history of statistics essay

history of statistics essay

The Evolution of Statistics: A Comprehensive Historical Analysis

1. Introduction to the Field of Statistics

Genres of thing have their pasts unravel in different ways: tombstones carry within themselves sufficient labeling and descriptive appreciation to define their worth, while animal, mineral, and human historical descriptions, after gaining a foothold from simple diagnostic labels, rise to the challenge of truth. Potted histories, torn from their alphabetic homes, generally cater for the full smorgasbord and are useful for quick ingestion and storage. A whole history might require the assimilation of a new trait, and the most comprehensive cater for a variety of equally likable dishes. The achievement of the best lies in encompassing exposure to the past and doing this to the very high level which deserves the designation of ‘best’. This metanomenclature is fishnets and airplane take-off points, touch-typists delight and gibbon retirement package, a beach-goer’s shade and Captain Cook’s library.

The best of the best has an element of prestige about its name, and this monograph’s title gives a peek into the high degree of esteem in which it holds its subject. The fact that historical periods are defined by extraordinary single names, some conjuring a second vision as well, is an indication of how leaders in a particular field or endeavor have brought about significant periods of advancement. The best is undoubtedly the effort of a number of ‘greats’ to prevent the best wine being kept for last. Statistical achievements are often conceptualized by invocations of an endless sequence of difficult-to-lay Asiatic rugs lined with images of bearded ancients with robes extended in a beckoning gesture. The process eventually has a conclusion, but the statuary of long-winded expositions often dissipates the message. Written history has the ability to shorten, straighten, and rejuvenate tradition while maintaining the thread of coherence which becomes frayed with excess verbiage.

2. Ancient Origins and Early Developments

In another discipline, the early astronomers and geographers of the ancient Greeks solved some pretty difficult statistical tasks related to the Monte Carlo concept long before current theory and applications addressed them. The Mannerists and some of their predecessors also developed an important concept of current ideas concerned with the estimation of probabilities. So far, historians have typically overlooked, misunderstood, or underestimated these practical and sophisticated applications of statistical concepts, i.e., the activity of investigators who actually employed statistical methods and a detailed inferential point of view methodologically and conceptually concerning the data processing of such data. This oversight could be remedied by taking a comprehensive historical view of statistics and considering the most early and, thus far, unrelated sources in a simple chronological sequence.

Hippocrates and the ancient Greeks used statistics in very practical ways. Although the word “statistics” was coined later, the concept of statistics is much older than Hippocrates. Until Hippocrates, people had used many methods to describe or summarize and compare various attributes inherent in groups. Hippocratic authors employed special ad hoc statistical methods applied to attribute-rich data, including frequencies of occurrence and the measurement of these occurrences, Simpson’s paradox, the unit value of life, and tests of significance. The Greeks used statistics and some probability methods, i.e., deriving the values of binomial and Poisson probabilities correctly and apparently without the use of combinatorial mathematics. Aristotle used the “statistical method” properly in his Logic. All these statistical methods and conclusions were used in practical applications, not in theoretical investigations.

3. The Emergence of Probability Theory

The theory of games of chance has ancient origins, fueled by mankind’s apparent historical fascination with games of skill and luck. Unlike games that are dominated by skill and strategy, such as chess and bridge, games of chance have no inherent right or wrong choices – the outcome is purely a matter of luck. The concept of probability, then, concerns the likelihood of certain events occurring based on previous empirical or observed experience, rather than pure logic or preexisting beliefs. This is the sense of probability that appears to be embedded in Archimedes’s treatment of the number of paths one could take walking from one point to another; that is, the work was more rooted in empirical computation than fundamental truth. The first development of a systematic theory of probability, however, can be traced to interactions between the three figures already discussed, along with contributions from a group of eccentric monks, alternately thriving and suffering during their time as religious recluses.

Just as the theory of statistical practice had its roots in the analysis of the games of chance and the proper assessment of the fairness of such games, a comprehensive theory of probability naturally preceded its application to statistical problems. Just as the theory of statistics was shaped by the evolution of mathematics and computing methods, so too was the field of probability theory. The purpose of this section is to outline the evolution of probability theory from its origins in the analysis of games of chance, through its amalgamation with different realms of mathematics, to its formal development within the context of measure theory. This part of the tutorial is divided into three subsections.

4. Statistical Methods in the Scientific Revolution

The art of physics can be regenerationly united with the science of probability in such a manner that we shall be able to reason probabilistically quantitatively about individual cases without becoming immediately buried in the vicious circle so long associated with the unique abruptness with which we can become overwhelmed by the multiplicative explosion of elementary possibilities – if, in short, we place in the service of finite human rationality these deliciously interesting multiple abilities which statistics and structural transformations have allowed all manner of previously unsuspected entities to acquire in the twentieth century and intellectually successful twelfth through fifteenth to eighteenth centuries.

Galileo may not have possessed a copy of Cardan’s Ars Magna when he lectured on the geometry of conic sections in the late sixteenth century, but since Cardan, Pascal, and later on Huygens did indeed possess geometric probability, some of the credit for his turning his mistakes into a useful system of probability is probably theirs. In his experiments with falling bodies, he clearly states that they were arranged quantitatively – the latter were subtended at the points of impact by equidistant vertical threads from a distance scaled off by apparently equal angled falling bodies, in turn. Hence the later arc figures – Salmon’s horn, Desargues’s spiral, Guldinus’ figure of quicksilver investment – displaying the relations between initial velocity, altitude, the conceptual angle of i rarely, and time appear probable. Equationally, Galileo’s work can be derived from equivocal initial equations of conditionally constant acceleration motion without interval error with positive probability, although his method of equational (I use the term to encompass definitional, like the secondary concepts of falling bodies without interval error with positive probability appropriate to his uniquely nonignorant initial definition of natural acceleration) maximization was higher Aristotelian and Copernican in character.

5. Modern Statistical Techniques and Applications

In data mining and data dredging, for instance, the overall objective of using advanced visualizations is to obtain a clearer understanding of data that have been organized into various tables using techniques from multiple correspondence analysis. Such understanding will usually lead to a better analysis of the data. Probability is the mathematical language of statistics. It uses the concepts and language of set theory and logic to quantify uncertainty. Since applications of statistics entail experimentation, modeling, and in general data, probability also measures the strength of belief.

Modern statistical methods and applications are vast and diverse. Developed and developing countries have extended and modified the classical techniques of statistics to the needs of modern data-centric applications. The list of such applications is sizable, so we restrict our discussion to some areas that are relatively new or have been emphasized of late. These include data mining and data dredging, which involve the use of visualization tools like boxplots and quantile plots, the study of the arrow of time in statistical mechanics using techniques from time series analysis, robust methods such as the support count algorithm and trimmed L-statistics for skewness and kurtosis, statistical surveillance for spatial queries like nearest neighbor queries and ortho-range queries in databases, and some applications in database marketing for targeted advertising.