# Goldfeld–Quandt test

In statistics, the Goldfeld–Quandt test checks for homoscedasticity in regression analyses.wikipedia

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### Homoscedasticity

**homoscedastichomogeneity of variancehomoskedastic**

In statistics, the Goldfeld–Quandt test checks for homoscedasticity in regression analyses.

Testing for groupwise heteroscedasticity requires the Goldfeld–Quandt test.

### Stephen Goldfeld

**Stephen M. GoldfeldGoldfeld, Stephen M.**

The Goldfeld–Quandt test is one of two tests proposed in a 1965 paper by Stephen Goldfeld and Richard Quandt.

### Richard E. Quandt

**Richard Quandt**

The Goldfeld–Quandt test is one of two tests proposed in a 1965 paper by Stephen Goldfeld and Richard Quandt.

* Goldfeld–Quandt test

### F-test of equality of variances

**F testF''-testFisher's F**

This test statistic corresponds to an F-test of equality of variances, and a one- or two-sided test may be appropriate depending on whether or not the direction of the supposed relation of the error variance to the explanatory variable is known.

### Statistics

**statisticalstatistical analysisstatistician**

In statistics, the Goldfeld–Quandt test checks for homoscedasticity in regression analyses.

### Regression analysis

**regressionmultiple regressionregression model**

In the context of multiple regression (or univariate regression), the hypothesis to be tested is that the variances of the errors of the regression model are not constant, but instead are monotonically related to a pre-identified explanatory variable.

### Dependent and independent variables

**dependent variableindependent variableexplanatory variable**

In the context of multiple regression (or univariate regression), the hypothesis to be tested is that the variances of the errors of the regression model are not constant, but instead are monotonically related to a pre-identified explanatory variable.

### Least squares

**least-squaresmethod of least squaresleast squares method**

The parametric test is accomplished by undertaking separate least squares analyses on two subsets of the original dataset: these subsets are specified so that the observations for which the pre-identified explanatory variable takes the lowest values are in one subset, with higher values in the other.

### Parametric statistics

**parametricparametric testparametric inference**

The parametric test assumes that the errors have a normal distribution.

### Normal distribution

**normally distributedGaussian distributionnormal**

The parametric test assumes that the errors have a normal distribution. The second test proposed in the paper is a nonparametric one and hence does not rely on the assumption that the errors have a normal distribution.

### Design matrix

**data matrixdesign matricesdata matrices**

There is an additional assumption here, that the design matrices for the two subsets of data are both of full rank.

### Test statistic

**Common test statisticst''-test of test statistics**

The test statistic used is the ratio of the mean square residual errors for the regressions on the two subsets.

### Power (statistics)

**statistical powerpowerpowerful**

Increasing the number of observations dropped in the "middle" of the ordering will increase the power of the test but reduce the degrees of freedom for the test statistic.

### Nonparametric statistics

**non-parametricnon-parametric statisticsnonparametric**

The second test proposed in the paper is a nonparametric one and hence does not rely on the assumption that the errors have a normal distribution.

### Resampling (statistics)

**resamplingstatistical supportpermutation test**

Critical values for this test statistic are constructed by an argument related to permutation tests.

### Breusch–Pagan test

**Cook–Weisberg testBreusch–Pagan statisticCook-Weisberg test**

However some disadvantages arise under certain specifications or in comparison to other diagnostics, namely the Breusch–Pagan test, as the Goldfeld–Quandt test is somewhat of an ad hoc test.

### Monotonic function

**monotonicitymonotonemonotonic**

Also, error variance must be a monotonic function of the specified explanatory variable.

### Quadratic function

**quadraticquadratic polynomialquadratically**

For example, when faced with a quadratic function mapping the explanatory variable to error variance the Goldfeld–Quandt test may improperly accept the null hypothesis of homoskedastic errors.

### Robust statistics

**robustbreakdown pointrobustness**

Unfortunately the Goldfeld–Quandt test is not very robust to specification errors.

### Statistical model specification

**Model specificationmisspecifiedmisspecification**

The Goldfeld–Quandt test detects non-homoskedastic errors but cannot distinguish between heteroskedastic error structure and an underlying specification problem such as an incorrect functional form or an omitted variable.

### Ramsey RESET test

**RESET test**

Jerry Thursby proposed a modification of the Goldfeld–Quandt test using a variation of the Ramsey RESET test in order to provide some measure of robustness.

### Glejser test

Herbert Glejser, in his 1969 paper outlining the Glejser test, provides a small sampling experiment to test the power and sensitivity of the Goldfeld–Quandt test.

### Monte Carlo method

**Monte CarloMonte Carlo simulationMonte Carlo methods**

Herbert Glejser, in his 1969 paper outlining the Glejser test, provides a small sampling experiment to test the power and sensitivity of the Goldfeld–Quandt test.

### R (programming language)

**RR programming languageCRAN**

* In R, the "lmtest" package offers the function to perform the Goldfeld–Quandt test.