F-test for the significance

The F-test for the significance of the factor effects is usually called the test for the significance of the regression. 

The test for the significance of a slope b is formally the same as a t-test (Section 1.5.2) if the confidence interval CI( ) includes zero, b cannot significantly differ from zero, thus ( = 0. If a horizontal line can be fitted between the plotted CL, the same interpretation applies, cf. Figures 2.6a-c. Note that si, corresponds to fx ean). that is, the standard deviation of a mean. In the above example the confidence interval clearly does not include zero this remains so even if a higher confidence level with t(f = 3, p = 0.001) = 12.92 is used. 

In this equation, n denotes the number of observations (i.e., data points), r is the correlation coefficient, i is the standard deviation of the residuals, F is the value of the Fisher test for the significance of the equation, and the P-value denotes the statistical significance level. The values in parenthesis of this QSPR equation indicate the 95% confidence inferval of fhe estimated coefficients. From the statistical parameters it can be derived that this QSPR model is significant at the 99% confidence level. 

Note that the Fisher F-ratio for the significance of lack of fit cannot be tested because there are no degrees of freedom for purely experimental uncertainty. This lack of degrees of freedom for replication is a usual feature of observational data. Any information about lack of fit must be obtained from patterns in the residuals. 

F test for statistical significance of the regression—MS i/MS, F test for lack of fit=MSLf/MSp5... 

To test for the significance of the parameters of a model, we have already used the F test for goodness-of-fit and for lack-of-fit (Section 6.1). In this type of test, a whole set of parameters is investigated. 

Student s test for the significance of the correlation coefficient. Reject Ho if fp- f, for df degrees of freedom and level of significance a... 

A last means for model discrimination, that is, when all methods described earlier are exhausted, is an assessment of the statistical performance of the model. The F test for the model adequacy being a rather severe test, which is only rather exceptionally satisfled, the F value for the global significance of the regression is a good measure for comparison. In addition, the width of the individual confidence intervals of the parameters as well as their correlation coefficients may contribute to the selection of the best model. 

Fisher s least significant difference a modified form of the f-test for comparing several sets of data. (p. 696) flame ionization detector a nearly universal GC detector in which the solutes are combusted in an H2/air flame, producing a measurable current, (p. 570)... 

Interpretation The model can only be improved upon if the residual standard deviation remains significantly larger (F-test ) than the experimental repeatability (standard deviation over many repeat measurements under constant conditions, which usually implies within a short period of time ). Goodness of fit can also be judged by glancing along the horizontal (residual = 0) and looking for systematic curvature. 

The F-test indicates the dependence of die dependent variables widi the independent variables, P level indicates the statistical significance of the correlafion(Table 4). The F-test results for the relation of the amount of ortho methylol phenols with F/P molar ratio and the reaction temperature were low, however, for the OH/P wt %, the F-test result was very significant, indicating a clear dependence of ortho methylol phenols on the OH/P wt %. It can also be seen that P level values for the relation between the amount of ortho methylol phenols and both F/P molar ratio and reaction temperature are above the set P value of 0.05, while for the OH/P wt%, the P value is under the set value. This data indicated that the relations of dependent variables ortho methylol phenols with independent variable OH/P wt% is statistically significant at the 0.05 significmitx level, while tiie relation of dependent variables ortho methylol phenols with F/P molar ratio and reaction temperature are not statistically significant. 

The quantity of RNA extracted from FFPE cell/tissue sections by the heating and nonheating methods, and extracted from fresh cell/tissue embedded in OCT without fixation, was comparable, showing no significant difference for all yields of RNA by Student s f-test, with the exception of one sample, MDA cells fixed in formalin for 24 h (p < 0.05). 

Carmichael, N.G., H. Enzmann, I. Pate, and F. Waechter, 1997. The significance of mouse hver tumor formation for carcinogenic risk assessment results and conclusions from a survey of ten years of testing by the agrochemical industry. Environ. Health Perspect. 105 1196-1203. 

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