Saturday, July 19, 2014

WHAT IS A POETRY ?

POETRY

poetry, literature that evokes a concentrated imaginative awareness of experience or a specific emotional response through language chosen and arranged for its meaning, sound, and rhythm.
Poetry is a vast subject, as old as history and older, present wherever religion is present, possibly—under some definitions—the primal and primary form of languages themselves. The present article means only to describe in as general a way as possible certain properties of poetry and of poetic thought regarded as in some sense independent modes of the mind. Naturally, not every tradition nor every local or individual variation can be—or need be—included, but the article illustrates by examples of poetry ranging between nursery rhyme and epic. This article considers the difficulty or impossibility of defining poetry; man’s nevertheless familiar acquaintance with it; the differences between poetry and prose; the idea of form in poetry; poetry as a mode of thought; and what little may be said in prose of the spirit of poetry.

Attempts to define poetry

Poetry is the other way of using language. Perhaps in some hypothetical beginning of things it was the only way of using language or simply was language tout court, prose being the derivative and younger rival. Both poetry and language are fashionably thought to have belonged to ritual in early agricultural societies; and poetry in particular, it has been claimed, arose at first in the form of magical spells recited to ensure a good harvest. Whatever the truth of this hypothesis, it blurs a useful distinction: by the time there begins to be a separate class of objects called poems, recognizable as such, these objects are no longer much regarded for their possible yam-growing properties, and such magic as they may be thought capable of has retired to do its business upon the human spirit and not directly upon the natural world outside.
Formally, poetry is recognizable by its greater dependence on at least one more parameter, the line, than appears in prose composition. This changes its appearance on the page; and it seems clear that people take their cue from this changed appearance, reading poetry aloud in a very different voice from their habitual voice, possibly because, as Ben Jonson said, poetry “speaketh somewhat above a mortal mouth.” If, as a test of this description, people are shown poems printed as prose, it most often turns out that they will read the result as prose simply because it looks that way; which is to say that they are no longer guided in their reading by the balance and shift of the line in relation to the breath as well as the syntax.
That is a minimal definition but perhaps not altogether uninformative. It may be all that ought to be attempted in the way of a definition: Poetry is the way it is because it looks that way, and it looks that way because it sounds that way and vice versa.

Poetry and prose

People’s reason for wanting a definition is to take care of the borderline case, and this is what a definition, as if by definition, will not do. That is, if an individual asks for a definition of poetry, it will most certainly not be the case that he has never seen one of the objects called poems that are said to embody poetry; on the contrary, he is already tolerably certain what poetry in the main is, and his reason for wanting a definition is either that his certainty has been challenged by someone else or that he wants to take care of a possible or seeming exception to it: hence the perennial squabble about distinguishing poetry from prose, which is rather like distinguishing rain from snow—everyone is reasonably capable of doing so, and yet there are some weathers that are either-neither.
Sensible things have been said on the question. The poet T.S. Eliot suggested that part of the difficulty lies in the fact that there is the technical term verse to go with the term poetry, while there is no equivalent technical term to distinguish the mechanical part of prose and make the relation symmetrical. The French poet Paul ValĂ©ry said that prose was walking, poetry dancing. Indeed, the original two terms, prosus and versus, meant, respectively, “going straight forth” and “returning”; and that distinction does point up the tendency of poetry to incremental repetition, variation, and the treatment of many matters and different themes in a single recurrent form such as couplet or stanza.
American poet Robert Frost said shrewdly that poetry was what got left behind in translation, which suggests a criterion of almost scientific refinement: when in doubt, translate; whatever comes through is prose, the remainder is poetry. And yet to even so acute a definition the obvious exception is a startling and a formidable one: some of the greatest poetry in the world is in the Authorized or King James Version of the Bible, which is not only a translation but also, as to its appearance in print, identifiable neither with verse nor with prose in English but rather with a cadence owing something to both.
There may be a better way of putting the question by the simple test alluded to above. When people are presented with a series of passages drawn indifferently from poems and stories but all printed as prose, they will show a dominant inclination to identify everything they possibly can as prose. This will be true, surprisingly enough, even if the poem rhymes and will often be true even if the poem in its original typographical arrangement would have been familiar to them. The reason seems to be absurdly plain: readers recognize poetry by its appearance on the page, and they respond to the convention whereby they recognize it by reading it aloud in a quite different tone of voice from that which they apply to prose (which, indeed, they scarcely read aloud at all). It should be added that they make this distinction also without reading aloud; even in silence they confer upon a piece of poetry an attention that differs from what they give to prose in two ways especially: in tone and in pace.

WHAT IS STATISTICS ? MEANING OF STATISTICS

WHAT IS STATISTICS?
Statistics is the mathematical science involved in the application of quantitative principles to the collection, analysis, and presentation of numerical data. The practice of statistics utilizes data from some population in order to describe it meaningfully, to draw conclusions from it, and make informed decisions. The population may be a community, an organization, a production line, a service counter, or a phenomenon such as the weather. Statisticians determine which quantitative model is correct for a given type of problem and they decide what kinds of data should be collected and examined. Applied statistics concerns the application of the general methodology to particular problems. This often calls for use of the techniques of computer-based data analysis. Some examples of statistical problems are:

  • Interpretation of evidence linking environmental factors and disease,
  • Design of experiments to evaluate effectiveness of pharmaceuticals,
  • Mining data to discover target segments in the population,
  • Market research to estimate demand for a new product,
  • Opinion polling in politics,
  • Estimation of the size of an animal population to aid in establishing regulations for conservation,
  • Reliability studies for determining warranties,
  • Improving the quality of a service or manufactured item,
  • Weather forecasting,
  • Analysis of errors in scientific experiments, and
  • Prediction of stock market prices.
  • Statisticians are key contributors to scientific methodologies. They use their quantitative knowledge to the design data collection schemes, process the data, analyze the data, and interpret the results. Further, statisticians often make critical evaluations on the reliability of data and whether inferences drawn from can be made confidently. They also help to identify misleading abuses of data that may be portraying an inaccurate account of a situation.
    Theoretical statistics concerns general classes of problems and the development of general methodology. Statisticians generally develop models based on probability theory. Probability theory is the branch of mathematics which develops models for "chance variations" or "random phenomena." It originated as a discipline when mathematicians of the 17th century began calculating the odds in various games of chance. It was soon realized how to make applications of the theory they developed to the study of errors in experimental measurements and to the study of human mortality (for example, by life insurance companies). Probability theory is now a major field with widespread applications in science and engineering. A few examples are:

  • Modeling the occurrence of sunspots to improve radio communication,
  • Modeling and control of congestion on highways, and
  • Reliability theory to evaluate the chance that a space vehicle will function throughout a mission.
  • According to the American Statistical Association, job characteristics of persons in the statistical professions include the following activities:
  • Use data to solve problems in a wide variety of fields,
  • Apply mathematical and statistical knowledge to social, economic, medical, political, and ecological problems,
  • Work individually and/or as part of an interdisciplinary team,
  • Travel to consult with other professionals or attend conferences, seminars, and continuing education activities, and
  • Advance the frontiers of statistics and probability through education and research.
  • STATISTICS

    STATISTICS

    More probability density is found as one gets closer to the expected (mean) value in a normal distribution. Statistics used in standardized testing assessment are shown. The scales include standard deviations, cumulative percentages, percentile equivalents, Z-scores, T-scores, standard nines, and percentages in standard nines.
    Statistics is the study of the collection, organization, analysis, interpretation and presentation of data.[1] It deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.[1] When analyzing data, it is possible to use one of two statistics methodologies: descriptive statistics or inferential statistics.[2]

    Scope

    Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data,[3] or as a branch of mathematics.[4] Some consider statistics to be a distinct mathematical science rather than a branch of mathematics.[vague][5][6]

    Mathematical statistics

    Mathematical statistics is the application of mathematics to statistics, which was originally conceived as the science of the state — the collection and analysis of facts about a country: its economy, land, military, population, and so forth. Mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory.[7][8]

    Overview

    In applying statistics to e.g. a scientific, industrial, or societal problem, it is necessary to begin with a population or process to be studied. Populations can be diverse topics such as "all persons living in a country" or "every atom composing a crystal".
    Ideally, statisticians compile data about the entire population (an operation called census). This may be organized by governmental statistical institutes. Descriptive statistics can be used to summarize the population data. Numerical descriptors include mean and standard deviation for continuous data types (like income), while frequency and percentage are more useful in terms of describing categorical data (like race).
    When a census is not feasible, a chosen subset of the population called a sample is studied. Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or experimental setting. Again, descriptive statistics can be used to summarize the sample data. However, the drawing of the sample has been subject to an element of randomness, hence the established numerical descriptors from the sample are also due to uncertainty. In order to still draw meaningful conclusions about the entire population, inferential statistics is needed. It uses patterns in the sample data to draw inferences about the population represented, accounting for randomness. These inferences may take the form of: answering yes/no questions about the data (hypothesis testing), estimating numerical characteristics of the data (estimation), describing associations within the data (correlation) and modeling relationships within the data (for example, using regression analysis). Inference can extend to forecasting, prediction and estimation of unobserved values either in or associated with the population being studied; it can include extrapolation and interpolation of time series or spatial data, and can also include data mining.

    Data collection

    Sampling

    In case census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting the use of data through statistical models. To use a sample as a guide to an entire population, it is important that it truly represent the overall population. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. A major problem lies in determining the extent that the sample chosen is actually representative. Statistics offers methods to estimate and correct for any random trending within the sample and data collection procedures. There are also methods of experimental design for experiments that can lessen these issues at the outset of a study, strengthening its capability to discern truths about the population.
    Sampling theory is part of the mathematical discipline of probability theory. Probability is used in "mathematical statistics" (alternatively, "statistical theory") to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures. The use of any statistical method is valid when the system or population under consideration satisfies the assumptions of the method. The difference in point of view between classic probability theory and sampling theory is, roughly, that probability theory starts from the given parameters of a total population to deduce probabilities that pertain to samples. Statistical inference, however, moves in the opposite direction—inductively inferring from samples to the parameters of a larger or total population.

    Experimental and observational studies

    A common goal for a statistical research project is to investigate causality, and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables or response. There are two major types of causal statistical studies: experimental studies and observational studies. In both types of studies, the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies in how the study is actually conducted. Each can be very effective. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation. Instead, data are gathered and correlations between predictors and response are investigated. While the tools of data analysis work best on data from randomized studies, they are also applied to other kinds of data – like natural experiments and observational studies[9] – for which a statistician would use a modified, more structured estimation method (e.g., Difference in differences estimation and instrumental variables, among many others) that will produce consistent estimators.

    Experiments

    The basic steps of a statistical experiment are:
    1. Planning the research, including finding the number of replicates of the study, using the following information: preliminary estimates regarding the size of treatment effects, alternative hypotheses, and the estimated experimental variability. Consideration of the selection of experimental subjects and the ethics of research is necessary. Statisticians recommend that experiments compare (at least) one new treatment with a standard treatment or control, to allow an unbiased estimate of the difference in treatment effects.
    2. Design of experiments, using blocking to reduce the influence of confounding variables, and randomized assignment of treatments to subjects to allow unbiased estimates of treatment effects and experimental error. At this stage, the experimenters and statisticians write the experimental protocol that shall guide the performance of the experiment and that specifies the primary analysis of the experimental data.
    3. Performing the experiment following the experimental protocol and analyzing the data following the experimental protocol.
    4. Further examining the data set in secondary analyses, to suggest new hypotheses for future study.
    5. Documenting and presenting the results of the study.
    Experiments on human behavior have special concerns. The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of the Western Electric Company. The researchers were interested in determining whether increased illumination would increase the productivity of the assembly line workers. The researchers first measured the productivity in the plant, then modified the illumination in an area of the plant and checked if the changes in illumination affected productivity. It turned out that productivity indeed improved (under the experimental conditions). However, the study is heavily criticized today for errors in experimental procedures, specifically for the lack of a control group and blindness. The Hawthorne effect refers to finding that an outcome (in this case, worker productivity) changed due to observation itself. Those in the Hawthorne study became more productive not because the lighting was changed but because they were being observed.[10]

    Observational study

    An example of an observational study is one that explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case, the researchers would collect observations of both smokers and non-smokers, perhaps through a case-control study, and then look for the number of cases of lung cancer in each group.

    Type of data

    Various attempts have been made to produce a taxonomy of levels of measurement. The psychophysicist Stanley Smith Stevens defined nominal, ordinal, interval, and ratio scales. Nominal measurements do not have meaningful rank order among values, and permit any one-to-one transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and permit any order-preserving transformation. Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit), and permit any linear transformation. Ratio measurements have both a meaningful zero value and the distances between different measurements defined, and permit any rescaling transformation.
    Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature. Such distinctions can often be loosely correlated with data type in computer science, in that dichotomous categorical variables may be represented with the Boolean data type, polytomous categorical variables with arbitrarily assigned integers in the integral data type, and continuous variables with the real data type involving floating point computation. But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented.
    Other categorizations have been proposed. For example, Mosteller and Tukey (1977)[11] distinguished grades, ranks, counted fractions, counts, amounts, and balances. Nelder (1990)[12] described continuous counts, continuous ratios, count ratios, and categorical modes of data. See also Chrisman (1998),[13] van den Berg (1991).[14]
    The issue of whether or not it is appropriate to apply different kinds of statistical methods to data obtained from different kinds of measurement procedures is complicated by issues concerning the transformation of variables and the precise interpretation of research questions. "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. Whether or not a transformation is sensible to contemplate depends on the question one is trying to answer" (Hand, 2004, p. 82).[15]

    Terminology and theory of inferential statistics

    Statistics, estimators and pivotal quantities

    Consider an independent identically distributed (iid) random variables with a given probability distribution: standard statistical inference and estimation theory defines a random sample as the random vector given by the column vector of these iid variables.[16] The population being examined is described by a probability distribution which may have unknown parameters.
    A statistic is random variable which is a function of the random sample, but not a function of unknown parameters. The probability distribution of the statistics, though, may have unknown parameters.
    Consider now a function of the unknown parameter: an estimator is a statistic used to estimate such function. Commonly used estimators include sample mean, unbiased sample variance and sample covariance.
    A random variable which is a function of the random sample and of the unknown parameter, but whose probability distribution does not depend on the unknown parameter is called a pivotal quantity or pivot. Widely used pivots include the z-score, the chi square statistic and Student's t-value.
    Between two estimators of a given parameter, the one with lower mean squared error is said to be more efficient. Furthermore an estimator is said to be unbiased if it's expected value is equal to the true value of the unknown parameter which is being estimated and asymptotically unbiased if its expected value converges at the limit to the true value of such parameter.
    Other desirable properties for estimators include: UMVUE estimators which have the lowest variance for all possible values of the parameter to be estimated (this is usually an easier property to verify than efficiency) and consistent estimators which converges in probability to the true value of such parameter.
    This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed: the method of moments, the maximum likelihood method, the least squares method and the more recent method of estimating equations.

    Null hypothesis and alternative hypothesis

    Interpretation of statistical information can often involve the development of a null hypothesis in that the assumption is that whatever is proposed as a cause has no effect on the variable being measured.
    The best illustration for a novice is the predicament encountered by a jury trial. The null hypothesis, H0, asserts that the defendant is innocent, whereas the alternative hypothesis, H1, asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H0 (status quo) stands in opposition to H1 and is maintained unless H1 is supported by evidence "beyond a reasonable doubt". However, "failure to reject H0" in this case does not imply innocence, but merely that the evidence was insufficient to convict. So the jury does not necessarily accept H0 but fails to reject H0. While one can not "prove" a null hypothesis, one can test how close it is to being true with a power test, which tests for type II errors.
    What statisticians call a alternative hypothesis is simply an hypothesis which contradicts the null hypothesis.

    Error

    Working from a null hypothesis two basic forms of error are recognized:
    • Type I errors where the null hypothesis is falsely rejected giving a "false positive".
    • Type II errors where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a "false negative".
    Standard deviation refers to the extent to which individual observations in a sample differ from a central value, such as the sample or population mean, while Standard error refers to an estimate of difference between sample mean and population mean.
    A statistical error is the amount by which an observation differs from its expected value, a residual is the amount an observation differs from the value the estimator of the expected value assumes on a given sample (also called prediction).
    Mean squared error is used for obtaining efficient estimators, a widely used class of estimators. Root mean square error is simply the square root of mean squared error.
    Many statistical methods seek to minimize the residual sum of squares, and these are called "methods of least squares" in contrast to Least absolute deviations. The later gives equal weight to small and big errors, while the former gives more weight to large errors. Residual sum of squares is also differentiable, which provides a handy property for doing regression. Least squares applied to linear regression is called ordinary least squares method and least squares applied to nonlinear regression is called non-linear least squares. Also in a linear regression model the non deterministic part of the model is called error term, disturbance or more simply noise.
    Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other important types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data and/or censoring may result in biased estimates and specific techniques have been developed to address these problems.[17]

    Interval estimation

    Main article: Interval estimation
    Most studies only sample part of a population, so results don't fully represent the whole population. Any estimates obtained from the sample only approximate the population value. Confidence intervals allow statisticians to express how closely the sample estimate matches the true value in the whole population. Often they are expressed as 95% confidence intervals. Formally, a 95% confidence interval for a value is a range where, if the sampling and analysis were repeated under the same conditions (yielding a different dataset), the interval would include the true (population) value in 95% of all possible cases. This does not imply that the probability that the true value is in the confidence interval is 95%. From the frequentist perspective, such a claim does not even make sense, as the true value is not a random variable. Either the true value is or is not within the given interval. However, it is true that, before any data are sampled and given a plan for how to construct the confidence interval, the probability is 95% that the yet-to-be-calculated interval will cover the true value: at this point, the limits of the interval are yet-to-be-observed random variables. One approach that does yield an interval that can be interpreted as having a given probability of containing the true value is to use a credible interval from Bayesian statistics: this approach depends on a different way of interpreting what is meant by "probability", that is as a Bayesian probability.
    In principle confidence intervals can be symmetrical or asymmetrical. An interval can be asymmetrical because it works as lower or upper bound for a parameter (left-sided interval or right sided interval), but it can also be asymmetrical because the two sided interval is built violating symmetry around the estimate. Sometimes the bounds for a confidence interval are reached asymptotically and these are used to approximate the true bounds.

    Significance

    Statistics rarely give a simple Yes/No type answer to the question asked of them. Interpretation often comes down to the level of statistical significance applied to the numbers and often refers to the probability of a value accurately rejecting the null hypothesis (sometimes referred to as the p-value).
    Referring to statistical significance does not necessarily mean that the overall result is significant in real world terms. For example, in a large study of a drug it may be shown that the drug has a statistically significant but very small beneficial effect, such that the drug is unlikely to help the patient noticeably.
    Criticisms arise because the hypothesis testing approach forces one hypothesis (the null hypothesis) to be "favored," and can also seem to exaggerate the importance of minor differences in large studies. A difference that is highly statistically significant can still be of no practical significance, but it is possible to properly formulate tests in account for this. (See also criticism of hypothesis testing.)
    One response involves going beyond reporting only the significance level to include the p-value when reporting whether a hypothesis is rejected or accepted. The p-value, however, does not indicate the size of the effect. A better and increasingly common approach is to report confidence intervals. Although these are produced from the same calculations as those of hypothesis tests or p-values, they describe both the size of the effect and the uncertainty surrounding it.

    Examples

    Some well-known statistical tests and procedures are:

    Misuse of statistics

    Main article: Misuse of statistics
    Misuse of statistics can produce subtle, but serious errors in description and interpretation—subtle in the sense that even experienced professionals make such errors, and serious in the sense that they can lead to devastating decision errors. For instance, social policy, medical practice, and the reliability of structures like bridges all rely on the proper use of statistics.
    Even when statistical techniques are correctly applied, the results can be difficult to interpret for those lacking expertise. The statistical significance of a trend in the data—which measures the extent to which a trend could be caused by random variation in the sample—may or may not agree with an intuitive sense of its significance. The set of basic statistical skills (and skepticism) that people need to deal with information in their everyday lives properly is referred to as statistical literacy.
    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.[18] A mistrust and misunderstanding of statistics is associated with the quotation, "There are three kinds of lies: lies, damned lies, and statistics". Misuse of statistics can be both inadvertent and intentional, and the book How to Lie with Statistics[18] outlines a range of considerations. In an attempt to shed light on the use and misuse of statistics, reviews of statistical techniques used in particular fields are conducted (e.g. Warne, Lazo, Ramos, and Ritter (2012)).[19]
    Ways to avoid misuse of statistics include using proper diagrams and avoiding bias.[20] Misuse can occur when conclusions are overgeneralized and claimed to be representative of more than they really are, often by either deliberately or unconsciously overlooking sampling bias.[21] Bar graphs are arguably the easiest diagrams to use and understand, and they can be made either by hand or with simple computer programs.[20] Unfortunately, most people do not look for bias or errors, so they are not noticed. Thus, people may often believe that something is true even if it is not well represented.[21] To make data gathered from statistics believable and accurate, the sample taken must be representative of the whole.[22] According to Huff, "The dependability of a sample can be destroyed by [bias]... allow yourself some degree of skepticism."[23]
    To assist in the understanding of statistics Huff proposed a series of questions to be asked in each case:[23]
    • Who says so? (Does he/she have an axe to grind?)
    • How does he/she know? (Does he/she have the resources to know the facts?)
    • What’s missing? (Does he/she give us a complete picture?)
    • Did someone change the subject? (Does he/she offer us the right answer to the wrong problem?)
    • Does it make sense? (Is his/her conclusion logical and consistent with what we already know?)

    Misinterpretation: correlation

    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. For example, a study of annual income that also looks at age of death might find that poor people tend to have shorter lives than affluent people. The two variables are said to be correlated; however, they may or may not be the cause of one another. The correlation phenomena could be caused by a third, previously unconsidered phenomenon, called a lurking variable or confounding variable. For this reason, there is no way to immediately infer the existence of a causal relationship between the two variables. (See Correlation does not imply causation.)

    History of statistical science

    R A Fisher is the founder of Statistics.
    Statistical methods date back at least to the 5th century BC.
    Some scholars pinpoint the origin of statistics to 1663, with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt.[24] 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. Today, statistics is widely employed in government, business, and natural and social sciences.
    Its mathematical foundations were laid in the 17th century with the development of the probability theory by Blaise Pascal and Pierre de Fermat. Mathematical probability theory arose from the study of games of chance, although the concept of probability was already examined in medieval law and by philosophers such as Juan Caramuel.[25] The method of least squares was first described by Adrien-Marie Legendre in 1805.
    Karl Pearson, the founder of mathematical statistics.
    The modern field of statistics emerged in the late 19th and early 20th century in three stages.[26] The first wave, at the turn of the century, was led by the work of Sir 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 to the field included introducing the concepts of standard deviation, correlation, regression and the application of these methods to the study of the variety of human characteristics – height, weight, eyelash length among others.[27] Pearson developed the Correlation coefficient, defined as a product-moment,[28] the method of moments for the fitting of distributions to samples and the Pearson's system of continuous curves, among many other things.[29] Galton and Pearson founded Biometrika as the first journal of mathematical statistics and biometry, and the latter founded the world's first university statistics department at University College London.[30]
    The second wave of the 1910s and 20s was initiated by William Gosset, and reached its culmination in the insights of Sir Ronald Fisher, who wrote the textbooks that were to define the academic discipline in universities around the world. Fisher's most important publications were his 1916 seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance and his classic 1925 work Statistical Methods for Research Workers. His paper was the first to use the statistical term, variance. He developed rigorous experimental models and also originated the concepts of sufficiency, ancillary statistics, Fisher's linear discriminator and Fisher information.[31]
    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. They introduced the concepts of "Type II" error, power of a test and confidence intervals. Jerzy Neyman in 1934 showed that stratified random sampling was in general a better method of estimation than purposive (quota) sampling.[32] Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a collated body of data and for making decisions in the face of uncertainty based on statistical methodology. The use of modern computers has expedited large-scale statistical computations, and has also made possible new methods that are impractical to perform manually.

    Trivia

    Applied statistics, theoretical statistics and mathematical statistics

    "Applied statistics" comprises descriptive statistics and the application of inferential statistics.[33][verification needed] Theoretical statistics concerns both the logical arguments underlying justification of approaches to statistical inference, as well encompassing mathematical statistics. Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to methods of estimation and inference, but also various aspects of computational statistics and the design of experiments.

    Machine learning and data mining

    Statistics has many ties to machine learning and data mining.

    Statistics in society

    Statistics is applicable to a wide variety of academic disciplines, including natural and social sciences, government, and business. Statistical consultants can help organizations and companies that don't have in-house expertise relevant to their particular questions.

    Statistical computing

    gretl, an example of an open source statistical package
    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. Early statistical models were almost always from the class of linear models, but powerful computers, coupled with suitable numerical algorithms, caused an increased interest in nonlinear models (such as neural networks) as well as the creation of new types, such as generalized linear models and multilevel models.
    Increased computing power has also led to the growing popularity of computationally intensive methods based on resampling, such as permutation tests and the bootstrap, while techniques such as Gibbs sampling have made use of Bayesian models more feasible. The computer revolution has implications for the future of statistics with new emphasis on "experimental" and "empirical" statistics. A large number of both general and special purpose statistical software are now available.

    Statistics applied to mathematics or the arts

    Traditionally, statistics was concerned with drawing inferences using a semi-standardized methodology that was "required learning" in most sciences. This has changed with use of statistics in non-inferential contexts. What was once considered a dry subject, taken in many fields as a degree-requirement, is now viewed enthusiastically.[according to whom?] Initially derided by some mathematical purists, it is now considered essential methodology in certain areas.
    • In number theory, scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns, which may then lead to hypotheses.
    • Methods of statistics including predictive methods in forecasting are combined with chaos theory and fractal geometry to create video works that are considered to have great beauty.
    • The process art of Jackson Pollock relied on artistic experiments whereby underlying distributions in nature were artistically revealed.[citation needed] With the advent of computers, statistical methods were applied to formalize such distribution-driven natural processes to make and analyze moving video art.[citation needed]
    • Methods of statistics may be used predicatively in performance art, as in a card trick based on a Markov process that only works some of the time, the occasion of which can be predicted using statistical methodology.
    • Statistics can be used to predicatively create art, as in the statistical or stochastic music invented by Iannis Xenakis, where the music is performance-specific. Though this type of artistry does not always come out as expected, it does behave in ways that are predictable and tunable using statistics.

    Specialized disciplines

    Statistical techniques are used in a wide range of types of scientific and social research, including: biostatistics, computational biology, computational sociology, network biology, social science, sociology and social research. Some fields of inquiry use applied statistics so extensively that they have specialized terminology. These disciplines include:
    In addition, there are particular types of statistical analysis that have also developed their own specialised terminology and methodology:
    Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systems variability, control processes (as in statistical process control or SPC), for summarizing data, and to make data-driven decisions. In these roles, it is a key tool, and perhaps the only reliable tool.

    See also

    Main article: Outline of statistics
    Foundations and major areas of statistics

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