Power of a test

Thus, the use of the concept of the Power of a Test allows specification of the number of samples (although it may turn out to be very high), and by virtue of that forms the basis for performing experiments as a sequential series. 

We see that in contrast to the type-1 error, the type-11 error is defined as occurring when accepting the null hypothesis if it is false. The power of a test is defined to be the probability of detecting a true difference and is equal to 1 — probability (type-11 error). The type-11 error and power depend upon the type-1 error, the sample size, the clinically relevant difference (CRD) that we are interested in detecting and the expected variability. Where do these values come from ... 

One can generally say that a and (3 are risks of accepting false hypotheses. Ideally we would prefer a test that minimized both types of errors. Unfortunately, as a decreases, (3 tends to increase, and vice versa. Apart from the terms mentioned we should introduce the new term power of a test. The power of a test is defined as the probability of rejecting H0 when it is false. Symbolically it is power of a test = 1- 3 or probability of making a correct decision. 

Only the two acute tests with D. magna and T. platyurus showed a high correlation coefficient. This confirms the need for using a wide range of different species covering different phyla to increase the power of a test battery to detect toxic... 

Coverage factor Expanded uncertainty Method of least squares Multivariate statistics Null hypothesis Power of a test Probability levels Regression of j on jc... 

The first approach mentioned was chosen in the C-QSAR database [34] using Hansch-type QSAR equations [35], Its advantage is that these models are easy to apply and interpret. However, each model has a limited applicability domain (Figure 12.1) thus only toxicity predictions for compounds belonging to these specific classes are suitable. Unfortunately, no analysis of the predictive power of a test set has been published to date. 

As for continuous data, a power curve can be generated for a number of scenarios for binary outcomes. As seen in Figure 12.2, the power of a test of proportions (for a fixed value of A) is quite sensitive to the particular assumed value of the response rate in the control (for example, placebo) group. 

Effects in males occupationally exposed to carbon disulfide have included teratospermia, decreased sperm motility, hypospermia, and decreased libido (Lancranjan 1972). Studies have stressed the importance of assessing the statistical power of a test for comparing sperm count or morphology (Wyrobek 1983) and the... 

Table I has a list or recipe for designing a good study to evaluate the detection power of a test. The ideal study is prospective and is usually harder, longer and more expensive than the type of evaluation commonly done, but an "inexpensive clinical evaluation may prove more costly in the long run if its erroneous conclusions lead to in roper test utilization or improper patient management.

This error is inversely related to the power of a test power = 1 - beta... 

There is inevitably a chance that any significance test may lead to an erroneous conclusion. If it is decided to reject a null hypothesis at the p = 0.05 level, there must be a 5% chance that it will be rejected when it should be retained. Such an error is called a type I error. Similarly, it is possible to retain a null hypothesis that should be rejected - a type II error. It is natural to consider that a good test procedure should reject an erroneous null hypothesis as often as possible, so (1 - the probability of a type II error) is called the power of a test. (For a given test in specified conditions the power is a calculable munber, not merely a vague concept.) It is clearly possible to reduce the chance of a type I error occurring by... 

There are a finite number of methods described in the sensory literature and a very large number of modifications, many of which are based on a need to try a different method, or belief that a modified method will improve results. In most instances, the modifications are driven by a statistical, not a behavioral approach. Increasing the power of a test is a goal and certainly will have a significant impact on the results, but how much more power can be achieved if one is not using qualified subjects. Confidence in results derives from knowing what subjects were used, the chosen design, and the analysis of the data. 

The probability that a false null hypothesis is rejected is known as the power of a test. That is, the power of a test is (1 - the probability of a Type II error). In the example above it is a function of the mean specified in the alternative hypothesis. It also depends on the sample size, the significance level of the test, and whether the test is one- or two-sided. In some circumstances where two or more tests are available to test the same hypothesis, it may be useful to compare the powers of the tests in order to decide which is most appropriate. 

A third commonly used type of plot is a test for the normality of the residuals. This has almost no serious application in routine analysis, because the number of observations is small (in a statistical context) and the power of such a test would be very low. (The power of a test is the probability of rejecting a false null hypothesis in favour of a specific alternative" ). 

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