Mean average deviation

These composite approaches have been, overall, very successful. For example, recent variants of G3 give the heats of formation of a test set of 222 molecules, many having second-row atoms, with overall mean absolute deviations of about 1 kcal/mole [42,43], Atomization reactions were used. The results are nearly as good when third-row atoms are included [44]. Similarly, the CBS-QB3 procedure, for 147 first- and second-row molecules, produced a mean average deviation of 1.08 kcal/mole [38]. A few molecules, often containing halogens, do give problems [38,42-44], but the errors are rarely more than 5 kcal/mole. However the size limitations mentioned above must be kept in mind. 

The mean average deviation between predicted and actual sensory heat ratings was less then 1 cm on the 15 cm scale (4). Thus, the equation "sensory heat rating = 31.26 (percent capsaicinoids) -0.21 precisely predicts sensory ratings for heat in ground red pepper. 

MAD is mean average deviation, the arithmetic mean of absolute deviations from experiment. Max. Errorl is the absolute value of the maximum deviation from experiment. The author has placed kj mol in parentheses beside the kcal mol- values. Taken with permission from J. B. Foresman and iE. Frisch, Exploring Chemistry with Electronic Structure Methods, 2nd edn, Gaussian Inc., Pittsburgh, PA, 1996. All four methods are available as keywords in Gaussian 94 and Gaussian 98. 

Table 3 Mean average deviation between calculated (AV5Z basis) and experimental dipole and quadrupole moment values (in au). The quadrupole moments were calculated with respect to the center of mass, with the molecules aligned along the z-axis. For non-linear molecules, the z-axis coincides with the axis of highest symmetry. The experimental values for the dipole moments were taken from [38], whereas those for the quadrupole moments were taken from [39]. Ab initio values were taken from references [40] (MRSDCI) and [41] (HF, MP2 and BD).

As can be seen from O TMe 10-3, the agreement between the computed and experimental geometrical parameters is excellent. The mean average deviation between the B3LYP/6-31G and experimental bond lengths is just 0.006 A, with a maximum error (for the C-N triple bond in HCN) of 0.022 A. The mean average deviation for bond angles is only 0.8°. Such results are typical. 

A statistical measure of the average deviation of data from the data s mean value (s). 

Fig. 3.46 Dynamical pivfiles for graph sequences Gs (defined in section 3.3.2), representing averages over Ng sequence samples. The x-axis labels each g G Gs, dashed lines denote pure range-r topologies r with gi = range-1, 1-dira lattice and vertical bars give the mean absolute deviations of a particular rneasiire. Each system has size. N = 12, with Ng and rules TZ as follows (a) Ng = 50, K = OTIO, (b) Ng = 25, Ti= OT26, (c) Ng = 50, 7 = T16, (d) dg = 50, 7 = T4.

Devarda s alloy 303, 679 Deviation mean (average), 134 standard, 134... 

Deviation Variation from the a specified dimension or design requirement, usually defining the upper and lower limits. The mean deviation (MD) is the average deviation of a series of numbers from their mean. In averaging the deviations, no account is taken of signs, and all deviations whether plus or minus, are treated as positive. The MD is also called the mean absolute deviation (MAD) or average deviation (AD). 

Mean absolute deviation MAD is a statistical measure of the mean (average) difference between a product s forecast and actual usage (demand). The deviations (differences) are included without regard to whether the forecast was higher than actual or lower. 

First, we define a mean (average) size of particles in the distribution as d, and then define what we call a "standard deviation as a, for the distribution of particles. From statistics, we know that this means that 68% of the particles are being counted (34% on either side of the mean, d), i.e. -... 

Table 10-3. Compilation of mean absolute deviations for static average polarizabilities [a.u.] of small main group molecules from different sources.

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. 

To compute the results shown in Tables 34-3 and 34-4, the precision of each set of replicates for each sample, method, and location are individually calculated using the root mean square deviation equation as shown (Equations 34-1 and 34-2) in standard symbolic and MathCad notation, respectively. Thus the standard deviation of each set of sample replicates yields an estimate of the precision for each sample, for each method, and for each location. The precision is calculated where each ytj is an individual replicate (/ ) measurement for the ith sample yt is the average of the replicate measurements for the ith sample, for each method, at each location and N is the number of replicates for each sample, method, and location. The results of these computations for these data... 

The analytical results for each sample can again be pooled into a table of precision and accuracy estimates for all values reported for any individual sample. The pooled results for Tables 34-7 and 34-8 are calculated using equations 34-1 and 34-2 where precision is the root mean square deviation of all replicate analyses for any particular sample, and where accuracy is determined as the root mean square deviation between individual results and the Grand Mean of all the individual sample results (Table 34-7) or as the root mean square deviation between individual results and the True (Spiked) value for all the individual sample results (Table 34-8). The use of spiked samples allows a better comparison of precision to accuracy, as the spiked samples include the effects of systematic errors, whereas use of the Grand Mean averages the systematic errors across methods and shifts the apparent true value to include the systematic error. Table 34-8 yields a better estimate of the true precision and accuracy for the methods tested. 

Chapter 7 Response 7.1 (a) The mean, standard deviation, robust average (median) and robust standard deviation (MADe) are shown in Table SAQ 7.1. Table SAQ 7.1 Data from a proficiency testing round for the determination of moisture in barley ... 

From a structural point of view the OPLS results for liquids have also shown to be in accord with available experimental data, including vibrational spectroscopy and diffraction data on, for Instance, formamide, dimethylformamide, methanol, ethanol, 1-propanol, 2-methyl-2-propanol, methane, ethane and neopentane. The hydrogen bonding in alcohols, thiols and amides is well represented by the OPLS potential functions. The average root-mean-square deviation from the X-ray structures of the crystals for four cyclic hexapeptides and a cyclic pentapeptide optimized with the OPLS/AMBER model, was only 0.17 A for the atomic positions and 3% for the unit cell volumes. 

If a large number of readings of the same quantity are taken, then the mean (average) value is likely to be close to the true value if there is no systematic bias (i.e., no systematic errors). Clearly, if we repeat a particular measurement several times, the random error associated with each measurement will mean that the value is sometimes above and sometimes below the true result, in a random way. Thus, these errors will cancel out, and the average or mean value should be a better estimate of the true value than is any single result. However, we still need to know how good an estimate our mean value is of the true result. Statistical methods lead to the concept of standard error (or standard deviation) around the mean value. 

Fig. 1. Mean reduced vapor pressure curve for the halides of sodium, potassium, rubidium, and cesium. Average deviation from the mean is shown by the vertical lines.

A reproducibility study of two series of 10 solutions containing 1000 and 2500pg of Oxamyl, respectively, gave an arithmetic mean, standard deviation and coefficient of variation of 997pg, 8.0pg and 0.80%, respectively, for the first series and 2489pg, 13.3pg and 0.53%, respectively, for the second. The average recovery varied from 85.5-100.8%. 

The procedure used to determine whether a given result is unacceptable involves running a series of identical tests on the same sample, using the same instrument or other piece of equipment, over and over. In such a scenario, the indeterminate errors manifest themselves in values that deviate, positively and negatively, from the mean (average) of all the values obtained. Given this brief background, let us proceed to define some terms related to elementary statistics. 

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