Statistics

"description of a state, a country"[1]) is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Inferences made using mathematical statistics employ the framework of probability theory, which deals with the analysis of random phenomena.

Multiple problems have come to be associated with this framework, ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.

The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.

Derived from this, political scientist Gottfried Achenwall, coined the German word statistik (a summary of how things stand).

There are also methods of experimental design that can lessen these issues at the outset of a study, strengthening its capability to discern truths about the population.

However, the study is heavily criticized today for errors in experimental procedures, specifically for the lack of a control group and blindness.

This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis.

"The relationship between the data and what they describe merely reflects the fact that certain kinds of statistical statements may have truth values which are not invariant under some transformations.

[29] Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates.

Interpretation of statistical information can often involve the development of a null hypothesis which is usually (but not necessarily) that no relationship exists among variables or that no change occurred over time.

The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.

Al-Khalil (717–786) wrote the Book of Cryptographic Messages, which contains one of the first uses of permutations and combinations, to list all possible Arabic words with and without vowels.

[37][38] The earliest writing containing statistics in Europe dates back to 1663, with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt.

[39] Early applications of statistical thinking revolved around the needs of states to base policy on demographic and economic data, hence its stat- etymology.

The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general.

The mathematical foundations of statistics developed from discussions concerning games of chance among mathematicians such as Gerolamo Cardano, Blaise Pascal, Pierre de Fermat, and Christiaan Huygens.

[43] The first wave, at the turn of the century, was led by the work of Francis Galton and Karl Pearson, who transformed statistics into a rigorous mathematical discipline used for analysis, not just in science, but in industry and politics as well.

Galton's contributions included introducing the concepts of standard deviation, correlation, regression analysis and the application of these methods to the study of the variety of human characteristics—height, weight and eyelash length among others.

[47] The second wave of the 1910s and 20s was initiated by William Sealy Gosset, and reached its culmination in the insights of Ronald Fisher, who wrote the textbooks that were to define the academic discipline in universities around the world.

[51] He also coined the term null hypothesis during the Lady tasting tea experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation".

[52][53] In his 1930 book The Genetical Theory of Natural Selection, he applied statistics to various biological concepts such as Fisher's principle[54] (which A. W. F. Edwards called "probably the most celebrated argument in evolutionary biology") and Fisherian runaway,[55][56][57][58][59][60] a concept in sexual selection about a positive feedback runaway effect found in evolution.

The final wave, which mainly saw the refinement and expansion of earlier developments, emerged from the collaborative work between Egon Pearson and Jerzy Neyman in the 1930s.

Statistics is applicable to a wide variety of academic disciplines, including natural and social sciences, government, and business.

[67] The rapid and sustained increases in computing power starting from the second half of the 20th century have had a substantial impact on the practice of statistical science.

For instance, social policy, medical practice, and the reliability of structures like bridges all rely on the proper use of statistics.

There is a general perception that statistical knowledge is all-too-frequently intentionally misused by finding ways to interpret only the data that are favorable to the presenter.

[75] Bar graphs are arguably the easiest diagrams to use and understand, and they can be made either by hand or with simple computer programs.

"[77] To assist in the understanding of statistics Huff proposed a series of questions to be asked in each case:[72] The concept of correlation is particularly noteworthy for the potential confusion it can cause.

Statistical analysis of a data set often reveals that two variables (properties) of the population under consideration tend to vary together, as if they were connected.