Standard errors p-values

Term Estimated coefficient Standard error p-value... 

Model Categories Coefficient Standard error P value k AIC SD (DF)... 

If you are plotting average values for several replicates and if you have the necessary statistical knowledge, you can calculate the standard error (p. 268), or the 95% confidence limits (p. 278) for each mean value and show these on... 

Houben [256] has compared the determination of flame-retardant elements Br, P, S, K, Cl and F in polycarbonate using commercial (X40 and UniQuant ) software. For the X40 method, a calibration line for each element in PC or PC/ABS blends was mapped for the conversion of intensities to concentrations. With the universal UniQuant method, sensitivity factors (ks) were calibrated with pure standards. The X40 method turned out to be more reliable than UniQuant for the determination of FRs in PC and PC/ABS blends, even in the case of calibration of k values with PC standards. Standard errors of 5 % were achieved for Br, P, S and K, and 20% for Cl and F the latter element could not be determined by means of UniQuant (Table 8.44). GFR PC cannot be quantified with these two methods, because of the heterogeneous nature of the composites. Other difficult matrices for XRF analysis are PBT, PS and PP compounds containing both BFRs and Sb203 (10-30wt %) due to self-absorption of Sb and interelement effects. 

You may be surprised that for our example data from Miller and Miller ([2], p. 106), the correlation coefficient calculated using any of these methods of computation for the r-value is 0.99887956534852. When we evaluate the correlation computation we see that given a relatively equivalent prediction error represented as (X - X), J2 (X - X), or SEP, the standard deviation of the data set (X) determines the magnitude of the correlation coefficient. This is illustrated using Graphics 59-la and 59-lb. These graphics allow the correlation coefficient to be displayed for any specified Standard error of prediction, also occasionally denoted as the standard error of estimate (SEE). It should be obvious that for any statistical study one must compare the actual computational recipes used to make a calculation, rather than to rely on the more or less non-standard terminology and assume that the computations are what one expected. 

These values were plotted against known log P values to generate standard curves such as those shown in Figure 6.43. The standard curves were then used to predict log P of the unknown compound. Results appear in Table 6.7. The slight variation (2%) between the values predicted by the two methods is reasonable within experimental error limits. 

For each compound, means standard error (SEM) were calculated and differences were assessed by ANOVA. Calculated p values < 0.05 were considered to be significantly different. The statistical procedures were performed with the software programme Instat Version 3 (Graphpad Software Inc.). 

The error in the isotope effect is l/ftplfAkn)2 + AhAd)2 x (A d)2]172 where Akn and A/. [, are the standard deviations for the rate constants for the reactions of the undeuterated and deuterated substrates, respectively. The Hammett p values were obtained by changing the para-substituent in the nucleophile. 

Figure 5. Inhibitory effect of NO on Fe -induced lipid peroxidation. Shown is the decreased generation of an oxidative marker (thiobarbituric acid reactive substances, TBARS) as a result of 0.9 iM NO. HL-60 cells (5 x loVral) were placed in an O2 monitor and at the designated time points, butylated hydroxytoluene was added and samples were quick frozen for determination of TBARS. The values represent the mean and standard error of 3-5 independent determinations. Also shown for comparison is the residual concentration of O2 after exposure to the the same conditions. This shows a decrease in utilization of O2 in the presence of NO. We conclude that NO reduces TBARS, and the percent inhibition is similar to the poeent inhibition of O2 consumption. (Modified from our data in Kelley, E.E., Wagner, B.A., Buettner, G.R., and Bums, C.P., 1999, Arch. Biochem. Biophys. 370 97-104).

Predictions of log P with regression. As would be expected, the largest values of the explained variation (r squared) and the smallest standard error of estimates found with the regression models were those that Included all 90 variables. These models... 

The fitted means and standard errors for log-transformed comet tail moments, as well as the percentage of cells exhibiting extensive DNA damage (e.g., cells labeled 3 and 4) are reported in Table 2 [see p. 137]. An adjusted p value indicated no differences existed between cells treated with extracts from exposed filters or with hydrogen peroxide. Cellular responses were significantly different (P < 0.05) between unloaded PMj 5 filter extracts and loaded PM2 5 extracts as well as extracts containing deferoxamine. 

It is not possible at this stage to say precisely what we mean by small and large in this context, we need the concept of the confidence interval to be able to say more in this regard and we will cover this topic in the next chapter. For the moment just look upon the standard error as an informal measure of precision high values mean low precision and vice versa. Further if the standard error is small, it is likely that our estimate x is close to the true mean, p,. If the standard error is large, however, there is no guarantee that we will be close to the true mean. 

Computer packages such as SAS can fit these models, provide estimates of the values of the b coefficients together with standard errors, and give p-values associated with the hypothesis tests of interest. These hypotheses will be exactly as Hqj, Hq2 and Hq3 in Section 6.3. Methods of stepwise regression are also available for the identification of a subset of the baseline variables/factors that are predictive of outcome. 

The lines would be co-incidental with = 02- Indeed the larger the treatment difference the bigger the difference between the two intercepts, and a2- Our main interest is to compare the treatments and within this framework we compare the values of Ui and U2 through the null hypothesis Hg Ui = U2 and the alternative hypothesis a a2- The signal is provided by the estimate of — U2 and the noise is the standard error of that estimate we compare the signal-to-noise ratio to t 3 to give the p-value. 

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