Testing Heteroskedasticity Statistically



Youtube Link: http://www.youtube.com/watch?v=3QcX4jqPn14

Parts:

Related Videos: Heteroscedasticity Adjusted Standard Errors

An assumption associated with regression is heteroskedasticity, which means that the error variance associated with the model is equal across all levels of the independent variable. Stated alternatively, heteroskedasticity is observed when the residuals associated with a regression analysis are not equal.

From a statistical standpoint, "are not equal" implies beyond sampling fluctuations. However, how does one test the assumption of hteroskedasticity statistically? Good question. Few textbooks discuss such matters.

Instead, researchers are instructed to examine the residuals qualitatively. Specifically, heteroskedasticity is argued to be present when the residuals exhibit a "fanning" effect in the residual plot. Personally, except in extreme cases, I've never felt confident using the qualitative method.

The consequences of violating the assumption of heterokedasticity are serious, as the standard errors associated with the beta weights are likely biased downward (and, thus, one will more likely declare a beta as statistically significant when it is in fact not).

Fortunately, there are a couple of methods to test for heteroskedasticity statistically. Namely, the Breusch-Pagan Test and the Koenker Test. I encourage you to watch the video above which demonstrates these tests in SPSS. Unfortunately, the method is not in-built into SPSS. One must use a macro that can be found here:

http://www.spsstools.net/Syntax/RegressionRepeatedMeasure/Breusch-PaganAndKoenkerTest.txt