Rubin (1987)’s combination formula for variance estimation in multiple imputation (MI) requires a imputation method to be Bayesian-proper. However, many census bureau have heavily relied on non-Bayesian imputations. Bjørnstad (2007) suggested an inflated factor (k1) in Rubin (1987)’s combination formula for non-Bayesian imputations. This paper aimed to verify the theoretical derivation of Bjørnstad (2007) in computer simulation. Within Bjørnstad (2007)’s pre-assumed environment, the inflated factor, k1, closely approached the simulated true value, E(k), irrespective of sample size and missing rate. With California schools’ data, confidence intervals using k1 also achieved a desired coverage, (1-a)%, across varying sample size and missing rate, except in case of MNAR because of biased imputation.