Tests of significance

In the next several sections, the theoretical distributions and tests of significance will be examined beginning with Student s distribution or t test. If the data contained only random (or chance) errors, the cumulative estimates x and 5- would gradually approach the limits p and cr. The distribution of results would be normally distributed with mean p and standard deviation cr. Were the true mean of the infinite population known, it would also have some symmetrical type of distribution centered around p. However, it would be expected that the dispersion or spread of this dispersion about the mean would depend on the sample size. 

In analysis of variance, the variance due to each source of variation is systematically isolated. A test of significance, the E-test, is then applied to establish roughly how seriously one must regard each source of variation. The interested reader is urged to consult books on statistics14 for discussions of this valuable statistical method. 

For work of the highest precision, it is highly advisable to carry through an analysis of variance together with suitable tests of significance, not only to establish what the precision is, but also to uncover individual sources of error so that they can be made less serious. How this is done for instrumental and manipulative errors has been demonstrated in this chapter. 

Analytical method validation, which must be performed by every regulated laboratory, deals with the testing of significant method characteristics to ensure that under... 

A test of significance is designed to assess whether the difference between two results is significant or can be accounted for merely by random variations. 

A comparison of the imprecision of two methods may assist in the choice of one for routine use. Statistical comparison of values for the standard deviation using the F test (Procedure 1.2) may be used to compare not only different methods but also the results from different analysts or laboratories. Some caution has to be exercised in the interpretation of statistical data and particularly in such tests of significance. Although some statistical tests are outlined in this book, anyone intending to use them is strongly recommended to read an appropriate text on the subject. 

In other analyses, such as the analysis of attractiveness, multiple regression analysis did not involve pseudo-replication and could be used as a test of significance in its own right. 

When the statistieally sophisticated psychologists realized what I was doing, they had a field day pointing out my failings unjustified assumptions, violations of statistical theory and other mathematical crimes. They talked about ordinal scales versus ratio scales and scolded me for not using analysis of variance instead of Chi-square and Student s T tests of significance. 

The test of significance that we used as an illustration utilised only the sign of the differences -whether it was negative or positive. Generally, the actual differences are used. If we think about the differences themselves then if there were no difference between the treatments we would expect the average difference to be zero. This defines the null hypothesis. The sample mean of the differences divided by its standard error, is the test statistic and a large value of this statistic would indicate that there is likely to be a difference between the treatments. 

There is a fair amount of language that we wrap around this process. We talk in terms of a test of significance. If p < 0.05, we declare statistical significance, and reject the null hypothesis at the 5 per cent level. We call 5 per cent the significance level, it is the level at which we declare statistical significance. If p > 0.05, then we say we have a non-significant difference and we are unable to reject the null hypothesis at the 5 per cent level. 

Sign test a test of significance based on the signs of certain observations and not their magnitude. 

It is particularly important that thought be given to the calculation of the error term in tests of significance. An error term based on repeated measures of a single sensor prototype will not be of any use in establishing the performance of prototypes in general. The sample size should be adequate to support the test of the null hypothesis, i.e. the test is of sufficient power—usually the sample size needs to be bigger than two or three. 

The experimenter should therefore perform the number of experiments indicated by Eq. (1.82) and make a test of significance at the level a. 

Sometimes the GOF test is called test of significance of the regression . 

The level of significance at which the null hypothesis of "no effect" will be rejected. The 5% level is proposed for screening purposes. For this kind of examination, a one-sided test of significance, directed solely at identifying adverse exposure effects, is appropriate. (In making such a test of significance, it is assumed that the chemical-test participants have not benefited from their exposure.)... 

Group means are calculated, and the significance of differences between groups is assessed by analysis of variance and appropriate tests of significance. 

For each parameter, means and standard error calculated, an analysis of variance is performed and the appropriate tests of significance are applied. The mean values of each parameter of the treated groups are compared with the values of the vehicle control group. It is important to compare the results with reference to their use for the rat strain commonly-used in the Laboratory. For many studies it may be advisable to include groups treated with reference compounds of established endocrine activity. 

The usual procedure for radio-immunoassay data is calculation by a computer programmme, from standard curves of the hormone to be measured, it is important to have a sufficient number of animals per group, to be able to perform analysis of variance and statistical evaluation by tests of significance... 

There are a large number of statistical distributions which have for the most part been derived from the normal frequency distribution. The principles underlying only three of these distributions will be presented here. These distributions form the basis for the most frequently used statistical tests of significance. 

Table for t Test of Significance between Two Sample Means ( i and X2)... 

The proper functioning of analytical methods should be verified on the new system. This covers testing of significant method characteristics, for example, limit of detection, limit of quantification, selectivity, and linearity. If the method has not been validated or if its scope did not cover the new instrument, the method should either be newly validated or revalidated. 

It was evident that to apply tests of significance conveniently and economically the experiments had to be planned in appropriate forms. It is considered that the methods outlined should be as much a standard tool of the industrial experimenter as a chemical balance is of the laboratory experimenter. In carrying out an industrial experiment the choice is not between using a statistical design with the application of the appropriate tests of significance or the ordinary methods the choice is between correct or incorrect methods. Even the simplest experiment requires an estimate of the significance of its results. 

The present monograph is intended to provide for those who carry out investigational work a guide to modern statistical methods, both the use of tests of significance to attain reliability in deductions from experimental data and the use of statistical design to attain the maximum precision with the minimum expenditure. 

Fisher s approach to experimentation differs in two fundamental aspects from the classical one-vaiiable-at-a-time ideology. Firstly, he stresses the importance of obtaining an accurate estimate of the magnitude of the error variation, rather than its minimisation. The accurate estimate of the error variation is necessary in order to apply an exact test of significance. 

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