Standard deviation absolute

Model Chemistry MAD Standard Deviation Absolute Max. Error... 

The precisions were found to be similar and the pooled standard deviation (absolute) computed to be 0.071%. Comment upon the efficiency of the mixing. 

Year Reported Sample Type Number of Results Standard Deviation (% Absolute)... 

Another measure of dispersion is the coefficient of variation, which is merely the standard deviation expressed as a fraction of the arithmetic mean, viz., s/x. It is useful mainly to show whether the relative or the absolute spread of values is constant as the values are changed. 

Standard Deviation The absolute standard deviation, s, describes the spread of individual measurements about the mean and is given as... 

The variance is just the square of the absolute standard deviation. Using the standard deviation found in Example 4.3 gives the variance as... 

Determine the density at least five times, (a) Report the mean, the standard deviation, and the 95% confidence interval for your results, (b) Eind the accepted value for the density of your metal, and determine the absolute and relative error for your experimentally determined density, (c) Use the propagation of uncertainty to determine the uncertainty for your chosen method. Are the results of this calculation consistent with your experimental results ff not, suggest some possible reasons for this disagreement. 

Determine Ks and the amount of sample needed to give a relative standard deviation for sampling of 2.0%. Predict the percent relative standard deviation and the absolute standard deviation if samples of 5 g are collected. 

To determine Ks we need to know the average mass of the cereal samples and the relative standard deviation for the %(w/w) ash. The average mass of the five cereal samples is 1.0007 g. The average %(w/w) ash and the absolute standard deviation are, respectively, 1.298% and 0.03194. The percent relative standard deviation, therefore, is... 

Values for 32 elements and the constant have been tabulated (159). An average absolute error of 9.6% for 721 soHd compounds (13% standard deviation) and 8.8% for 477 Hquid compounds (11.5% standard deviation) has been reported. 

The square root of the variance is the standard deviation. The mean absolute error MAE is... 

For sources having a large component of emissions from low-level sources, the simple Gifford-Hanna model given previously as Eq. (20-19), X = Cqju, works well, especially for long-term concentrations, such as annual ones. Using the derived coefficients of 225 for particulate matter and 50 for SO2, an analysis of residuals (measured minus estimated) of the dependent data sets (those used to determine the values of the coefficient C) of 29 cities for particulate matter and 20 cities for SOj and an independent data set of 15 cities for particulate matter is summarized in Table 20-1. For the dependent data sets, overestimates result. The standard deviations of the residuals and the mean absolute errors are about equal for particulates and sulfur dioxide. For the independent data set the mean residual shows... 

We are now in a position to examine the relative accuracies of a variety of different model chemistries by considering their performance on the G2 molecule set. The following table lists the mean absolute deviation from experiment, the standard deviation and the largest positive and negative deviations from experiment for each model chemistry. The table is divided into two parts the first section lists results for single model chemistries, and the remaining sections present results derived from... 

This same data is plotted in the chart on the following page. The mean absolute deviation and standard deviation are plotted as points with error bars, and the shaded blocks plot the largest positive and negative-magnitude errors. 

The foregoing close agreement of the geometric mean diameter and geometric standard deviation results indicates that accuracy evaluations were made on an absolute scale, and did not refer to some arbitrary scale... 

The precision of the rate constants as a function of temperature determines the standard deviations of the activation parameters. The absolute error, not the percentage error in the activation parameters, represents the agreement to the model, because of the exponential functions. If, for example, one wished to examine the values of AS for two reactions that were reported as -4 3 and 26 3 J mol 1K 1, then it should be concluded that the two are known to the same accuracy. Since AS and A// are correlated parameters, the uncertainty in AS will be about 1/Tav times that in A//. At ambient temperature this amounts to an approximate factor of three (that is, 1000/T, converting from joules for AS to kilojoules for A// ). Thus, the uncertainty in A//, 0 of 2.50 kJ mol 1 is consistent with the uncertainty in ASn of 7.21 J mol1 K-1 at Tav - 350 K. 

Figure 1.24. Rejection of suspected outliers. A series of normally distributed values was generated by the Monte Carlo technique the mean and the standard deviation were calculated the largest normalized absolute deviate (residual) z = xi - /.i is plotted versus n (black...

Conclusions the residual standard deviation is somewhat improved by the weighting scheme note that the coefficient of determination gives no clue as to the improvements discussed in the following. In this specific case, weighting improves the relative confidence interval associated with the slope b. However, because the smallest absolute standard deviations. v(v) are found near the origin, the center of mass Xmean/ymean moves toward the origin and the estimated limits of detection resp. quantitation, LOD resp. 

An eye should also be kept on the absolute size of the standard deviation before and after a proposed elimination. If the elimination of a questionable point results in a standard deviation that is markedly smaller than what is common experience for the test at hand, the P-test cannot be used for confirmation, unless S2 is replaced by either the method obtained during the validation, or its lower confidence limit. 

Figure 5.7. The Output Option (Table of Values). A option identification and data path B data set identity and size, derived Student s f, selected p C abscissa and ordinate values D estimated Y = flx) E absolute residuals F relative residuals G mean over absolute residuals and residual standard deviation.

The closeness of agreement between independent results obtained with the same method on identical test material but under different conditions (different operators, different apparatus, different laboratories, and/or after different intervals of time). The measure of reproducibility is the standard deviation qualified with the term reproducibility as reproducibility standard deviation. In some contexts reproducibility may be defined as the value below which the absolute difference between two single test results on identical material obtained under the above conditions may be expected to lie with a specified probability. Note that a complete statement of reproducibility requires specification of the experimental conditions which differ. 

In these cases it is not necessary to determine the absolute bioavailability or the absorption rate constant for the product under study. It is only necessary to prove that the plasma concentration versus time curve is not significantly different from the reference product s curve. This is done by comparing the means and standard deviations of the plasma concentrations for the two products at each sampling time using an appropriate statistical test. 

The sensitivity of this system is 430 pg/0.0044 absolute. The standard deviation of the baseline noise is about 0.0007 absolute, resulting in a noise-limited detection limit of 140 pg of germanium at the 95% confidence level. 

In this method, inorganic lead in seawater samples are converted to tetra-ethylead using sodium tetraethylboron (NaB(C2H5)4) which is then trapped in a graphite furnace at 400 °C. Quantitation is achieved by using a simple calibration graph prepared from aqueous standards. An absolute detection limit of (3relative standard deviation. 

To calculate the robust standard deviation for this data set, you first have to calculate the absolute difference between each result and the median, x, — median, and then find the median of these values. The median absolute deviation (MAD) is 0.02 %abv. This is converted to a standard deviation equivalent (MADe) by multiplying by 1.483 ... 

---