Table 2 

Summary of significance tests for combining different estimates from m imputed datasets after MI 

Estimate 
F 
Test statistic 
Degrees of freedom (df) 
Relative increase in variance (r) 


A) Scalar 
F_{1, v} 
, H_{0}: Q = Q_{0} 
v = (m  1)(1 + r^{1})^{2} 



B) Multivariate 
H_{0}:Q = Q_{0}, k = number of parameters 
where a = k(m  1) 



C) χ^{2 }statistics w_{1},..., w_{m} 
k = df associated with χ^{2 }tests 



D) Likelihood Ratio χ^{2 }statistics w_{L1},..., w_{Lm} 
k = number of parameters in fitted model 
where a = k(m  1) 



KEY: F = value from the Fdistribution, which the test statistic is compared to. = average of the m imputed data estimates. = within imputation variance. B = between imputation variance. T = total variance for the combined MI estimate. w_{j}, j = 1,..., m = χ^{2 }statistics associated with testing the null hypothesis H_{o }: Q = Q_{o }on each imputed dataset, such that the significance level for the j^{th }imputed dataset is P{ > w_{j}}, where is the χ^{2 }value with k degrees of freedom (Rubin 1987). = average of the repeated χ^{2 }statistics. = average of the m likelihood ratio statistics, w_{L1},..., w_{Lm}, evaluated using the average MI parameter estimates and the average of the estimates from a model fitted subject to the null hypothesis. 

Marshall et al. BMC Medical Research Methodology 2009 9:57 doi:10.1186/14712288957 