Statistical table

“ The uniform arrangement of statistics is a matter requiring the greatest labor and statistical ability. Compiling a single table of statistics is a simple matter, but arranging a vast mass of statistics, relating to many diverse subjects, on a uniform and intelligible basis, is entirely another matter, and requires the highest skill of the statistician. In the Mineral Industry this has been accomplished in a most successful manner; everything is clear and intelligible at the first glance, and everything is in its proper place. ”

“ Composite pictures, are, however, much more than averages; they are rather the equivalents of those large statistical tables whose totals, divided by the number of cases, and entered in the bottom line, are the averages. ”

“ One long engaged in statistical work feels more and more keenly, as the results of original investigation, not only the limitations of statistics, but the fact that perfectly honest and truthful statistical tables may not only be vicious in themselves, but may also lead to the most worthless conclusions, the tables themselves not indicating, and it not being possible to fully indicate by them, the exact truth they contain. ”

“ The attempt to make comparison between the percentage of growth of population and the percentage of growth in the expenditures of the Federal Government, using no facts relative to the great increase in mechanical production and of wealth, is a vicious use of statistical data. Such showings are the results of the work of the statistical mechanic, the man who constructs statistical tables to order.
Statistics really take the place of observation. ”

“ Why do we hear so much of the "approximate correctness" of so many statistical tables, when, in point of fact, the primary data are incapable of proof, and the averages and conclusions built upon them are all assumed? "Statisticians," says one of the fraternity, "are generally held to be eminently practical people; on the contrary, they are more given to theorizing than any other class of writers ”

“ The pretended exactness of statistical tables is too often little better than an imposture; and those founded not on direct estimation by competent observers, but on the report of persons who have no particular interest in knowing the truth, but often have a motive for distorting it, are commonly to be regarded as but vague guesses at the actual fact. ”

“ To those who value no information but such as assumes the shape of detail of facts, or can be reduced to [Pg 138] figures, and exhibited in the shape of statistical tables, we shall perhaps appear to be wasting time in examining the mere errors of reasoning on this important subject of penal discipline. We think otherwise. We apprehend there is nothing more necessary than to keep active and zealous men steady to first principles in subjects of great general interest. We are not guilty of underrating the value of statistical tables ”

“ In order to form statistics properly so called the primary statistical quantities must be formed into tables, and in the formation of these tables lies the art of the statistician. It is not a very difficult art when the principles relating to it have been properly grasped, but those who are unfamiliar with the subject are apt to underrate the difficulty of correctly practising it. ”

“ It would seem, therefore, that we might find a sort of measure of the deviation of an ensemble from statistical equilibrium in the excess of the average index above the minimum which is consistent with the condition of the invariability of the distribution with respect to the constant functions of phase. But we have seen that the index of probability is constant in time for each system of the ensemble. The average index is therefore constant, and we find by this method no approach toward statistical equilibrium in the course of time. ”

“ The statistician is primarily the man of facts, not merely a recorder of facts, but one upon whom is laid the duty of their orderly arrangement, their exposition and scientific coordination. Our author inferentially recognizes these functions by mapping out a general work to bear the title of the science of the statistics. Herein will be arranged the principal contents of statistical knowledge, in two separate volumes, the one having particular reference to the needs of sociology, the other of economics. ”

“ The probability-coefficient for a generic phase will be times as great, viz., We shall say that such an ensemble as has been described is canonically distributed, and shall call the constant its modulus. It is evidently what we have called a grand ensemble. The petit ensembles of which it is composed are canonically distributed, according to the definitions of Chapter IV, since the expression
is constant for each petit ensemble. The grand ensemble, therefore, is in statistical equilibrium with respect to specific phases. ”

“ When the word "significantly" is used in comparisons, it is meant to show that there is a significant statistical difference between two or more samples. Whenever eight or more specimens from one locality were available, the mean, range, standard deviation, standard error of the mean, and coefficient of variability were calculated. ”

“ Theorem VII. If a system which in its different phases constitutes an ensemble consists of two parts, and we consider the average index of probability for the whole system, and also the average indices for each of the parts taken separately, the sum of the average indices for the parts will be either less than the average index for the whole system, or equal to it, but cannot be greater. The limiting case of equality occurs when the distribution in phase of each part is independent of that of the other, and only in this case. ”

“ Every article on statistics requires at least one caveat. Here is ours: we refer in this article to “science” as a convenient shorthand for investigations using data to study questions of interest. This includes social science, engineering, digital humanities, finance, and so on. Statisticians are not shy about reminding administrators that statistical science has an impact on nearly every part of almost all organizations. ”

“ Let us consider three attributes, say A, B and C, of the individuals of a population and suppose that the attribute C is positively correlated to the attributes A and B, so that to great or small values of A or B correspond respectively great or small values of C. Now if the individuals in the population are statistically selected in such a way that we choose out individuals having great values of the attributes A and small values of the attribute B, then we get a statistical series regarding the attribute C, which consists of two seemingly distinct normal frequency distributions. ”

“ A central and common task for us as research investigators is to decipher what our data are able to say about the problems we are trying to solve. Statistics is a language constructed to assist this process, with probability as its grammar. While rudimentary conversations are possible without good command of the language (and are conducted routinely) , principled statistical analysis is critical in grappling with many subtle phenomena to ensure that nothing serious will be lost in translation and to increase the likelihood that your research findings will stand the test of time. ”

“ The methods of interpolation are usually the same in the two groups of cases, but special considerations have to be taken into account in the second group. The line of demarcation of the two groups is not absolutely fixed; the tables used by actuaries, for instance, which are of great importance in practical life, are based on statistical observations, but the tables formed directly from the observations have been “smoothed” so as to obtain series which correspond in form to the series of values of mathematical functions. ”

“ Hence also, if the change in the external coördinates of an ensemble initially in statistical equilibrium consists in successive very small changes separated by very long intervals of time in which the disturbance of statistical equilibrium becomes sensibly effaced, the final diminution in the average index of probability will in general be negligible, although the total change in the external coördinates is large. ”

“ As becomes the orderly mind of a statistician, the society has been very regular in its publications, having for seventy years issued a yearly volume in quarterly parts, which form a veritable mine of statistical information. ”

“ To analyze statistically significant differences between variables, we selected appropriate statistical tests based on the distribution of data including the Kruskal Wallis test, chi square tests, Wilcoxon Rank sum test, and Spearman’s correlations for non-parametric data and one-way analysis of variance and Pearson’s correlations for continuous data. ”

“ Provide Assessments of Variability Nearly all biological measurements, when repeated, exhibit substantial variation, and this creates uncertainty in the result of every calculation based on the data. A basic purpose of statistical analysis is to help assess uncertainty, often in the form of a standard error or confidence interval, and one of the great successes of statistical modeling and inference is that it can provide estimates of standard errors from the same data that produce estimates of the quantity of interest. ”

“ On account, then, of the difficulties of the subject and of the profound importance of results which can be reached by no other known method, it is of the utmost consequence that the principles and processes of statistical mechanics should be put upon a firm and certain foundation. ”

“ The word 'statistics,' illustrating fixed and settled conditions, indicates the soundness of the German writer's thought and the true spirit in which the statistician should work.
The use of the statistical method in a scientific way is practically modern. In ancient times there were counts of the people, but no scientific use of the results that would warrant the application of the name statistics. ”

“ Statistical facts are usually numerical or quantitative in character, so that, if many causal agencies are in operation at the same time, their effects are simply added together algebraically, and are inextricably merged into a general total. ”

“ The quicker and surer method, however, in driving home the essential points of statistics is their graphic presentation. For the majority of business men the graphic method will accomplish what statistical tabulation fails to do. ”

“ We must, however, draw a very important distinction. There is one method by which uniformities of a certain kind can be detected in the behaviour of purposive intelligent beings, without insight into the nature of their individual purposes—the method of statistical averages. ”

“ The cultivation of statistics must be the source of all future improvement in the science of political economy, because it is to the table of the statistician that the economist must look for his facts ”

“ Not only is this true, but the further interesting fact may be discovered that social statistics of every category employed or known are based upon a frank recognition of that coefficient of resemblance, physical or mental, which I have contended is a mark of social phenomena. The first step in statistical tabulation is classification, and classification invariably starts from an assumption of real or supposed resemblance. ”

“ The nature of the difficulty is at once apparent if we try to distribute a finite number of material points with this particular value of the energy as nearly as possible in statistical equilibrium, or if we ask: What is the probability that a point taken at random from an ensemble in statistical equilibrium with this value of the energy will be found in any specified part of the circle? ”

“ We have also shown that the average square of the anomalies of , that is, of the deviations of the individual values from the average, is in general of the same order of magnitude as the reciprocal of the number of degrees of freedom, and therefore to human observation the individual values are indistinguishable from the average values when the number of degrees of freedom is very great. ”

“ Statistical Methods Should Enable Data to Answer Scientific Questions A big difference between inexperienced users of statistics and expert statisticians appears as soon as they contemplate the uses of some data. While it is obvious that experiments generate data to answer scientific questions, inexperienced users of statistics tend to take for granted the link between data and scientific issues and, as a result, may jump directly to a technique based on data structure rather than scientific goal. ”

“ All that is necessary to make the examples appropriate is that we should admit that in their case statistical data are our ultimate appeal in the present state of knowledge. Of course if the empirical laws can be resolved into their component causes we may appeal to direct deduction, and in this case the employment of statistics, and consequently the use of the theory of Probability, may be superseded. ”

“ Tinkering around with the data, also known as exploratory data analysis, is often the most informative part of the analysis. Exploratory plots can reveal data quality issues and outliers. Simple summaries, such as means, standard deviations, and quantiles, can help refine thinking and offer face validity checks for hypotheses. Many studies, especially when going in completely new scientific directions, are exploratory by design; the area may be too novel to include clear a priori hypotheses. Working with the data informally can help generate new hypotheses and ideas. ”