# What is the appropriate use of the Wald test in statistics and epidemiology?

Can a Wald test be used to test the influence of parameters on distribution of patients between 2 groups? I thought that this test was only intended to test parameters in a construction of a logistic regression or Cox model.

## All Answers (13)

Mitchell Maltenfort· Rothman InstituteAndreas M Brandmaier· Max Planck Institute for Human DevelopmentTodd Mackenzie· Dartmouth CollegeA Wald test is distinguished by the property that it is based on the parameter estimates and their covariances (e.g., standard errors) derived using maximum likelihood or least squares (or other), whereas a likelihood ratio tests is based on the likelihood function evaluated at two points.

Wald tests and likelihood ratio tests typically yield very similar results, especially as the sample size increases.

Thiago Augusto Da Cunha· Universidade Federal do AcreDennis Cox· Rice UniversityI do agree with a previous responder that the (for a given frequentist model) unique Likelihood Ratio Test (LRT) may be better (the LRT is a.k.a. Wilks' Test; though Wilks and Wald share a common first letter for their family name, they seem to have had rather different personalities; Wald contributed to many fields whereas Wilks was mainly a statistician; perhaps that explains the difference in their methodologies; but in defense of Wald, his tests are more generally applicable). I hope that answers your question.

Robert Thomas Brennan· Harvard UniversityRavi Varadhan· Johns Hopkins UniversityAlexandrowicz Rainer· Alpen-Adria-Universität KlagenfurtManoj Bansidas Agravat· University of South Floridahttp://www.ats.ucla.edu/stat/mult_pkg/faq/general/nested_tests.htm

Lawan Adamu· University of MaiduguriAzubuike Victor Chukwuka· National Environmental Standards and Regulations Enforcement Agency (NESREA)Azubuike Victor Chukwuka· National Environmental Standards and Regulations Enforcement Agency (NESREA)a known probability distribution (a chi-square distribution) that is used to test whether the b coefficient for a predictor in a logistic regression model is significantly different from zero. It is analogous to the t-statistic in a regression model in that it is simply

the b coefficient divided by its standard error. The Wald statistic is inaccurate when the regression coefficient (b) is large, because the standard error tends to become

inflated, resulting in the Wald statistic being underestimated.

Rajesh Sharma· Indian Institute of Technology Roparhttp://www.stern.nyu.edu/rengle/LagrangeMultipliersHandbook_of_Econ__II___Engle.pdf

It will give complete information and is quite easy to understand.

Best Regards,

Rajesh Sharma

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