# Goldfeld - Quandt test statistic equal to 1

I wonder what it means if the statistic (ratio) of this 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.

• 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 Jun 12 '15 at 12:12
• And, it would be better to include this information in the question rather than in a comment. – Alecos Papadopoulos Jun 12 '15 at 12:26
• It is just a therorical question. Any regression was made in this case. – Newbie Jun 12 '15 at 15:19

## 1 Answer

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 (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.