Which statement about the Wald statistic is accurate?

Which statement about the Wald statistic is accurate?

• A. It is inaccurate when the regression coefficient is large due to inflated standard errors.
• B. It is exact for all sample sizes.
• C. It does not rely on standard errors.
• D. It is only applicable to logistic regression.

Answer: (A)

The Wald statistic tests a regression coefficient by standardizing its estimate with its standard error and comparing that to what we'd expect under a normal (or chi-square) distribution. This relies on the estimated coefficient being approximately normally distributed and the standard error being accurately estimated. As sample size grows, this normal approximation becomes more reliable. However, when the regression coefficient is large, the sampling distribution can deviate from normal, and the standard error can become unstable or inflated, especially with sparse data or separation. That instability makes the Wald statistic’s p-values less trustworthy in finite samples, so its accuracy suffers in those situations. This is why that statement is correct. The other options aren’t accurate because the Wald test is not exact for all sample sizes, it does rely on standard errors, and it isn’t restricted to logistic regression—it’s used in linear regression and other generalized linear models as well.

The Wald statistic tests a regression coefficient by standardizing its estimate with its standard error and comparing that to what we'd expect under a normal (or chi-square) distribution. This relies on the estimated coefficient being approximately normally distributed and the standard error being accurately estimated. As sample size grows, this normal approximation becomes more reliable. However, when the regression coefficient is large, the sampling distribution can deviate from normal, and the standard error can become unstable or inflated, especially with sparse data or separation. That instability makes the Wald statistic’s p-values less trustworthy in finite samples, so its accuracy suffers in those situations. This is why that statement is correct.

The other options aren’t accurate because the Wald test is not exact for all sample sizes, it does rely on standard errors, and it isn’t restricted to logistic regression—it’s used in linear regression and other generalized linear models as well.