What Heteroscedasticity in hypothesis testing is
In hypothesis testing, heteroscedasticity is a phenomenon in which the variance of the error term in a regression model is unequal across different values of the independent variable. This can lead to results that are not valid and lead to incorrect conclusions.
Steps for Heteroscedasticity in Hypothesis Testing:
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Check the residuals from the regression model: Residuals are the differences between the observed values and the predicted values. If the variance of the residuals changes across values of the independent variables, then heteroscedasticity is likely present.
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Use a statistical test to assess heteroscedasticity: There are several statistical tests that can be used to assess whether heteroscedasticity is present in a regression model. These include the Goldfeld-Quandt test, the Breusch-Pagan test, and the White test.
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Transform the data: If the data is transformed (e.g. taking the log of the dependent variable) and the variance of the residuals is reduced, then heteroscedasticity may have been present.
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Use a robust estimation procedure: Robust estimation procedures are designed to take into account the presence of heteroscedasticity. These include the Huber-White estimator, the M-estimator, and the iteratively reweighted least squares (IRLS) procedure.
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Use a different model: If the data is still heteroscedastic after taking the above steps, then a different model may be needed. Other models, such as a generalized linear model or a nonlinear model, may be better suited to the data.
Examples
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A researcher tests whether a new drug is effective for treating a particular disease. She performs a t-test to compare the mean outcome for treatment and control groups. However, the variance of the outcome in the treatment group is much higher than that of the control group, indicating that heteroscedasticity is present.
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A researcher tests if there is a significant difference between the average salary of men and women in a particular company. He performs a t-test to compare the mean salaries of the two groups. However, the variance of the salary in the male group is much higher than that of the female group, indicating that heteroscedasticity is present.