Sample size design

Increase the sample size Design test to detect larger differences Use a more powerful significance test Increase the significance level Use one-tailed decision rule Greater resources required Less useful conclusions Stronger assumptions required Higher statistical false-p>ositive rate Blind to effects in the op>posite direction... 

Since the t distribution relies on the sample standard deviation. s, the resultant distribution will differ according to the sample size n. To designate this difference, the respec tive distributions are classified according to what are called the degrees of freedom and abbreviated as df. In simple problems, the df are just the sample size minus I. In more complicated applications the df can be different. In general, degrees of freedom are the number of quantities minus the number of constraints. For example, four numbers in a square which must have row and column sums equal to zero have only one df, i.e., four numbers minus three constraints (the fourth constraint is redundant). 

The maximum sample size is limited only by the design of the sample chamber. Typically, samples up to several cm in diameter can be accommodated. A diameter of a few mm is generally the lower limit because high-energy ion beams focused through standard beam optics are on the order of a few mm in diameter however, microbeam setups permit the use of samples an order of magnitude smaller. 

FIGURE 11.23 Power analysis.The desired difference is >2 standard deviation units (X, - / = 8). The sample distribution in panel a is wide and only 67% of the distribution values are > 8. Therefore, with an experimental design that yields the sample distribution shown in panel a will have a power of 67% to attain the desired endpoint. In contrast, the sample distribution shown in panel b is much less broad and 97% of the area under the distribution curve is >8. Therefore, an experimental design yielding the sample distribution shown in panel B will gave a much higher power (97%) to attain the desired end point. One way to decrease the broadness of sample distributions is to increase the sample size. 

In pharmaceutical and medical device development, clinical trials are classified into four main phases designated with Roman numerals 1,11, III and lY The various phases of development trials differ in purpose, length and number of subjects involved. Phase I trials are conducted to determine safe dose levels of a medication, treatment or product (National Institutes of Health, 2002). The main purpose is often to determine an acceptable single dosage - how much can be given without causing serious side-effects. Phase I trials will also involve studies of metabolism and bioavailabity (Pocock, 1983). The sample size of a Phase 1 clinical trial is usually small, ranging from 10-80 subjects (National Institutes of Health, 2002 Pocock, 1983). 

Similarly, the number and types of tests completed will influence the cost in ways that can be very complex. Recently, the author was involved in designing a proof-of-principle study intended to assess the ability of a dietary supplement to enhance weight loss among subjects instructed to follow a reduced energy diet. Sample size calculations were run for two scenarios, the first using change in body weight as the primary outcome variable, the... 

Power Analysis for ANOVA Designs can be used to calculate sample size for one and two-way factorial designs with fixed effects http //evall.crc.uiuc.e du/ fp o wer. html/... 

Extensive testing was also carried out to assess future hazards for human habitation and residential use of the area. This testing was carried out in an extensive program funded by EPA In 1980-81 after remedial drainage construction work at the Canal was complete (O. All of the survey design and technical laboratory problems described above were encountered in this program. Despite extensive efforts to meet requirements for sample size and distribution, to provide for adequate control sampling away from the Canal area, and... 

To discuss the development of CRMs for the emerging use of microanalytical techniques, one has to be concerned chiefly with the degree of homogeneity of the components in the material at the designated sample size. Basic indications for the homogeneity properties of a CRM for microanalytical methods and the assessment of these properties can be derived from the general requirements ... 

LSMBSs are designed so that the types of data to be collected meet particular objectives regarding how the data will be used. For example, the number of exemplars collected in the LSMBS will depend on the use planned for the study results. Thus, if the levels of plasticizer in packaged foods will be determined to address an acute (i.e., short-term) dietary exposure and risk concern, the sample size (i.e., number of food packages to be collected) must be adequate to support the higher percentiles... 

The experimental design used was nested plots. Main plots had a total area of 100 m2 and were rectangular plots. The criterion used to determine sample size for each stratum was an estimation of AGB of trees with a diameter at breast height (dbh) >10 cm during pre-sampling (90% probability and 20% mean standard error). 

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