<P> With indefinitely large samples, limiting results like the central limit theorem describe the sample statistic's limiting distribution, if one exists . Limiting results are not statements about finite samples, and indeed are irrelevant to finite samples . However, the asymptotic theory of limiting distributions is often invoked for work with finite samples . For example, limiting results are often invoked to justify the generalized method of moments and the use of generalized estimating equations, which are popular in econometrics and biostatistics . The magnitude of the difference between the limiting distribution and the true distribution (formally, the' error' of the approximation) can be assessed using simulation . The heuristic application of limiting results to finite samples is common practice in many applications, especially with low - dimensional models with log - concave likelihoods (such as with one - parameter exponential families). </P> <P> For a given dataset that was produced by a randomization design, the randomization distribution of a statistic (under the null - hypothesis) is defined by evaluating the test statistic for all of the plans that could have been generated by the randomization design . In frequentist inference, randomization allows inferences to be based on the randomization distribution rather than a subjective model, and this is important especially in survey sampling and design of experiments . Statistical inference from randomized studies is also more straightforward than many other situations . In Bayesian inference, randomization is also of importance: in survey sampling, use of sampling without replacement ensures the exchangeability of the sample with the population; in randomized experiments, randomization warrants a missing at random assumption for covariate information . </P> <P> Objective randomization allows properly inductive procedures . Many statisticians prefer randomization - based analysis of data that was generated by well - defined randomization procedures . (However, it is true that in fields of science with developed theoretical knowledge and experimental control, randomized experiments may increase the costs of experimentation without improving the quality of inferences .) Similarly, results from randomized experiments are recommended by leading statistical authorities as allowing inferences with greater reliability than do observational studies of the same phenomena . However, a good observational study may be better than a bad randomized experiment . </P> <P> The statistical analysis of a randomized experiment may be based on the randomization scheme stated in the experimental protocol and does not need a subjective model . </P>

Descriptive statistics is a type of statistics that is used to make predictions about a larger group