Choosing and using statistical tests

This chapter outlines the philosophy of hypothesis-testing statistics, indicates the steps to be taken when choosing a test, and discusses features and assumptions of some important tests. For details of the mechanics of tests, consult appropriate texts (e.g. Miller and Miller, 2000). Most tests are now available in statistical packages for computers (see p. 315). 

Decide what it is you wish to test (create a null hypothesis and its alternative). 

Determine whether your data fit a standard distribution pattern. 

Hjrpothesis-testing statistics are used to compare the properties of samples either with other samples or with some theory about them. For instance, you may be interested in whether two samples can be regarded as having different means, whether the concentration of a pesticide in a soil sample can be regarded as randomly distributed, or whether soil organic matter is linearly related to pesticide recovery. 

You can t use statistics to prove any hypothesis, but they can be used to assess how likely it is to be wrong. 

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It is not the intention to give a detailed assessment of how to choose the correct statistical test and apply it for a given clinical study. (For this the reader is referred to Chapter 8.) Rather, some general guidelines to the use of statistical analysis will be provided. 

At any rate the practitioner must follow a two-step process in setting up a calibration graph 1. Stabilize the response variance across the range needed and 2. choose an appropriate calculation function model. The response data is stabilized currently in two ways, either by weighting on a level-by-level basis or by applying some transformation function in the same manner to all the response values. The model chosen must approximate the data. It can be that a simple linear (as shown by a statistical test) function can serve this purpose adequately. The use of Mitchell s multiple linear function has been successfully... 

The choice between the baseline and alternative conditions is easy if the mean concentration significantly differs from the action level. But how can we determine, which of the two conditions is correct in a situation when a sample mean concentration approximates the action level This can be achieved by the application of hypothesis testing, a statistical testing technique that enables us to choose between the baseline condition and the alternative condition. Using this technique, the team defines a baseline condition that is presumed to be true, unless proven otherwise, and calls it the null hypothesis (H0). An alternative hypothesis (Ha) then assumes the alternative condition. These hypotheses can be expressed as the following equations ... 

An excellent review on outlier treatment is given by Beckman and Cook [42], and by Miller [43]. Some scientists do prefer the use of robust statistics instead of outlier detection and rejection [45]. Whether one prefers the use of statistical tests or chooses to use robust statistics, one should be critical of the dataset. Data points should not be eliminated on the basis of statistical significance only. A cause analysis should be performed before discarding outliers. 

The common approach to detection decisions in radioanalytical chemistry is based on statistical hypothesis testing. In a hypothesis test, one formulates two mutually exclusive hypotheses, called the null hypothesis and the alternative hypothesis, and uses the data to choose between them. The null hypothesis is presumed to be true unless there is strong evidence to the contrary. When such evidence is present, the null hypothesis is rejected and the alternative hypothesis is accepted. 

In practice, the sample size calculation is not done by hand, but by computer programs (such as the free G Power ), which lets you choose a statistical test, asks for the necessary inputs (i.e., a, P, variance, and effect size), and gives you the minimum required sample size. They can also be used to determine the power of your test given the sample size, a, S, and effect size. Because of all these unknowns, it is a good idea to consult a biostatistician on these matters if possible. 

ABSTRACT There are many properties correlated with maintenance costs. Due to minimize the maintenance costs we should recognize them and assess the level of influence and choose them of which the mitigation is the most cost effective. One of the most important property is lifetime which is assessed using statistical methods during accelerated tests. And may be improved based on real data. The parametric and non-parametric statistics could be applied to assessment the lifetime of aviation items. In the paper their advantages and disadvantages were recognized. 

A general method for testing the suitability of a particular ANN architecture with respect to the approximation capability is cross-validation, more precisely k-fold cross-validation (k > 2). This can be equally well used to test the suitability of any particular choice of any ANN property that has to be selected from various possibilities, e.g., a particular choice of the activation function. Cross-validation is actually a general method for choosing parameters and other properties of statistical models (Hand, 1997 Berthold and Hand, 2002). In the context of ANNs trained with catalytic data, the method proceeds as follows ... 

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