Hi! I am analyzing a two-level dataset, including student level and school level. The coefficient of one interaction variable was not significant in the HLM model but significant at .05 level in the OLS model. I found that the standard error of this variable from HLM is similar to the one from OLS. However, its coefficient in the OLS model was about 5 times larger than in the HLM.

Some statistical papers claimed that comparing to OLS, HLM can give the more accurate standard errors. It seems that in this condition HLM does not have obvious advantages over OLS. So, I'm a little confused that which method I should employ in my study.

Would you please give me some advice?