To build good models, we need to know the appropriate model size. To handle this problem, a variety of information criteria have already been proposed, each with a different background. In this paper, we consider the problem of model selection and investigate the performance of a number of proposed information criteria and whether the assumption to obtain the formulae that fitting errors are normally distributed hold or not in some conditions (different data points and noise levels). The results show that although the application of information criteria prevents over-fitting and under-fitting in most cases, there are cases where we cannot avoid even involving many data points and low noise levels in ideal situations. The results also show that the distribution of the fitting errors is not always normally distributed, although the observational noise is Gaussian, which contradicts an assumption of the information criteria.