F-values calculated

From a knowledge of various values of P it is possible to calculate F values for specific polymers and G values for specific gases if the G value for one of the gases, usually nitrogen, is taken as unity. These values are generally found to be accurate within a factor of 2 for gases but urtreliable with water vapour. Some... 

Interpretation Because the calculated F-value (0.36108/0.00246 = 148) is much larger than the tabulated critical one (2.04, p = 0.05), the group means cannot derive from the same population. 

From the intensity, the value for the observed F is obtained. This is substituted into the electron density equation for locating the atoms that determine the structure of the protein. Through an iterative process, the observed and calculated F values are compared to determine the goodness of fit and hence the quality of the structure. 

As an example, a calculated t value of 4 with one degree of freedom (see Equation 6.9) is significant at the 84.4% level of confidence (a = 0.156). Similarly, a calculated F value of 16 with one degree of freedom in the numerator and one degree of freedom in the denominator (see Equation 6.38) is also significant at the 84.4% level of confidence. 

Since the stability data from individual lots are pooled, these data are examined for validity by the F test. The mean square of the regression coefficient (slope) is divided by the mean square of the deviation within lots, and similarly, the adjusted mean (y intercept) is divided by the common mean square to give the respective F ratios. The latter values then are compared with the critical 5% F values. When the calculated F values are smaller than the critical F values, the data may be combined and the pooled data analyzed. 

A set of aliphatic compounds was used for the correlation between the activation energy and EHomo- The dataset contained acetamide, methanol, and ethanol. The regression coefficient (r2) for this relationship was 0.998. The probability of getting a correlation was 0.995 for a sample size of five. The significance of F(13) = 2610 can be ascertained by consulting the F values in distribution tables. The F(1/3)oco 005 distribution value is found to be 55.6. When the calculated F value and F distribution values are compared, it can... 

Then there is no evidence against H0 if the experimental (calculated) F-value is less than a critical F-value obtained from statistical tables ... 

Table 2 depicts the analysis of variance for % yield and productivity. Both responses present a high correlation coefficient, and the model can be considered statistically significant according to the F-test with 99% confidence. As a practical rule, a model has statistical significance if the calculated F value is at least three to five times greater than the listed value (9). 

This calculated F value is then compared to the critical value, Fa(1) VlV2, where Vj = regression DF = 1, and v2 = residual DF = n — 2. The residual mean square is often written as sfx, a representation denoting that it is the variance of Y after taking into account the dependence of Y on X. The square root of this quantity — that is, Syj—is called the standard error of estimate (occasionally termed the standard error of the regression). The ANOVA calculations are summarized in Table 2.2. 

The calculated f values for the unpulsed pattern at 265 nm and the difference pattern at 405 nm are given in Table II. The crosstalk for the first pattern was higher in fact an f value should have been included. The higher values are due to the effect of the fluorescent film. We have no way of determining whether a 10 ym line centered on a channel would give the same values with our system as the values given by the manufacturer... 

If the null hypothesis is retained, i.e., there is no statistical significant difference between the two variances, then the calculated F value will approach 1. Some critical values of F can be found in Table 2.2a and Table 2.2b. The test can be used in two ways to test for a significant difference in the variances of the two samples or to test whether the variance is significantly higher or lower for either of the two data sets, hence two tables are shown, one for the one-tailed test and one for the two-tailed test. 

If the calculated F value is higher than the tabled F at the chosen level of significance (often 0.05), the use of the more detailed model is supported. Another commonly used parameter is the Akaike s Information Criterion (AIC) value. It is calculated for each model, and the model producing the lowest value (most negative value) is considered the better model. The AIC value is calculated using the number of data (n), WSS, and the number of parameters (m). 

Table 11. Calculated f values for different types of molecules...

The calculated F value is compared vith the critical value Fcnt provided the same degrees of freedom. Since the F test compares the model explained variance with the residual variance, high values of the F-ratio test should indicate reliable models. 

The theoretical two tailed F value for F4 4 is 9.605, which was found to be greater than the calculated F value indicating that both the methods do not differ in their precision, when the analysis was carried out on the same day. The value of standard deviation in both the techniques is relatively small, which indicates that the stability of both the instruments is good at the time of analysis on the same day. 

Additionally, in order to accurately calculate F values from exchange data we need to account for the salt effect on the oxygen and hydrogen equilibrium isotope fractionation between minerals and fluids, based on results reported by Horita et al. (1993a,b 1995) and Chacko et al. (this volume). These results indicate the mineral - salt fractionation may be 0.6 to 1 per mil smaller than the mineral-pure water fractionation at 300°C for a 5 m NaCl solution (Horita et al. 1995). This type of data will play an important role in the ultimate accuracy of the rate constants calculated from partial exchange experiments involving minerals and salt solutions. 

X have been measured for the adsorbent in question, and when the adsorbent is not too active (a < 0.8), relatively accurate, predictions can be expected. It is assumed, of course, that secondary adsorption effects involving large values of Ag s or are either absent or incorporated into the experimental value of 5 . When one or more of the above conditions is not met, however, the accuracy of calculated /f values ranges from fair to semiquantitative ( 0.2-0.5 log units). A few examples will illustrate the calculation of X values from data provided in this book. 

If no experimental results are available for particular solute/solvent mixtures UNIFAC provides a method of calculating f values. 

When the uncertainty in the parameter values becomes too large, the analyst should consider reducing the model. The correlation matrix between parameters can be useful in selecting the parameters that can be removed to make the model smaller. There are statistical criteria that can be used to select the better model. These include the Akaike Information Criterion (AIC) value and the F-test. The AIC value is calculated using the WSS, the number of parameters in the model, and the number of data points. The model with the lower AIC values is usually selected as the better model. The statistical F-test involves the calculation of an F value from the WSS and degrees of freedom from two analyses. The calculated F value is compared with the tabled values and a decision can be made whether the more complex model provides a significant improvement in the fit to the data. The analyst using a combination of subjective and objective criteria can make an educated decision about the best model. 

The calculated f-value is lower than the tabulated one, that is, the test is not significant and the variances differ only randomly. 

For the tabulated critical F value, we obtain f (0.95 1, 1) = 161 (cf. Table A.4). The F test for lack-of-fit is not significant, since the calculated F value is smaller than the critical value. The significance level is only 0.779, as the p value shows in Table 6.3. 

Since the gas nodes on the interface are fixed to move with the Uquid nodes, this liquid velocity is used as the gas phase boundary crmdition q = —q) to calculate , value on the gas side of the interface. 

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