For example, as we note in

Unit 9, for largish cell frequencies the distribution of Pearson's X

^{2} statistic approximates to a Chi-squared distribution - and exact analytical methods can cope with the small-sample situation perfectly adequately.

However some estimators, most especially those which are complex multi-variate models, or where observations are not independent, or which include probability density parameter estimates, adopt their large sample properties extremely slowly indeed.

For many popularly used statistics, even for known populations, there is a gap between exact-analytical and large-sample approximations. Until quite recently this gap was addressed using very approximate approximations, progressively it being filled by computer-intensive methods: exact-analytical, improved large sample approximations, and Monte Carlo simulation.