Power of the statistical test

Statistical methods are based on specific assumptions. Parametric statistics, those most familiar to the majority of scientists, have more stringent underlying assumptions than do nonparametric statistics. Among the underlying assumptions for many parametric statistical methods (such as the analysis of variance) is that the data are continuous. The nature of the data associated with a variable (as described previously) imparts a value to that data, the value being the power of the statistical tests which can be employed. 

When an observable value was missing, no collocated difference was obtained for that observable. However, to calculate a mean value if one of the observables was missing, the valid collocated measurement was taken as the mean. For a week which contained one or more missing daily samples the derived weekly and the corresponding measured weekly samples were discarded from the comparison only if the precipitation of the missing daily sample(s) accounted for more than 20% of the week s total. This was done to maximize the number of data points and the power of the statistical tests. 

The power of the statistical test is a quantitative measure of the ability to differentiate accurately differences in populations. The usual case in toxicity testing is the comparison of a treatment group to control group. Depending on the expected variability of the data and the confidence level chosen, an enormous sample size or number of replicates may be required to achieve the necessary discrimination. If the sample size or replication is too large, then the experimental design may have to be altered. 

However, by definition, these univariate methods of hypothesis testing are inappropriate for multispecies toxicity tests. As such, these methods are an attempt to understand a multivariate system by looking at one univariate projection after another, attempting to find statistically significant differences. Often the power of the statistical tests is quite low due to the few replicates and the high inherent variance of many of the biotic variables. 

The probability of committing a type I error is the probability of rejecting the null hypothesis when it is true (for example, claiming that the new treatment is superior to placebo when they are equivalent in terms of the outcome). The probability of committing a type I error is called a, which is sometimes referred to as the size of the test. The probability of committing a type II error is the probability of failing to reject the null hypothesis when it is false. This probability is also called beta (P). The quantity (1 - P) is referred to as the power of the statistical test. It is the probability of rejecting the null hypothesis (in favor of the alternate) when the alternate is true. As stated earlier it is desirable to have low error probabilities associated with a test. As we would like a and p to be as low as possible the quanti-... 

To demonstrate that this was not the case, the shaded trays shown in Figure 4A were sampled and for each tray 3x2 vials were assayed for protein content. The protein content results were analyzed with a two-cell analysis-of-variance model including a factor, the left/right positioning, and a covariate, the shelf number. In order to increase the power of the statistical testing, the shelf number was handled as a covariate and not as a factor, based on the assumption that the filling was progressing at a constant rate. 

Why First consider which factors influence the power of a statistical test. Gad (1988) established the basic factors that influence the statistical performance of any... 

The first precise or calculable aspect of experimental design encountered is determining sufficient test and control group sizes to allow one to have an adequate level of confidence in the results of a study (that is, in the ability of the study design with the statistical tests used to detect a true difference, or effect, when it is present). The statistical test contributes a level of power to such a detection. Remember that the power of a statistical test is the probability that a test results in rejection of a hypothesis, H0 say, when some other hypothesis, H, say, is valid. This is termed the power of the test with respect to the (alternative) hypothesis H. ... 

In the design of a toxicity test there is often a compromise between the statistical power of the toxicity test and the practical considerations of personnel and logistics. In order to make these choices in an efficient and informed manner, several parameters are considered ... 

Random variability of the experimental data plays a major role in the power and detection levels of a statistic. The smaller the variance s, the greater the power of any statistical test. The lesser the variability, the smaller the value and the greater the detection level of the statistic. An effective way to determine if the power of a specific statistic is adequate for the researcher is to compute the detection limit S. The detectimi limit simply informs the researcher how sensitive the test is by stating what the difference needs to be between test groups to state that a significant difference exists. 

Why First consider which factors influence the power of a statistical test. Gad [11] established the basic factors that influence the statistical performance of any bioassay in terms of its sensitivity and error rates. Recently, Healy [21] presented a review of the factors that influence the power of a study (the ability to detect a dose-related effect when it actually exists). In brief, the power of a study depends on seven aspects of study design ... 

The availability of this tremendous computing power naturally makes it all the more important that the scientist applies statistical methods rationally and correctly. To limit the length of the book, and to emphasize its practical bias, we have made no attempt to describe in detail the theoretical background of the statistical tests described. But we have tried to make it clear to the practising analyst which tests are appropriate to the types of problem likely to be encountered in the laboratory. There are worked examples in the text, and exercises for the reader at the end of each chapter. Many of these are based on the data provided by research papers published in The Analyst. We are deeply grateful to Mr. Phil Weston, the Editor, for... 

It is standard practice in safety pharmacology to conduct a power analysis (i.e. establishes the sensitivity of the statistical test or the ability of a test to detect an effect, if the effect exists) by using data derived from each nonclinical model in order to assess the minimum detectable difference (MDD) for the parameter to be investigated. With regard to blood pressure changes, an effect size of 14-16 % (Ewart et al. 2013) was calculated as the MDD for haemodynamic measurements... 

Our previous two chapters based on references [1,2] describe how the use of the power concept for a hypothesis test allows us to determine a value for n at which we can state with both a- and / -% certainty that the given data either is or is not consistent with the stated null hypothesis H0. To recap those results briefly, as a lead-in for returning to our main topic [3], we showed that the concept of the power of a statistical hypothesis test allowed us to determine both the a and the j8 probabilities, and that these two known values allowed us to then determine, for every n, what was otherwise a floating quantity, D. 

Tarone s trend test is most powerful at detecting dose-related trends when tumor onset hazard functions are proportional to each other. For more power against other dose related group differences, weighted versions of the statistic are also available see Breslow (1984) or Crowley and Breslow (1984) for details. 

Minimizes both type I (false positive) and type II (false negative) error rates, thereby increasing power of the test statistic to be employed while decreasing inconsistent significant effects. 

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