Statistics standard error

In this method it is assumed that the molecular constants of one state are known and can be fixed while the molecular constants of the other state and the band origin are varied. The method has the advantage that all the data can be used unfortunately, however, the Hamiltonians used may not reproduce the energy levels exactly. As indicated above, the standard deviations of the constants are much smaller than for a two-state fit. The method can be used with either the upper or lower state constants fixed and is particularly useful if the ground-state rotational constants are known from microwave spectroscopy. Unfortunately, there is no case known where the excited state constants are also determined with microwave accuracy otherwise it would be possible to check the accuracy of the one-state fit method and the significance of the statistical standard errors of the rotational constants. 

Tentative values based on a modified Urey-Bradley model with nine parameters. e Statistical standard errors digit(s) within parentheses correspond generally to last digit(s) in values tabulated. 

Statistic Standard error of estimate (SEE), also termed standard error of calibration (SEC). Abbreviations SEE, SEC Summation Notation ... 

Statistic Standard Error of Cross-Validation (SECV)... 

Statistics Standard Error of the Laboratory (SEE) for Wet Chemical Methods Abbreviation(s) SEE... 

Calculated Including Thermal Competitors Only. Uncertainties Represent Radioactive Statistics Standard Errors. 

This sum, when divided by the number of data points minus the number of degrees of freedom, approximates the overall variance of errors. It is a measure of the overall fit of the equation to the data. Thus, two different models with the same number of adjustable parameters yield different values for this variance when fit to the same data with the same estimated standard errors in the measured variables. Similarly, the same model, fit to different sets of data, yields different values for the overall variance. The differences in these variances are the basis for many standard statistical tests for model and data comparison. Such statistical tests are discussed in detail by Crow et al. (1960) and Brownlee (1965). 

Vitha, M. F. Carr, P. W. A Laboratory Exercise in Statistical Analysis of Data, /. Chem. Educ. 1997, 74, 998-1000. Students determine the average weight of vitamin E pills using several different methods (one at a time, in sets of ten pills, and in sets of 100 pills). The data collected by the class are pooled together, plotted as histograms, and compared with results predicted by a normal distribution. The histograms and standard deviations for the pooled data also show the effect of sample size on the standard error of the mean. 

Standard deviation, 227—228 Standard error of the difference, 230 Standard values, 249—251 Statistical power, 253 Statistical significance, 227 Statistics descriptive... 

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... 

The major disadvantage of the integral method is the difficulty in computing an estimate of the standard error in the estimation of the specific rates. Obviously, all linear least squares estimation routines provide automatically the standard error of estimate and other statistical information. However, the computed statistics are based on the assumption that there is no error present in the independent variable. 

Scale bar 200 pm. Red arrows indicate the avascular zones. Quantification of digital analysis of the fluorescence angiography images number of branching points (mm2) (B) and mean mesh size (102 pm2) (C) as markers of vessel density for CAM. P < 0.05 was considered to be statistically significant. Error bars represent standard error of the mean. 

They include simple statistics (e.g., sums, means, standard deviations, coefficient of variation), error analysis terms (e.g., average error, relative error, standard error of estimate), linear regression analysis, and correlation coefficients. 

Continuing from our previous discussion in Chapter 18 from reference [1], analogous to making what we have called (and is the standard statistical terminology) the a error when the data is above the critical value but is really from P0, this new error is called the [3 error, and the corresponding probability is called the (3 probability. As a caveat, we must note that the correct value of [3 can be obtained only subject to the usual considerations of all statistical calculations errors are random and independent, and so on. In addition, since we do not really know the characteristics of the alternate population, we must make additional assumptions. One of these assumptions is that the standard deviation of the alternate population (Pa) is the same as that of the hypothesized population (P0), regardless of the value of its mean. 

Now we come to the Standard Error of Estimate and the PRESS statistic, which show interesting behavior indeed. Compare the values of these statistics in Tables 25-IB and 25-1C. Note that the value in Table 25-1C is lower than the value in Table 25-1B. Thus, using either of these as a guide, an analyst would prefer the model of Table 25-1C to that of Table 25-1B. But we know a priori that the model in Table 25-1C is the wrong model. Therefore we come to the inescapable conclusion that in the presence of error in the X variable, the use of SEE, or even cross-validation as an indicator, is worse than useless, since it is actively misleading us as to the correct model to use to describe the data. 

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. 

The attached worksheet from MathCad ( 1986-2001 MathSoft Engineering Education, Inc., 101 Main Street Cambridge, MA 02142-1521) is used for computing the statistical parameters and graphics discussed in Chapters 58 through 61, in references [b-l-b-4]. It is recommended that the statistics incorporated into this series of Worksheets be used for evaluations of goodness of fit statistics such as the correlation coefficient, the coefficient of determination, the standard error of estimate and the useful range of calibration standards used in method development. If you would like this Worksheet sent to you, please request this by e-mail from the authors. 

Statistical analysis In each treatment, 10 microspores were used to measure the maximal fluorescence. The means and their standard errors are determined, if the investigator has microspectrofluorimeter or microspectrofluorimeter having special statictic t- test programme. 

Statistical analysis Statistical analysis consists of determination of Standard error of means (SEM) or the Student- t-testing. The measurement error was about 1-2% (10 spectra per one variant, n=10). Counting was performed in four or five replicates (the number of Petri dishes per a treatment). SEM for the fluorescence spectra was 2 %. 

A variety of statistical parameters have been reported in the QSAR literature to reflect the quality of the model. These measures give indications about how well the model fits existing data, i.e., they measure the explained variance of the target parameter y in the biological data. Some of the most common measures of regression are root mean squares error (rmse), standard error of estimates (s), and coefficient of determination (R2). 

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.). 

---