the question assumes that the two sub-samples have equal size (which is not necessary for the test to go through).

In such a situation, if the ratio $RSS2/RSS1$ equals **unity**, then the null-hypothesis of homoskedasticity won't indeed be rejected *for any significance level up to $0.5$*, (to be compared to the conventional levels of $0.1,\; 0.05,\; 0.01$) because the statistic used, under the null hypothesis follows an [**F-distribution**](https://en.wikipedia.org/wiki/F-distribution) (exactly or asymptotically), and more over, one that has equal degrees of freedom for the numerator and the denominator (due to the equal sub-sample sizes).

This also makes intuitive sense: if the obtained estimates for the sub-sample variance are equal, then, in order to reject the null, we should accept that it would be more probable than not, that the rejection will be mistaken.


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