Statistical design power

The triangle test is a measure of odor discrimination. The candidate is presented, in random order, with three blotters, of which two are identical and the third is slightly different. The task is to indicate the odd blotter. This test can be designed to range from easy to very difficult. It is statistically most powerful if the difference between the paired blotters is such that the odd one is correctly identified by about 50% of the candidates. 

There are four primary methods. First, there is the statistically designed experiment, in which experiments are set up in a (normally regular) matrix to estimate the coefficients in a mathematical model that predicts responses within the limits of formulation or operating conditions being studied. This is generally the most powerful method, provided the experimentation zone has been correctly identified, and is the subject of most of this article. 

It is customary to design studies to have a power of at least 80%, and offen 90% or 95% power will be used. For any given power, the larger a study, the smaller the difference it is capable of detecting. A simple equation shows the relationship between sample size, the level of statistical significance, power and the difference between the two treatments ... 

Reduction refers to efforts to minimise the number of animals used during an experiment, as well as the prevention of unnecessary replication of previous experiments. To satisfy this requirement, statistical design of experimentation (SDE) methodology and other mathematical calculations of statistical power are employed to determine the minimum number of animals that must be used to get a statistically significant experimental result. 

Improvement in the statistical design of large-scale clinical trials such that there are few confounding variables and enough power to detect a statistically significant difference between test populations. 

In earlier detailed studies on phenol we reported on a statistically designed experiments where we investigated eight major variables, whose ranges are indicated in Table 4, for the oxidation and eventual mineralization of 50 ppm phenol. Most of the variables had high, low, and middle values in the case of the uv lamp power, the lamp was either on or off. Carbonate was either 0 or 10 mM, and was non-zero only when the pH was high at the lower pH s of 2 and 5 carbonate would be converted to CO2, and purged from the solution by the gas... 

In this paper, we discuss studies based on comparison with background measurements that may have a skew distribution. We discuss below the design of such a study. The design is intended to insure that the model for the comparison is valid and that the amount of skewness is minimized. Subsequently, we present a statistical method for the comparison of the background measurements with the largest of the measurements from the suspected region. This method, which is based on the use of power transformations to achieve normality, is original in that it takes into account estimation of the transformation from the data. 

These designs are extremely powerful (from a statistical point of view) if we do not have a mathematical model of the system under investigation and we simply wish to establish the effect of each of these three independent variables (or their interaction) on the measured response variables. 

The number of subjects needed so that a study is likely to have an acceptable statistical power depends on a number of factors, including analytical parameters (precision, etc.), subject selection and control, and protocol design (cross-over, parallel). 

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