Testing Heteroskedasticity and Using Robust SEs in SPSS

Heteroskedasticity invalidates conventional OLS standard errors; it does not automatically bias OLS coefficients. A common response is to use robust standard errors for inference and revisit the specification.

SPSS AND REGRESSION DIAGNOSTICSPrepared by Lê Minh3 minUpdated 16/10/2026

KEY ARGUMENT

Use residual-versus-fitted plots to inspect patterns and Breusch–Pagan/Koenker or White tests for formal assessment. When heteroskedasticity is present, report HC3 or an appropriate estimator; Levene’s test is not a substitute for regression error-variance diagnostics.

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Heteroskedasticity: separate estimation and inference

Residuals
Inspect plots and spread patterns
Diagnostics
Check specification and influential cases
Standard errors
Consider appropriate robust SEs
Interpretation
Report the inference procedure

Conceptual diagram. Robust SEs do not fix functional form, endogeneity or measurement quality.

Source: Lê Minh · Conceptual illustration, not software output.

1. What does heteroskedasticity affect?

Homoskedasticity requires constant Var(εᵢ|X). When variance changes with X or fitted values, OLS may remain unbiased under the other assumptions, but conventional standard errors, t/F tests and CIs can be incorrect (MacKinnon & White, 1985; White, 1980).

Levene’s test examines variance equality between groups in t-tests/ANOVA; it does not replace regression residual heteroskedasticity tests.

Table 1
Tool	Purpose
Residual plot	Inspect fan shapes, nonlinearity and outliers
Breusch–Pagan/Koenker	Variance related to predictors/fitted values
White	More general patterns; also sensitive to misspecification
HC3 robust SE	Correct SEs/CIs while retaining OLS coefficients

2. SPSS workflow

Fit the original regression

Save ZPRED, ZRESID and unstandardized residuals as needed.

Plot residuals

Inspect residual spread over fitted values and nonlinear patterns.

Run diagnostic tests

Use BP/modified BP/White where supported; older versions may need syntax or another tool.

Review the specification

Check omitted variables, functional form, interactions and outliers.

Use robust estimation

Use HC3 or a suitable alternative; interpret robust SEs/CIs rather than the old conventional SE table.

*Application screenshot 1. The original SPSS Univariate Options dialog shows heteroskedasticity checks and robust standard errors. Apply options only when they match the fitted model.* Source: amosleminh.com · View full size

3. Interpret the null hypothesis correctly

H0 for BP/White tests is homoskedasticity under the tested specification. A small p-value supports heteroskedasticity or misspecification; a large p-value means only that it was not detected, particularly in small samples (Breusch & Pagan, 1979; White, 1980).

White’s test uses many degrees of freedom with numerous predictors, squares and cross-products; power or estimation stability can suffer. Modified BP/Koenker tests and robust SEs can provide complementary information.

Robust SEs do not correct nonlinearity

HC3 corrects the estimator covariance under heteroskedasticity. It does not fix omitted variables, endogeneity, influential outliers or an incorrect functional form.

4. Reporting template

Reporting example in English

The residual plot showed [description]. Breusch–Pagan χ²(df) = [ ], p = [ ]; White χ²(df) = [ ], p = [ ]. Given [evidence/no detected evidence] of heteroskedasticity, we report [HC3/OLS] SEs. The [X] coefficient was B = [ ], robust SE = [ ], 95% CI [ ; ], p = [ ].

Do not use Levene’s test for regression residuals.
Include a residual plot.
State the test’s H0.
Use robust SEs when appropriate.
Check functional form and outliers.
Do not interpret the previous OLS SE table after selecting HC3.

Conclusion

Heteroskedasticity assessment is one part of regression diagnostics. Robust SEs improve inference, but specification and data quality still need examination.

References

Breusch, T. S., & Pagan, A. R. (1979). A simple test for heteroscedasticity. Econometrica, 47(5), 1287–1294.https://doi.org/10.2307/1911963
White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test. Econometrica, 48(4), 817–838.https://doi.org/10.2307/1912934
MacKinnon, J. G., & White, H. (1985). Some heteroskedasticity-consistent covariance matrix estimators. Journal of Econometrics, 29(3), 305–325.https://doi.org/10.1016/0304-4076(85)90158-7

Methodological note: BP/White/HC3 availability depends on the SPSS version. Report the actual version and syntax/menu used rather than assuming identical support in every release.