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. Author manuscript; available in PMC: 2010 Sep 27.
Published in final edited form as: J Am Stat Assoc. 2010 Jun 1;105(490):612–620. doi: 10.1198/jasa.2010.tm09386

Table 2.

Type I error rate for small sample sizes and violation of model assumptions (%)

Analysis method n = 50 n = 100 Misspecified P(X|Z)
T1 empirical 4.7 4.4 5.2
T1 asymptotic 6.0 4.8 4.9
T2 empirical 5.1 4.7 5.2
T2 asymptotic 7.0 5.6 5.3
T3 empirical 5.6 5.0 5.0
T3 asymptotic 4.0 4.1 5.2
X linear 5.3 4.8 5.1
X categorical 4.2 4.5 5.2
Isotonic 7.1 7.0 7.1
Splines 5.2 4.6 5.2