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function

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288503 occurrences (No.**86** in the rank) during 5 years in the PubMed. [cache]

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288503 occurrences (No.

27) We finally present simple equations for the total sample size needed to test each effect of interest in a balanced design, as a function of effect size, power and type I error α. |

PMID:24030312 DOI:10.1177/0962280213502145 |

2015 Statistical methods in medical research |

* Efficient treatment allocation in two-way nested designs. |

- Cluster randomized and multicenter trials sometimes combine two treatments A and B in a factorial design, with conditions such as A, B, A and B, or none. This results in a two-way nested design. The usual issue of sample size and power now arises for various clinically relevant contrast hypotheses. Assuming a fixed total sample size at each level (number of clusters or centers, number of patients), we derive the optimal proportion of the total sample to be allocated to each treatment arm. We consider treatment assignment first at the highest level (cluster randomized trial) and then at the lowest level (multicenter trial). We derive the optimal allocation ratio for various sets of clinically relevant hypotheses. We then evaluate the efficiency of each allocation and show that the popular balanced design is optimal or highly efficient for a range of research questions except for contrasting one treatment arm with all other treatment arms. We finally present simple equations for the total sample size needed to test each effect of interest in a balanced design, as a function of effect size, power and type I error α. All results are illustrated on a cluster-randomized trial on smoking prevention in primary schools and on a multicenter trial on lifestyle improvement in general practices. |

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--- **WordNet** output for **function** ---
=>1.機能, 関数, 役割, 働き, 2.機能する, 作用する, 働く, 役目を果たす, 3.社交的会合, パーティー, 儀式
Overview of noun function
The noun function has 7 senses (first 3 from tagged texts)
1. (43) function, mathematical function, single-valued function, map, mapping -- ((mathematics) a
mathematical relation such that each element of a given set (the domain of the function) is
associated with an element of another set (the range of the function))
2. (24) function, purpose, role, use -- (what something is used for; "the function of an auger is to
bore holes"; "ballet is beautiful but what use is it?")
3. (7) function, office, part, role -- (the actions and activities assigned to or required or
expected of a person or group; "the function of a teacher"; "the government must do its part"; "play
its role")
4. function -- (a relation such that one thing is dependent on another; "height is a function of
age"; "price is a function of supply and demand")
5. function -- (a formal or official social gathering or ceremony; "it was a black-tie function")
6. affair, occasion, social occasion, function, social function -- (a vaguely specified social
event; "the party was quite an affair"; "an occasion arranged to honor the president"; "a seemingly
endless round of social functions")
7. routine, subroutine, subprogram, procedure, function -- (a set sequence of steps, part of larger
computer program)
Overview of verb function
The verb function has 3 senses (first 3 from tagged texts)
1. (9) function, work, operate, go, run -- (perform as expected when applied; "The washing machine
won't go unless it's plugged in"; "Does this old car still run well?"; "This old radio doesn't work
anymore")
2. (3) serve, function -- (serve a purpose, role, or function; "The tree stump serves as a table";
"The female students served as a control group"; "This table would serve very well"; "His freedom
served him well"; "The table functions as a desk")
3. (1) officiate, function -- (perform duties attached to a particular office or place or function;
"His wife officiated as his private secretary")
--- **WordNet** end ---