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== Techniques ==

== Techniques ==

[[File:Stratified sampling.PNG|thumb|Simple random sampling after stratification step]]

[[File:Simple_random_sampling_after_stratification_step.png|thumb|Simple random sampling after stratification step]]

Block randomization is commonly used in the experiment with a relatively big sampling size to avoid the imbalance allocation of samples with important characteristics. In certain fields with strict requests of randomization such as clinical trials, the allocation would be predictable when there is no blinding process for conductors and the block size is limited. The blocks permuted randomization in strata could possibly cause an imbalance of samples among strata as the number of strata increases and the sample size is limited, For instance, there is a possibility that no sample is found meeting the characteristic of certain strata.

Block randomization is commonly used in the experiment with a relatively big sampling size to avoid the imbalance allocation of samples with important characteristics. In certain fields with strict requests of randomization such as clinical trials, the allocation would be predictable when there is no blinding process for conductors and the block size is limited. The blocks permuted randomization in strata could possibly cause an imbalance of samples among strata as the number of strata increases and the sample size is limited, For instance, there is a possibility that no sample is found meeting the characteristic of certain strata.

In order to guarantee the similarity of each treatment group, the "minimization" method attempts are made, which is more direct than random permuted block within strats. In the minimization method, samples in each stratum are assigned to treatment groups based on the sum of samples in each treatment group, which makes the number of subjects keep balance among the group.<ref name=":0" /> If the sums for multiple treatment groups are the same, simple randomization would be conducted to assign the treatment. In practice, the minimization method needs to follow a daily record of treatment assignments by prognostic factors, which can be done effectively by using a set of index cards to record.  The minimization method effectively avoids imbalance among groups but involves less random process than block randomization because the random process is only conducted when the treatment sums are the same. A feasible solution is to apply an additional random list which makes the treatment groups with a smaller sum of marginal totals possess a higher chance (e.g.¾) while other treatments have a lower chance(e.g.¼ ).<ref name=":1">{{Cite journal|last=Pocock|first=S. J.|date=March 1979|title=Allocation of Patients to Treatment in Clinical Trials|journal=Biometrics|volume=35|issue=1|pages=183–197|doi=10.2307/2529944|jstor=2529944|pmid=497334|issn=0006-341X}}</ref>

In order to guarantee the similarity of each treatment group, the "minimization" method attempts are made, which is more direct than random permuted block within strats. In the minimization method, samples in each stratum are assigned to treatment groups based on the sum of samples in each treatment group, which makes the number of subjects keep balance among the group.<ref name=":0" /> If the sums for multiple treatment groups are the same, simple randomization would be conducted to assign the treatment. In practice, the minimization method needs to follow a daily record of treatment assignments by prognostic factors, which can be done effectively by using a set of index cards to record.  The minimization method effectively avoids imbalance among groups but involves less random process than block randomization because the random process is only conducted when the treatment sums are the same. A feasible solution is to apply an additional random list which makes the treatment groups with a smaller sum of marginal totals possess a higher chance (e.g.¾) while other treatments have a lower chance(e.g.¼ ).<ref name=":1">{{Cite journal|last=Pocock|first=S. J.|date=March 1979|title=Allocation of Patients to Treatment in Clinical Trials|journal=Biometrics|volume=35|issue=1|pages=183–197|doi=10.2307/2529944|jstor=2529944|pmid=497334|issn=0006-341X}}</ref>

== Application ==

== Application ==