Avoiding Experimental Errors

Following is a list of common experimental problems that can ruin quantitative analyses. Avoiding these problems is key to insuring the accuracy of your calibrations. 

Run standards in random order to insure that sample order has no effect on the results. 

Obtain two spectra of each standard, and subtract them using a subtraction factor of 1.0 to see if a flat residual is obtained. If not, it means that a variable in the sample or the experiment has caused spectra of the same sample to be different. The source of variability must be found and eliminated before continuing. 

Obtain standards with accurate concentrations. The accuracy of a predicted concentration is no better than the accuracy to which we know the concentration in the standards. 

The minimum number of standards to run is 2n -f 2, where n is the number of analytes. Thus, for one analyte the minimum number of standards to run is [(2 X 1) -F 2] or 4. However, running more standards typically will give a better calibration. 

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The primary act in a photochemical reaction is absorption of a quantum of radiation by the photoactive molecule. In a quantitative study, therefore, a radiation source of known intensity and frequency a suitable cel for the photolyte and an appropriate detector of light intensity are absolutely necessary for the determination of rates of reaction. To avoid experimental error due to geometry of the reaction cell, the best arrangement is to have a plane parallel beam of monochromatic radiation, incident upon a flat cuvette with proper stirring arrangement, as given in Figure 1.2. 

Roseler et al., 1993). However the spectrally multiplexing procedure requires a photometric technique to be applied. To circumvent an absolute calibration of the intensity scale and to avoid experimental errors due to different optical paths and particularly, different irradiated areas, the evaluation should be based on quotients of intensities which were obtained under identical conditions except the polarization states. 

There are two types of measurement errors, systematic and random. The former are due to an inherent bias in the measurement procedure, resulting in a consistent deviation of the experimental measurement from its true value. An experimenter s skill and experience provide the only means of consistently detecting and avoiding systematic errors. By contrast, random or statistical errors are assumed to result from a large number of small disturbances. Such errors tend to have simple distributions subject to statistical characterization. 

Design of experiments. When conclusions are to be drawn or decisions made on the basis of experimental evidence, statistical techniques are most useful when experimental data are subject to errors. The design of experiments may then often be carried out in such a fashion as to avoid some of the sources of experimental error and make the necessary allowances for that portion which is unavoidable. Second, the results can be presented in terms of probability statements which express the reliabihty of the results. Third, a statistical approach frequently forces a more thorough evaluation of the experimental aims and leads to a more definitive experiment than would otherwise have been performed. 

In addition to the chemical inferences that can be drawn from the values of AS and AH, considered in Section 7.6, the activation parameters provide a reliable means of storing and retrieving the kinetic data. With them one can easily interpolate a rate constant at any intermediate temperature. And, with some risk, rate constants outside the experimental range can be calculated as well, although the assumption of temperature-independent activation parameters must be kept in mind. For archival purposes, values of AS and AH should be given to more places than might seem warranted so as to avoid roundoff error when the exponential functions are used to reconstruct the rate constants. 

When the isokinetic relationship holds, it is useless to discuss separately the values of AH and AS in addition to AG. In fact, it has happened many times that it was the experimental errors in AH and AS which were discussed. To avoid this possibility, it has been suggested (163) that isokinetic enthalpy AHj o and isokinetic entropy ASjso be defined as values computed with the isokinetic constraint. The values of AH o are directly connected to the slopes b of isokinetic lines in eqs. (39), (39a), (49), (54) and (59) e.g., for Al lo,... 

In order to avoid the SET process, we chose diphenylmethylsilyl anions (PI MeSiM 8a, M = K 8b, M = Na 8c, M = Li) as initiators for 7 instead of alkyllithium and benzene as a solvent. The polymerization did not take place in benzene with silyl anions alone. However, in the presence of an equimolar amount of suitable cryptands, the silyl anions initiated the polymerization. The results are summarized in Table 2. The molecular weights of polysilylenes thus obtained were in good agreement with the calculated values within experimental error. 

The effect could be considerable for solvent-exposed parts of the backbone and could render the NOE values inaccurate. These systematic errors could be minimized by using water flip-back pulses in order to avoid saturation of H20 magnetization [11]. The NOE data are generally more susceptible to errors than Ri and R2 because (i) the NOE experiments start with the equilibrium 15N magnetization that is 10 fold lower than that of (XH) in the Hi and R2 experiments, hence relatively low sensitivity, and (ii) the NOE values are derived from only two sets of measurements, whereas R1 and R2 data are obtained from fitting multiple sets of data the latter is expected to result in a more efficient averaging of experimental errors. 

The simplest but also the least reliable calibration method is the use of a single standard solution. The electrode response is assumed to be Nernstian. The slope of the potential versus concentration dependence can also be determined experimentally, by using two standard solutions with different concentrations. To avoid large errors, the standard concentration should be as close as possible to the sample concentration in calibration with a single standard solution. 

Experimental error the variation to be expected under repetition of the experiment excluding mistakes in design or avoidable imperfections in technique. 

Before calculating G and R, it is advisable to review the experimental value of B to avoid the influence of experimental errors. This is done whenever the number of ... 

In general, results from investigations based on measurements may be falsified by three principal types of errors gross, systematic, and random errors. In most cases gross errors are easily detected and avoidable. Systematic errors (so-called determinate errors) affect the accuracy and therefore the proximity of an empirical (experimental) result to the true result, which difference is called bias. Random errors (so-called indeterminate errors) influence the precision of analytical results. Sometimes precision is used synonymously with reproducibility and repeatability. Note that these are different measures of precision, which, in turn, is not related to the true value. 

In such statistically designed experiments one wants to exclude the random effects of a limited number of features by varying them systematically, i.e. by variation of the so-called factors. At the same time the order in which the experiments are performed should be randomized to avoid systematic errors in experimentation. In another basic type of experiment, sequential experiments, the set-up of an experiment depends on the results obtained from previous experiments. For help in deciding which design is preferable, see Section 3.6. In principle, statistical design is one recommendation of how to perform the experiments. The design should always be based on an exact question or on a working hypothesis. These in turn are often based on models. 

Similar expressions can be developed for other weak acids and weak bases to permit the evaluation of their dissociation constants. The constants normally are evaluated at points on the titration curve where the pH is changing slowly relative to the added titrant equivalence points are to be avoided because of the significant experimental errors that are possible at this point on the titration curve. 

The dimensionless relative solubility constant Sr = K in Eq. (9-32) is a measure of the partitioning of a substance between two phases, as is the absolute solubility constant coming from Henry s law in Eq. (9-3). The absolute solubility constants can be directly determined using one of the methods for gases, but this is limited to only relatively volatile substances. Large experimental errors like adsorption on the polymer surface and cell walls cannot be avoided in these methods for substances with low volatilities. 

More detailed computer analyses indicate that methods based on measurements at low conversion are not sufficiently accurate. The method should avoid systematic errors caused by unsubstantiated linearization of the copolymerization equation, and it should respect the structure of experimental errors for which it should be able to compensate. 

It is always wise to check calculations of order from fractional lifetimes experimentally by making runs under conditions of different initial concentrations to avoid fortuitous errors. 

Phase correction in contrast to the theoretical expectation, the measured interferogram is typically not symmetric about the centerburst (.v = 0). This is a consequence of experimental errors, e.g., frequency-dependent optical and electronic phase delays. One remedy is to measure a small part of the interferogram doublesided. Since the phase is a weak function of the wavenumber, one can easily interpolate the low resolution phase function and use the result later for phase correction. If there is considerable background absorption, phase errors may falsify the intensities of bands in the difference spectra. To avoid such phase errors for difference spectroscopy, the background absorbance should therefore be less than one. 

Harkins remarked that the history of the methods [used for the determination of surface tension] may be described as a comedy of errors when experimental errors were avoided, the calculations were based on wrong theory or vice versa, so that in practically all the best work between 1896 and 1916 errors of 3 per cent were made. He gave a table showing the relative advantages and disadvantages of the different methods. 

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