Significant F-test

As for testing other characteristics of a univariate calibration, there are also ways to test for statistical significance of the slope, to see whether unity slope adequately describes the relationship between test results and analyte concentration. These are described in the book Principles and Practice of Spectroscopic Calibration [10]. The Statistics are described there, and are called the Data Significance f test and the Slope Significance t test (or DST and SST tests ). Unless the DST is statistically significant, the SST is meaningless, though. 

Results of iodine determined by radiochemioal neutron activation analysis for control and AD subjects are summarized in this table. Applying statistical treatment to the data sets, mean, SD, confidence interval and significance (F-test, t-test) were calculated. Where a trend is indicated to be significant the p value is <0.05. Mean values cannot be given if we have only few data (parenthetic values) therefore, statistical treatment is not possible (-). n.s. there is no significant difference between the control and AD values. 

The larger variance is placed in the numerator. For example, the F test allows judgment regarding the existence of a significant difference in the precision between two sets of data or between two analysts. The hypothesis assumed is that both variances are indeed alike and a measure of the same a. 

A typical application of this significance test, which is known as a f-test of A to p, is outlined in the following example. 

The value of fexp is then compared with a critical value, f(a, v), which is determined by the chosen significance level, a, the degrees of freedom for the sample, V, and whether the significance test is one-tailed or two-tailed. For paired data, the degrees of freedom is - 1. If fexp is greater than f(a, v), then the null hypothesis is rejected and the alternative hypothesis is accepted. If fexp is less than or equal to f(a, v), then the null hypothesis is retained, and a significant difference has not been demonstrated at the stated significance level. This is known as the paired f-test. 

A statistical analysis allows us to determine whether our results are significantly different from known values, or from values obtained by other analysts, by other methods of analysis, or for other samples. A f-test is used to compare mean values, and an F-test to compare precisions. Comparisons between two sets of data require an initial evaluation of whether the data... 

In this experiment students measure the length of a pestle using a wooden meter stick, a stainless-steel ruler, and a vernier caliper. The data collected in this experiment provide an opportunity to discuss significant figures and sources of error. Statistical analysis includes the Q-test, f-test, and F-test. 

If systematic errors due to the analysts are significantly larger than random errors, then St should be larger than sd. This can be tested statistically using a one-tailed F-test... 

Once a significant difference has been demonstrated by an analysis of variance, a modified version of the f-test, known as Fisher s least significant difference, can be used to determine which analyst or analysts are responsible for the difference. The test statistic for comparing the mean values Xj and X2 is the f-test described in Chapter 4, except that Spool is replaced by the square root of the within-sample variance obtained from an analysis of variance. 

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)... 

Student s f-test. This is a test1 used for small samples its purpose is to compare the mean from a sample with some standard value and to express some level of confidence in the significance of the comparison. It is also used to test the difference between the means of two sets of data x, and x2. 

It should be stressed that there must not be a significant difference between the precisions of the methods. Hence the F-test (Section 4.12) is applied prior to using the -test in equation (5). 

The F-test must be applied to establish that there is no significant difference between the precisions of the two methods. 

Alternatively, the experimental error can be given a particular value for each reaction of the series, or for each temperature, based on statistical evaluation of the respective kinetic experiment. The rate constants are then taken with different weights in further calculations (205,206). Although this procedure seems to be more exact and more profoundly based, it cannot be quite generally recommended. It should first be statistically proven by the F test (204) that the standard errors in fact differ because of the small number of measurements, it can seldom be done on a significant level. In addition, all reactions of the series are a priori of the same importance, and it is always a... 

Of course, Sqo Sq if the difference is significant, the hypothesis of a common point of intersection is to be rejected. Quite rigourously, the F test must not be used to judge this significance, but a semiquantitative comparison may be sufficient when the estimated experimental error 6 is taken into consideration. We can then decide whether the Arrhenius law holds within experimental error by comparing Soo/(mi-21) with 6 and whether the isokinetic relationship holds by comparing So/(ml — i— 2) with 5. ... 

ANOVA) if the standard deviations are indistinguishable, an ANOVA test can be carried out (simple ANOVA, one parameter additivity model) to detect the presence of significant differences in data set means. The interpretation of the F-test is given (the critical F-value for p = 0.05, one-sided test, is calculated using the algorithm from Section 5.1.3). 

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 superscript a,b,c,d,e,f,g,h indicates significance difference from 1,2,3,4,5,6,7,8 groups, respectively. The data is analyzed by one-way ANOVA(F-test) followed by Newmann Keul s Studentized range test... 

The significance of the overall regression can be tested by means of the F-test. The quantity... 

Other authors used a simple 2 standard deviation criteria or an outlier test (F-test) to check for significant differences between within-bottle and between-bottle results (Martin-Esteban et al. 1997 Quevauviller et al. 1995). The degree of homogeneity of elements and compounds in the materials tested in these studies does not seem to be adequately described and, hence, the asigned uncertainties in the mean values may represent only the bias between the analytical methods used in the certification. 

This PROC TTEST runs a two-sample f-test to compare the LDL change-from-baseline means for active drug and placebo. ODS OUTPUT is used to send the p-values to a data set called pvalue and to send the test of equal mean variances to a data set called variance test. The final pvalue DATA step checks the test for unequal variances. If the test for unequal variances is significant at the alpha =. 05 level, then the mean variances are unequal and the unequal variances p-value is kept. If the test for unequal variances is insignificant, then the equal variances p-value is kept. The final pvalue data set contains the Probt variable, which is the p-value you want. 

The f-test in this form can only be applied under the condition that the variances of the two sample subsets, sf and sf, do not differ significantly. This has to be checked by the F-test beforehand. The test statistic f has to be compared to the related quantile of the (-distribution h-a,v where v = mx + n2 — 2. 

In Table 8.1 three different analytical results are listed, the uncertainties of which are estimated in several ways (A) measurement uncertainty only, as sometimes can be done in analytical practice, (B) additionally uncertainty of calibration considered, and (C) uncertainty of sample preparation included (partially nonstatistically estimated). Whereas in cases (A) and (B) the results are judged to be significantly false, in case (C) the difference is statistically not significant. The situation is illustrated in Fig. 8.4a when a comparison is carried out on the basis of the f-test (Eq. 8.6). 

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