Statistical data

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ Statistics has thrown a flood of light upon important phases of societary life, such as the economic, where wage scales and price levels are significant concepts. Statistics has been widely utilized in the study of crime and poverty. The various methods of graphic presentations are valuable in interpreting tables of statistical data to the lay483 mind.
Statistical methods can be used, however, to prove almost anything. The ordinary individual is helpless when statistical methods are treated unscrupulously. ”

“ Asking questions at the design stage can save headaches at the analysis stage: careful data collection can greatly simplify analysis and make it more rigorous. Or, as Sir Ronald Fisher put it: “To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. ”

“ 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. ”

“ The second inquiry through which we may learn somewhat of the present position of sociology relates to the development of method. Exact method in social research is statistical. Wherever we can obtain numerical data within the domain of social phenomena, there we arrive at exact or quantitative knowledge. The development and application of statistical methods to social problems has been one of the most striking scientific achievements of the present century. ”

“ This class of statistics demands higher statistical qualifications, both in preparing for the enumeration and in the tabulation, classification and analysis of the results.
The third kind of statistics are those secured through a special investigation of certain representative facts. For instance if it is desired to learn the cost of producing iron and steel, it is not necessary, as in the previous case, to secure data for all the establishments engaged in such production. A few representative works offer ample information for determining cost of production. ”

“ Data have now been gathered in regard to the families of the men of science previously selected. In our present state of ignorance a statistical study of any homogeneous and objectively chosen group should be of value, both as a contribution to psychological and vital statistics in general and for comparison with other groups which may be similarly studied. ”

“ Having said this, scientific data have detailed structure, and simple models can’t always accommodate important intricacies. The common assumption of independence is often incorrect and nearly always needs careful examination. See Rule 8. Large numbers of measurements, interactions among explanatory variables, nonlinear mechanisms of action, missing data, confounding, sampling biases, and so on, can all require an increase in model complexity.
Keep in mind that good design, implemented well, can often allow simple methods of analysis to produce strong results. ”

“ 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 ”

“ But psychology is passing into a less simple phase. Within a few years what one may call a microscopic psychology has arisen in Germany, carried on by experimental methods, asking of course every moment for introspective data, but eliminating their uncertainty by operating on a large scale and taking statistical means. This method taxes patience to the utmost, and could hardly have arisen in a country whose natives could be bored. Such Germans as Weber, Fechner, Vierordt, and Wundt obviously cannot; ”

“ 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. ”

“ It is true that statistical research can be called a scientific method of determining facts, and for studying various phenomena from which laws relating to life, production, distribution, consumption, etc., can be drawn ”

“ 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. ”

“ 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. ”

“ 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. ”

“ In statistics, it is evident that empirical laws may sometimes be traced; and the tracing them forms an important part of that system of indirect observation on which we must often rely for the data of the Deductive Science. ”

“ 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. ”

“ 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 method, I believe, is the surest for ascertaining conditions, and the truest on which to base conclusions; but the method must be supplemented by full and frank analysis. A statistical table, independent of such analysis, is to me what a red flag is to a bull. It immediately excites antagonism and invites attack. The value of any statistical presentation must depend upon the basis upon which it is made, the integrity of the collection of the various elements of it, and the analysis which accompanies it. ”

“ 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. ”

“ He uses the results of statistical inquiry because the method of obtaining and presenting them is scientific, and because he recognizes with the German Schlosser, that "statistics is history ever advancing," and that if he wishes to grow with advancing history and keep himself fully and thoroughly informed of progress in every direction, he must use the statistical or historical method ”

“ X. I took the liberty of telling you last night that statistics are a mathematical form of telling a lie, and that, to use the expression of a clever Frenchman, a statistical table is like a loose woman who is at the service of anyone who wants her. ”

“ We developed our list of rules with researchers in mind: researchers having some knowledge of statistics, possibly with one or more statisticians available in their building, or possibly with a healthy do-it-yourself attitude and a handful of statistical packages on their laptops. ”

“ We have put the emphasis on defending ourselves against fraudulent claims wrapped up as statistics. We close this section on a more positive note. Just as important as detecting the deceptive use of statistics is the appreciation of the proper use of statistics. You must also learn to recognize statistical evidence that supports a stated conclusion. Statistics are all around you, sometimes used well, sometimes not. ”

“ He defines the statistical science as “die systematische Darlegung and Erdrterung der thatsächlichen Vorgänge and der aus diesen sich ergebenden Gesetze des gesellschaftlichen menschlichen Lebens auf Grundlage quantitativer Massenbeobachtungen” (the systematic statement and explanation of actual events, and of the laws of man's social life that may be deduced from these, on the basis of the quantitative observation of aggregates) . ”

“ 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. ”

“ Every one who is engaged in statistical inquiry must acknowledge the possibility of natural laws governing such statistical facts. Hence we must allot a distinct place to numerical information relating to the numbers, ages, physical and sanitary condition, mortality, &c., of different peoples, in short, to vital statistics. ”

“ 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 experiments to which allusions have been frequently made during the present chapter, favourably as they were received, might have shared the fate of many other discoveries which did not admit of an immediate and obvious application to the purposes of common life; for statistical value is a necessary passport to popular favour. ”

“ 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. ”

“ It is of this form of probability that Mill advises to know, before applying a calculation of probability, the necessary facts, i.e., the relative frequency with which the various events occur, and to understand clearly the causes of these events. If statistical tables show that five of every hundred men reach, on an average, seventy years, the inference is valid because it expresses the existent relation between the causes which prolong or shorten life. ”