Statistical Data Treatment and Evaluation

Chapter 3 Using Spreadsheets in Analytical Chemistry 54 Chapter 4 Calculations Used in Analytical Chemistry 71 Chapter 5 Errors in Chemical Analyses 90 Chapter 6 Random Errors in Chemical Analysis 105 Chapter 7 Statistical Data Treatment and Evaluation 142 Chapter 8 Sampling, Standardization, and Calibration 175... 

Up to now (1971) only a limited number of reaction series have been completely worked out in our laboratories along the lines outlined in Sec. IV. In fact, there are rather few examples in the literature with a sufficient number of data, accuracy, and temperature range to be worth a thorough statistical treatment. Hence, the examples collected in Table III are mostly from recent experimental work and the previous ones (1) have been reexamined. When evaluating the results, the main attention should be paid to the question as to whether or not the isokinetic relationship holds i.e., to the comparison of standard deviations of So and Sqo The isokinetic temperature /J is viewed as a mere formal quantity and is given no confidence interval. Comparison with previous treatments is mostly restricted to this value, which has generally and improperly been given too much atention. 

Data obtained from animal experiments were expressed as mean standard error ( SEM). Statistical differences between the treatments and the control were evaluated by ANOVA and Students-Newman-Keuls post-hoc tests, p < 0.05 was considered to be significant ( p < 0.05 p < 0.01 p < 0.001). 

Statistics is concerned with the treatment of numerical data where there is an associated uncertainty or chance. Many situations contain some element of chance, e.g. the outcome from throwing a die or the response of a patient to a drug. Even though it may be impossible to predict a particular outcome with certainty, its probability can often be quantified. Knowledge of statistical principles is essential in designing clinical trials and in the interpretation and evaluation of the results. PROBABILITY... 

The technical evaluation may also lead to the comparison of the results obtained from different methods. It will allow participants to extract information by comparing and possibly discussing their performance and method with other participants applying similar procedures, i.e. it may allow to discover biases in methods. If several enriched materials have been prepared and analysed the organiser may produce Youden plots where trends and systematic errors can appear [10-12]. Such more elaborated data presentations have to be issued with sufficient explanations to avoid misunderstanding and wrong conclusions. More advanced data treatment require the application of suitable robust statistics which have to be carefully chosen to arrive at sound scientific conclusions. Their meaning should always be explained and documented. 

In the interpretation of the numerical results that can be extracted from Mdssbauer spectroscopic data, it is necessary to recognize three sources of errors that can affect the accuracy of the data. These three contributions to the experimental error, which may not always be distinguishable from each other, can be identified as (a) statistical, (b) systematic, and (c) model-dependent errors. The statistical error, which arises from the fact that a finite number of observations are made in order to evaluate a given parameter, is the most readily estimated from the conditions of the experiment, provided that a Gaussian error distribution is assumed. Systematic errors are those that arise from factors influencing the absolute value of an experimental parameter but not necessarily the internal consistency of the data. Hence, such errors are the most difficult to diagnose and their evaluation commonly involves measurements by entirely independent experimental procedures. Finally, the model errors arise from the application of a theoretical model that may have only limited applicability in the interpretation of the experimental data. The errors introduced in this manner can often be estimated by a careful analysis of the fundamental assumptions incorporated in the theoretical treatment. 

Each treatment was conducted in triplicate and all experiments were repeated at least twice. The statistical significance of the evaluated data was analyzed by one-way analysis of variance. Differences among the mean values were tested using the least significant difference multiple range test. Values were considered significant when p<0.05, except when otherwise indicated. 

No one has yet actually applied the statistical method to the evaluation of substituent constants. The closest to it is the work of Wold and Sjostrom (35,36) who have used a large number of sets in the statistical evaluation of what they refer to as the inductive substituent constants. These constants are actually equivalent to the cfi or a" values. Wold and Sjostrom have argued that the statistical treatment is the best approach to the evaluation of substituent constants. In the course of their work, they have used data for ionization of benzoic acids in alcohol-water, acetone-water, and dioxane-water mixtures on the assumption that the competition of the electrical effect was the same in all of these sets. The results of Ehrenson, Brownlee, and Taft (1) and our own results show that the composition of the electrical effect varies with solvent. This would seem to throw some doubt on the results of Wold and Sjostrom and to suggest that the third objection to the statistical evaluation of substituent constants may indeed be valid. 

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