Final answer:
When heteroskedasticity-robust standard error is greater than the regular standard error, the t-statistic will likely decrease, p-values will likely become greater, and confidence intervals will likely become wider. The correct option is (c) The p-value will likely become greater.
Step-by-step explanation:
When comparing heteroskedasticity-robust standard error to the regular standard error, if the heteroskedasticity-robust standard error is greater than the regular standard error, it will impact the resulting t-statistic and the p-value. First, let's define heteroskedasticity-robust standard errors: these are adjusted standard errors that take into account variability that is not consistent across all levels of the independent variables (i.e., heteroskedasticity). When these are larger than the typical, unadjusted standard errors, it indicates that there is more variability in the error terms that is not captured by the model.
Regarding the impact of this on statistical metrics:
- The t-statistic is calculated as the coefficient estimate divided by its standard error. If the standard error increases and the coefficient remains the same, the t-statistic will likely decrease,
- This would, in turn, lead to a larger p-value, making it less likely to reject the null hypothesis,
- Moreover, a larger standard error would also result in a wider confidence interval, reflecting more uncertainty in the estimate.
Therefore, the correct answer to what is likely to happen when the heteroskedasticity-robust standard error is greater than the regular standard error is:
(c) The p-value will likely become greater.