I want to calculate the p-value for the beta estimated in Total (orthogonal) least squares regression. Do I need to calculate the standard error of the estimates in a similar manner as done for OLS (with n-2) DF, with the t-stat being beta/SE?
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The short answer is yes. You need to take care to calculate the covariance matrix correctly. In particular, the matrix of weights will contain weights for errors in the dependent and independent variables and the jacobian will include differences with respect to the latent variables (measurement errors). The user's guide to ODRpack95 is a useful reference, in particular section 4B addresses your question. The ODRpack95 routines and user manual can be found on netlib: http://netlib.org/toms/869.zip
