# Download PDF Introduction to the practice of statistics : extended version

He found that many of these could be fitted to a normal curve distribution. Galton submitted a paper to Nature in on the usefulness of the median. The actual weight was pounds: the median guess was The guesses were markedly non-normally distributed. Galton's publication of Natural Inheritance in sparked the interest of a brilliant mathematician, Karl Pearson , [29] then working at University College London , and he went on to found the discipline of mathematical statistics.

His work grew to encompass the fields of biology , epidemiology , anthropometry, medicine and social history. In , with Walter Weldon , founder of biometry , and Galton, he founded the journal Biometrika as the first journal of mathematical statistics and biometry. His work, and that of Galton's, underpins many of the 'classical' statistical methods which are in common use today, including the Correlation coefficient , defined as a product-moment; [31] the method of moments for the fitting of distributions to samples; Pearson's system of continuous curves that forms the basis of the now conventional continuous probability distributions; Chi distance a precursor and special case of the Mahalanobis distance [32] and P-value , defined as the probability measure of the complement of the ball with the hypothesized value as center point and chi distance as radius.

He also founded the statistical hypothesis testing theory , [32] Pearson's chi-squared test and principal component analysis. The second wave of mathematical statistics was pioneered by Ronald Fisher who wrote two textbooks, Statistical Methods for Research Workers , published in and The Design of Experiments in , that were to define the academic discipline in universities around the world.

He also systematized previous results, putting them on a firm mathematical footing. In his seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance , the first use to use the statistical term, variance. In , at Rothamsted Experimental Station he started a major study of the extensive collections of data recorded over many years. This resulted in a series of reports under the general title Studies in Crop Variation. In he published The Genetical Theory of Natural Selection where he applied statistics to evolution.

Over the next seven years, he pioneered the principles of the design of experiments see below and elaborated his studies of analysis of variance. He furthered his studies of the statistics of small samples.

## Quiz: Populations, Samples, Parameters, and Statistics

Perhaps even more important, he began his systematic approach of the analysis of real data as the springboard for the development of new statistical methods. He developed computational algorithms for analyzing data from his balanced experimental designs. In , this work resulted in the publication of his first book, Statistical Methods for Research Workers. In , this book was followed by The Design of Experiments , which was also widely used.

In addition to analysis of variance, Fisher named and promoted the method of maximum likelihood estimation. Fisher also originated the concepts of sufficiency , ancillary statistics , Fisher's linear discriminator and Fisher information. His article On a distribution yielding the error functions of several well known statistics presented Pearson's chi-squared test and William Sealy Gosset 's t in the same framework as the Gaussian distribution , and his own parameter in the analysis of variance Fisher's z-distribution more commonly used decades later in the form of the F distribution.

Before this deviations exceeding three times the probable error were considered significant.

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For a symmetrical distribution the probable error is half the interquartile range. Other important contributions at this time included Charles Spearman 's rank correlation coefficient that was a useful extension of the Pearson correlation coefficient. William Sealy Gosset , the English statistician better known under his pseudonym of Student , introduced Student's t-distribution , a continuous probability distribution useful in situations where the sample size is small and population standard deviation is unknown.

Jerzy Neyman in showed that stratified random sampling was in general a better method of estimation than purposive quota sampling. In , while serving as surgeon on HM Bark Salisbury , James Lind carried out a controlled experiment to develop a cure for scurvy. The men were paired, which provided blocking. From a modern perspective, the main thing that is missing is randomized allocation of subjects to treatments.

Lind is today often described as a one-factor-at-a-time experimenter. A theory of statistical inference was developed by Charles S. Peirce in " Illustrations of the Logic of Science " — and " A Theory of Probable Inference " , two publications that emphasized the importance of randomization-based inference in statistics. In another study, Peirce randomly assigned volunteers to a blinded , repeated-measures design to evaluate their ability to discriminate weights.

Peirce's experiment inspired other researchers in psychology and education, which developed a research tradition of randomized experiments in laboratories and specialized textbooks in the s. The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, was pioneered [47] by Abraham Wald in the context of sequential tests of statistical hypotheses.

- Quiz: Populations, Samples, Parameters, and Statistics!
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He was described by Anders Hald as "a genius who almost single-handedly created the foundations for modern statistical science. Perhaps even more important, Fisher began his systematic approach to the analysis of real data as the springboard for the development of new statistical methods. He began to pay particular attention to the labour involved in the necessary computations performed by hand, and developed methods that were as practical as they were founded in rigour.

In , this work culminated in the publication of his first book, Statistical Methods for Research Workers. A methodology for designing experiments was proposed by Ronald A. Fisher , in his innovative book The Design of Experiments which also became a standard. While this sounds like a frivolous application, it allowed him to illustrate the most important ideas of experimental design: see Lady tasting tea. Agricultural science advances served to meet the combination of larger city populations and fewer farms. But for crop scientists to take due account of widely differing geographical growing climates and needs, it was important to differentiate local growing conditions.

To extrapolate experiments on local crops to a national scale, they had to extend crop sample testing economically to overall populations. As statistical methods advanced primarily the efficacy of designed experiments instead of one-factor-at-a-time experimentation , representative factorial design of experiments began to enable the meaningful extension, by inference, of experimental sampling results to the population as a whole. The term Bayesian refers to Thomas Bayes — , who proved a special case of what is now called Bayes' theorem.

However it was Pierre-Simon Laplace — who introduced a general version of the theorem and applied it to celestial mechanics , medical statistics, reliability , and jurisprudence. After the s, inverse probability was largely supplanted [ citation needed ] by a collection of methods that were developed by Ronald A. Fisher , Jerzy Neyman and Egon Pearson. Their methods came to be called frequentist statistics. In the 20th century, the ideas of Laplace were further developed in two different directions, giving rise to objective and subjective currents in Bayesian practice.

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In the objectivist stream, the statistical analysis depends on only the model assumed and the data analysed. In contrast, "subjectivist" statisticians deny the possibility of fully objective analysis for the general case. In the further development of Laplace's ideas, subjective ideas predate objectivist positions.

The idea that 'probability' should be interpreted as 'subjective degree of belief in a proposition' was proposed, for example, by John Maynard Keynes in the early s. Objective Bayesian inference was further developed by Harold Jeffreys at the University of Cambridge. His seminal book "Theory of probability" first appeared in and played an important role in the revival of the Bayesian view of probability. In , Dennis Lindley 's 2-volume work "Introduction to Probability and Statistics from a Bayesian Viewpoint" brought Bayesian methods to a wide audience.

Good , B. In the s, there was a dramatic growth in research and applications of Bayesian methods, mostly attributed to the discovery of Markov chain Monte Carlo methods, which removed many of the computational problems , and an increasing interest in nonstandard, complex applications. From Wikipedia, the free encyclopedia.

Main article: History of probability. See also: Timeline of probability and statistics. This section relies too much on references to primary sources. Please improve this section by adding secondary or tertiary sources. February Learn how and when to remove this template message. See also: List of statisticians and Founders of statistics.

Thomas Bayes George E. Box Pafnuty Chebyshev David R. Peirce Adolphe Quetelet C. Rao Walter A. Thiele John Tukey Abraham Wald. Critical Mass.

Farrar, Straus and Giroux. History of the Peloponnesian War. New York: Penguin Books, Ltd. The American Statistician. The code book : the science of secrecy from ancient Egypt to quantum cryptography 1st Anchor Books ed. New York: Anchor Books. Retrieved on Philosophical Transactions of the Royal Society of London. Harvard University Press. Heyde and E. Seneta , Springer, pp. Peirce Theory of errors of observations.

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Appendix no. In David H. Studies in the history of statistical method. Arno Press. Handbook of statistics. The Mathematics Teacher. Statistical Science. Philosophical Magazine. Series 5. Series 6. Principal Component Analysis, 2nd ed. New York: Springer-Verlag. Hichcock Retrieved Memoirs of the National Academy of Sciences. Stigler November American Journal of Education.

Coast Survey Report : — Reprinted in Collected Papers 7 , paragraphs —, also in Writings 4 , pp. July—August Operations Research. In: Ghosh, S. Bulletin of the American Mathematical Society. New York: Wiley. Fisher: The Life of a Scientist , Wiley. Fisher, Statistical Methods for Research Workers, ".

In Grattan-Guinness, Ivor ed. Landmark writings in Western mathematics Amsterdam Boston: Elsevier. American Educational Research Journal. Fisher and the Design of Experiments, ". Fienberg, When did Bayesian Inference become "Bayesian"? Archived at the Wayback Machine Bayesian Analysis , 1 1 , 1— See page 5.

### Theory and application

Fisher used it in the notes he wrote to accompany the papers in his Contributions to Mathematical Statistics Fisher thought Bayes's argument was all but extinct for the only recent work to take it seriously was Harold Jeffreys 's Theory of Probability In L. Soon after, however, Savage changed from being an unBayesian to being a Bayesian. Reference analysis. Handbook of Statistics. Chichester: Wiley. Berger" , Statistical Science , 9, — doi : Outline Index. Descriptive statistics.

Mean arithmetic geometric harmonic Median Mode. Central limit theorem Moments Skewness Kurtosis L-moments. Index of dispersion. Grouped data Frequency distribution Contingency table. Pearson product-moment correlation Rank correlation Spearman's rho Kendall's tau Partial correlation Scatter plot. Data collection.

Sampling stratified cluster Standard error Opinion poll Questionnaire. Scientific control Randomized experiment Randomized controlled trial Random assignment Blocking Interaction Factorial experiment. Adaptive clinical trial Up-and-Down Designs Stochastic approximation. Cross-sectional study Cohort study Natural experiment Quasi-experiment. Statistical inference. Z -test normal Student's t -test F -test. Bayesian probability prior posterior Credible interval Bayes factor Bayesian estimator Maximum posterior estimator.

Correlation Regression analysis. Pearson product-moment Partial correlation Confounding variable Coefficient of determination. Simple linear regression Ordinary least squares General linear model Bayesian regression. Regression Manova Principal components Canonical correlation Discriminant analysis Cluster analysis Classification Structural equation model Factor analysis Multivariate distributions Elliptical distributions Normal. Spectral density estimation Fourier analysis Wavelet Whittle likelihood.

Tibsharani is a coauthor of both. You can download them for free. The field of machine learning is all about feeding huge amounts of data into algorithms to make accurate predictions. Statistics is concerned with predictions as well, says Tibshirani, but also with determining how confident we can be about the importance of certain inputs. This is because the authors focus on intuition rather than mathematics. He believes this helps them think conceptually. And also, a situation where it might not work. I think people really appreciate that.

Bootstrapping is a way to assess the accuracy of an estimate by generating multiple datasets from the same data. For example, lets say you collected the weights of 1, randomly selected adult women in the US, and found that the average was pounds.