It is shown that the likelihood ratio test for heteroscedasticity, assuming the Laplace distribution, gives good results for Gaussian and fat‐tailed data. The likelihood ratio test, assuming normality, is very sensitive to any deviation from normality, especially when the observations are from a distribution with fat tails. Such a likelihood test can also be used as a robust test for a constant variance in residuals or a time series if the data is partitioned into groups.