Statistics - Knowledge

2049: 9004: 8627: 8025: 91: 841: 300: 38: 1886: 341: 2374: 1975: 8639: 8011: 905: 1455: 361: 2586: 728: 8663: 8049: 8651: 8037: 1195:. 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 2002:. 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 1163:. 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 2345:

and claimed to be representative of more than they really are, often by either deliberately or unconsciously overlooking sampling bias. Bar graphs are arguably the easiest diagrams to use and understand, and they can be made either by hand or with simple computer programs. Most people do not look for

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defined nominal, ordinal, interval, and ratio scales. Nominal measurements do not have meaningful rank order among values, and permit any one-to-one (injective) transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and

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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

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An example of an observational study is one that explores the association 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

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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

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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

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Other categorizations have been proposed. For example, Mosteller and Tukey (1977) distinguished grades, ranks, counted fractions, counts, amounts, and balances. Nelder (1990) described continuous counts, continuous ratios, count ratios, and categorical modes of data. (See also: Chrisman (1998), van

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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

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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

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Traditionally, statistics was concerned with drawing inferences using a semi-standardized methodology that was "required learning" in most sciences. This tradition has changed with the use of statistics in non-inferential contexts. What was once considered a dry subject, taken in many fields as a

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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

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Statistics rarely give a simple Yes/No type answer to the question under analysis. 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

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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

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of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized:

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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."

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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

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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 bias within the sample and data

1251:. 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. 619:

setting. Again, descriptive statistics can be used to summarize the sample data. However, drawing the sample contains an element of randomness; hence, the numerical descriptors from the sample are also prone to uncertainty. To draw meaningful conclusions about the entire population,

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to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of

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relied on artistic experiments whereby underlying distributions in nature were artistically revealed. With the advent of computers, statistical methods were applied to formalize such distribution-driven natural processes to make and analyze moving video

532:(null hypothesis fails to be rejected when an it is in fact false, giving a "false negative"). Multiple problems have come to be associated with this framework, ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis. 1082:

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

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is the largest p-value that allows the test to reject the null hypothesis. This test is logically equivalent to saying that the p-value is the probability, assuming the null hypothesis is true, of observing a result at least as extreme as the

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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

2350:. To make data gathered from statistics believable and accurate, the sample taken must be representative of the whole. According to Huff, "The dependability of a sample can be destroyed by ... allow yourself some degree of skepticism." 2605:

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

837:. 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. 1329:

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.

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has expedited large-scale statistical computations and has also made possible new methods that are impractical to perform manually. Statistics continues to be an area of active research, for example on the problem of how to analyze

2143:) to be favored, since what is being evaluated is the probability of the observed result given the null hypothesis and not probability of the null hypothesis given the observed result. An alternative to this approach is offered by 2072:

is the set of values of the estimator that leads to refuting the null hypothesis. The probability of type I error is therefore the probability that the estimator belongs to the critical region given that null hypothesis is true

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or process to be studied. Populations can be diverse topics, such as "all people living in a country" or "every atom composing a crystal". Ideally, statisticians compile data about the entire population (an operation called a

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rather than a branch of mathematics. While many scientific investigations make use of data, statistics is generally concerned with the use of data in the context of uncertainty and decision-making in the face of uncertainty.

2334:, 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)). 1933:, which also describes the variance in a prediction of the dependent variable (y axis) as a function of the independent variable (x axis) and the deviations (errors, noise, disturbances) from the estimated (fitted) curve. 2108:

A difference that is highly statistically significant can still be of no practical significance, but it is possible to properly formulate tests to account for this. One response involves going beyond reporting only the

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in 1749 who started using the term as a collection of quantitative information, in the modern use for this science. The earliest writing containing statistics in Europe dates back to 1663, with the publication of

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are needed. It uses patterns in the sample data to draw inferences about the population represented while accounting for randomness. These inferences may take the form of answering yes/no questions about the data

5518:. There is growing determination to reform statistical analysis... Some suggest changing statistical methods, whereas others would do away with a threshold for defining "significant" results." (p. 63.) 3354: 923:, 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 974: 2421:

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

476:, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a 2653:

more feasible. The computer revolution has implications for the future of statistics with a new emphasis on "experimental" and "empirical" statistics. A large number of both general and special purpose

889:. This was the first book where the realm of games of chance and the realm of the probable (which concerned opinion, evidence, and argument) were combined and submitted to mathematical analysis. The 1929:. Also in a linear regression model the non deterministic part of the model is called error term, disturbance or more simply noise. Both linear regression and non-linear regression are addressed in 3972:"On the Criterion that a given System of Deviations from the Probable in the Case of a Correlated System of Variables is such that it can be reasonably supposed to have arisen from Random Sampling" 5184: 1390:), 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. 1136:

collection procedures. 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.

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between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, an

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is another type of observational study in which people with and without the outcome of interest (e.g. lung cancer) are invited to participate and their exposure histories are collected.

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and production and operations, including services improvement and marketing research. A study of two journals in tropical biology found that the 12 most frequent statistical tests are:

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ii. 19, "We may speak of this hypothesis as the 'null hypothesis', and the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation."

2863:, 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. 1985:

Most studies only sample part of a population, so results do not fully represent the whole population. Any estimates obtained from the sample only approximate the population value.

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or importance of the observed effect and can also seem to exaggerate the importance of minor differences in large studies. A better and increasingly common approach is to report

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permit any order-preserving transformation. Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary (as in the case with

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Statistical measurement processes are also prone to error in regards to the data that they generate. Many of these errors are classified as random (noise) or systematic (

972:, who wrote the textbooks that were to define the academic discipline in universities around the world. Fisher's most important publications were his 1918 seminal paper 2814:

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.

9044: 2077:) and the probability of type II error is the probability that the estimator does not belong to the critical region given that the alternative hypothesis is true. The 1591:. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. 5394: 1716:

estimators that 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

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The modern field of statistics emerged in the late 19th and early 20th century in three stages. The first wave, at the turn of the century, was led by the work of

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degree-requirement, is now viewed enthusiastically. Initially derided by some mathematical purists, it is now considered essential methodology in certain areas.

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by finding ways to interpret only the data that are favorable to the presenter. A mistrust and misunderstanding of statistics is associated with the quotation, "

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and the application of these methods to the study of the variety of human characteristics—height, weight and eyelash length among others. Pearson developed the

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Planning the research, including finding the number of replicates of the study, using the following information: preliminary estimates regarding the size of

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using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve

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Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systems variability, control processes (as in

8694: 2573:, and correlation. Modern fundamental statistical courses for undergraduate students focus on correct test selection, results interpretation, and use of 121: 4372:

Neyman, J (1934). "On the two different aspects of the representative method: The method of stratified sampling and the method of purposive selection".

1203:. Instead, data are gathered and correlations between predictors and response are investigated. While the tools of data analysis work best on data from 8816: 5161: 1393:

Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as

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This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed: the

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around the estimate. Sometimes the bounds for a confidence interval are reached asymptotically and these are used to approximate the true bounds.

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is studied. Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or

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Edwards, A.W.F. (2000) Perspectives: Anecdotal, Historical and Critical Commentaries on Genetics. The Genetics Society of America (154) 1419:1426

8687: 8087: 7146: 2218: 1433:. But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented. 936: 5544: 8846: 7651: 4183: 1905:. The latter gives equal weight to small and big errors, while the former gives more weight to large errors. Residual sum of squares is also 327: 3409: 3056:

In addition, there are particular types of statistical analysis that have also developed their own specialised terminology and methodology:

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is the amount an observation differs from the value the estimator of the expected value assumes on a given sample (also called prediction).

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refers to the extent to which individual observations in a sample differ from a central value, such as the sample or population mean, while

1079:. Jerzy Neyman in 1934 showed that stratified random sampling was in general a better method of estimation than purposive (quota) sampling. 830:. Early applications of statistical thinking revolved around the needs of states to base policy on demographic and economic data, hence its 3175: 1643:. The probability distribution of the statistic, though, may have unknown parameters. Consider now a function of the unknown parameter: an 561:

Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of

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Fisher|1971|loc=Chapter II. The Principles of Experimentation, Illustrated by a Psycho-physical Experiment, Section 8. The Null Hypothesis

2006:. 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 7801: 2873: 440:. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An 7425: 6066: 2555: 2228: 1679: 1406: 5566: 4785: 5721:. Developed by Rice University (Lead Developer), University of Houston Clear Lake, Tufts University, and National Science Foundation. 4287: 3170: 2283:

can be used or not, but primarily EDA is for seeing what the data can tell us beyond the formal modeling or hypothesis testing task.

1948:), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of 1402: 1024: 1865: 1857: 1850: 1782:" in this case does not imply innocence, but merely that the evidence was insufficient to convict. So the jury does not necessarily 1131:

To use a sample as a guide to an entire population, it is important that it truly represents the overall population. Representative

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Even when statistical techniques are correctly applied, the results can be difficult to interpret for those lacking expertise. The

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The final wave, which mainly saw the refinement and expansion of earlier developments, emerged from the collaborative work between

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experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation". In his 1930 book

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where the null hypothesis fails to be rejected and an actual difference between populations is missed, giving a "false negative".

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Stanley, Julian C. (1966). "The Influence of Fisher's "The Design of Experiments" on Educational Research Thirty Years Later".

3201: 3165: 1990:(yielding a different dataset), the interval would include the true (population) value in 95% of all possible cases. This does 1981:: the red line is true value for the mean in this example, the blue lines are random confidence intervals for 100 realizations. 62: 57: 5351: 5336: 539:), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of 8874: 8869: 5380: 5115: 4951: 4705: 4449: 3814: 3572: 3537: 3508: 3487: 3348: 3080: 500:) characterizes the extent to which members of the distribution depart from its center and each other. Inferences made using 5577: 4333: 3875: 3578: 3384: 8450: 6061: 5761: 2531: 2486:

models are statistical and probabilistic models that capture patterns in the data through use of computational algorithms.

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A random variable that is a function of the random sample and of the unknown parameter, but whose probability distribution

706: 263: 2425:. For this reason, there is no way to immediately infer the existence of a causal relationship between the two variables. 404:, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of 8791: 8746: 6665: 5813: 5734: 3756: 3454: 2101: 1755:

which is usually (but not necessarily) that no relationship exists among variables or that no change occurred over time.

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Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as

871:. Although the idea of probability was already examined in ancient and medieval law and philosophy (such as the work of 8976: 8916: 8889: 8595: 8080: 5595: 5587: 5533: 5304: 5217: 5095: 4529: 3869: 3831: 3738: 2703: 1312:. The researchers were interested in determining whether increased illumination would increase the productivity of the 689:

Mathematical statistics is the application of mathematics to statistics. Mathematical techniques used for this include

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are now available. Examples of available software capable of complex statistical computation include programs such as

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may be correlated, not because there is causal relationship between them, but because both depend on a third variable

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bias or errors, so they are not noticed. Thus, people may often believe that something is true even if it is not well

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Andersson, M. and Simmons, L.W. (2006) Sexual selection and mate choice. Trends, Ecology and Evolution (21) 296:302

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Warne, R. Lazo; Ramos, T.; Ritter, N. (2012). "Statistical Methods Used in Gifted Education Journals, 2006–2010".

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can help organizations and companies that do not have in-house expertise relevant to their particular questions.

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Increased computing power has also led to the growing popularity of computationally intensive methods based on

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of a test is the probability that it correctly rejects the null hypothesis when the null hypothesis is false.

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The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H

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of the unknown parameter being estimated, and asymptotically unbiased if its expected value converges at the

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Lydia Denworth, "A Significant Problem: Standard scientific methods are under fire. Will anything change?",

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is the set of values to the right of the observed data point (observed value of the test statistic) and the

408:. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a 8836: 8796: 8655: 7529: 7478: 7463: 7453: 7322: 7194: 7161: 6987: 6942: 6772: 5724: 4569:(1990). The knowledge needed to computerise the analysis and interpretation of statistical information. In 3185: 2655: 2559: 2461:

necessary for deriving results related to methods of estimation and inference, but also various aspects of

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To assist in the understanding of statistics Huff proposed a series of questions to be asked in each case:

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sense is the process of using and analyzing those statistics. Descriptive statistics is distinguished from

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J. Franklin, The Science of Conjecture: Evidence and Probability before Pascal, Johns Hopkins Univ Pr 2002

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of treatment effects and experimental error. At this stage, the experimenters and statisticians write the

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Palacios, Bernardo; Rosario, Alfonso; Wilhelmus, Monica M.; Zetina, Sandra; Zenit, Roberto (2019-10-30).

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when reporting whether a hypothesis is rejected or accepted. The p-value, however, does not indicate the

2015: 1583:, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is 1472: 1287: 1275: 1204: 1160: 156: 77: 67: 20: 8994: 8936: 8906: 8141: 7758: 7730: 7725: 7473: 7232: 7138: 7118: 7026: 6737: 6555: 6038: 5910: 4875: 3655:

Broemeling, Lyle D. (1 November 2011). "An Account of Early Statistical Inference in Arab Cryptology".

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Statistical techniques are used in a wide range of types of scientific and social research, including:

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that only works some of the time, the occasion of which can be predicted using statistical methodology.

2774: 2642: 2326: 2097:. Therefore, the smaller the significance level, the lower the probability of committing type I error. 1422: 1167:

probabilities that pertain to samples. Statistical inference, however, moves in the opposite direction—

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Numerous texts are available, reflecting the scope and reach of the discipline in the business world:

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may result in biased estimates and specific techniques have been developed to address these problems.

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Rubin, Donald B.; Little, Roderick J.A., Statistical analysis with missing data, New York: Wiley 2002

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Although in principle the acceptable level of statistical significance may be subject to debate, the

2069: 2057: 1902: 1766:, asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H 1430: 1216: 1068: 990: 958: 957:(then called biometry), and the latter founded the world's first university statistics department at 278: 268: 258: 4362:

Gayon, J. (2010) Sexual selection: Another Darwinian process. Comptes Rendus Biologies (333) 134:144

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When full census data cannot be collected, statisticians collect sample data by developing specific

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as a mathematical discipline only took shape at the very end of the 17th century, particularly in

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Further examining the data set in secondary analyses, to suggest new hypotheses for future study.

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in 1589 with reference to a collection of facts and information about a state, it was the German

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The dependability of a sample can be destroyed by ... allow yourself some degree of skepticism.

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is particularly noteworthy for the potential confusion it can cause. Statistical analysis of a

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heavily criticized today for errors in experimental procedures, specifically for the lack of a

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imply that the probability that the true value is in the confidence interval is 95%. From the

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Does it make sense? (Is his/her conclusion logical and consistent with what we already know?)

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Did someone change the subject? (Does he/she offer us the right answer to the wrong problem?)

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There is a general perception that statistical knowledge is all-too-frequently intentionally

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being examined is described by a probability distribution that may have unknown parameters.

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in computer science, in that dichotomous categorical variables may be represented with the

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The Art of Conjecturing, Together with Letter to a Friend on Sets in Court Tennis (trans.)

8: 9024: 8946: 8896: 8806: 8756: 8605: 8515: 8437: 8336: 8270: 8227: 8217: 8197: 8015: 7940: 7863: 7544: 7308: 7301: 7263: 7171: 7151: 7123: 6856: 6722: 6717: 6707: 6699: 6517: 6478: 6368: 6358: 6267: 6046: 6002: 5920: 5845: 5747: 5487: 4815: 4545: 3255: 3101: 2949: 2754: 2566: 2539: 2535: 2523: 2495: 2433: 2233: 2223: 2128:. Although these are produced from the same calculations as those of hypothesis tests or 2125: 2011: 1969: 1910: 1706: 1690: 1547: 1215:—for which a statistician would use a modified, more structured estimation method (e.g., 1212: 1192: 1168: 1164: 1076: 1003: 932: 816: 698: 644: 446: 437: 422: 345: 82: 8679: 5432: 4596: 3913: 2068:

The standard approach is to test a null hypothesis against an alternative hypothesis. A

1409:, due to their numerical nature. Such distinctions can often be loosely correlated with 9008: 8631: 8550: 8490: 8422: 8412: 8351: 8326: 8202: 8159: 8154: 8029: 7840: 7694: 7590: 7539: 7415: 7312: 7296: 7273: 7050: 6784: 6767: 6727: 6638: 6533: 6495: 6466: 6426: 6386: 6332: 6249: 5935: 5930: 5686: 5659: 5618: 5523: 5511: 5459: 5416: 5160:

Natalia Loaiza Velásquez, María Isabel González Lutz & Julián Monge-Nájera (2011).

5062: 4934:

Drennan, Robert D. (2008). "Statistics in archaeology". In Pearsall, Deborah M. (ed.).

4913: 4846: 4819: 4755: 4489: 4462: 4409: 4391: 4260: 4175: 4133: 4125: 4090: 4053: 3761: 3672: 3109: 3090: 3024: 2778: 2719: 2144: 2110: 2089: 1871: 1846: 1732: 1694: 1686: 1344: 1248: 1208: 1200: 1148: 1144: 1011: 924: 876: 868: 785: 754: 738: 668: 628: 597: 505: 469: 461: 441: 418: 303: 207: 95: 3288: 2683: 2154:

Rejecting the null hypothesis does not automatically prove the alternative hypothesis.

2139:: criticisms arise because the hypothesis testing approach forces one hypothesis (the 2132:-values, they describe both the size of the effect and the uncertainty surrounding it. 840: 9003: 8626: 8346: 8331: 8275: 8222: 8024: 7935: 7905: 7897: 7717: 7708: 7633: 7564: 7420: 7405: 7380: 7268: 7209: 7075: 7063: 6689: 6606: 6550: 6473: 6317: 6239: 6018: 5892: 5691: 5583: 5529: 5464: 5446: 5386: 5376: 5314: 5300: 5213: 5176: 5111: 5091: 5054: 4947: 4936: 4917: 4880: 4851: 4761: 4701: 4653: 4525: 4514: 4494: 4445: 4323: 4291: 4252: 4137: 4020: 3865: 3810: 3734: 3676: 3632: 3607: 3568: 3533: 3504: 3483: 3434: 3344: 3221: 3095: 3044: 3029: 2915: 2758: 2570: 2565:

A typical statistics course covers descriptive statistics, probability, binomial and

2527: 2338: 2280: 2247: 2148: 2078: 2007: 1957: 1914: 1799: 1656: 1617: 1527: 1414: 1125: 1045: 632: 604:(like income), while frequency and percentage are more useful in terms of describing 536: 528:(null hypothesis is rejected when it is in fact true, giving a "false positive") and 413: 392: 299: 90: 4264: 4179: 37: 8560: 8535: 8407: 8255: 8192: 7960: 7915: 7679: 7666: 7559: 7534: 7468: 7400: 7278: 6886: 6779: 6712: 6625: 6572: 6391: 6262: 6056: 5940: 5855: 5822: 5681: 5671: 5646: 5622: 5610: 5454: 5436: 5346: 5331: 5046: 4983: 4979: 4905: 4841: 4831: 4600: 4484: 4474: 4383: 4277:

Fisher, R.A. (1915) The evolution of sexual preference. Eugenics Review (7) 184:192

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is supported by evidence "beyond a reasonable doubt". However, "failure to reject H

1667: 1326: 1156: 1101: 1049: 1037: 1019: 864: 856: 812: 605: 482: 8500: 8427: 8356: 8149: 7877: 7621: 7483: 7410: 7085: 6959: 6932: 6909: 6878: 6505: 6500: 6454: 6184: 5835: 5730: 5676: 5614: 5570: 5441: 5417:"Pollock avoided hydrodynamic instabilities to paint with his dripping technique" 5355: 5340: 4836: 4583:

Chrisman, Nicholas R (1998). "Rethinking Levels of Measurement for Cartography".

4317: 4235:

Edwards, A.W.F. (1998). "Natural Selection and the Sex Ratio: Fisher's Sources".

4034:

Box, JF (February 1980). "R.A. Fisher and the Design of Experiments, 1922–1926".

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Interpretation of statistical information can often involve the development of a

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The mathematical foundations of statistics developed from discussions concerning

774: 733: 520: 387: 225: 7367: 5650: 3376: 2445:

comprises descriptive statistics and the application of inferential statistics.

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is a statistic used to estimate such function. Commonly used estimators include

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Expert systems and artificial intelligence: the need for information about data

2895: 2860: 2849: 2770: 2663: 2650: 2646: 2506:, government, and business. Business statistics applies statistical methods in 2503: 2094: 2053: 1998:

perspective, such a claim does not even make sense, as the true value is not a

1861: 1762:, asserts that the defendant is innocent, whereas the alternative hypothesis, H 1698: 1426: 1124:. Statistics itself also provides tools for prediction and forecasting through 916: 852: 750: 694: 401: 375:

to show the observed relationships between different variables, here using the

340: 253: 5390: 4171: 4121: 3987: 2906:. Some fields of inquiry use applied statistics so extensively that they have 2337:

Ways to avoid misuse of statistics include using proper diagrams and avoiding

2324:". Misuse of statistics can be both inadvertent and intentional, and the book 1639:

A statistic is a random variable that is a function of the random sample, but

1546:(or inductive statistics), in that descriptive statistics aims to summarize a 511:

A standard statistical procedure involves the collection of data leading to a

9029: 9018: 8366: 8298: 8250: 7983: 7950: 7813: 7774: 7585: 7554: 7018: 6972: 6577: 6279: 6106: 5870: 5865: 5450: 5324: 5058: 4909: 2930: 2879: 2855:

Statistics can be used to predicatively create art, as in the statistical or

2807: 2727: 2273: 1898: 1889:

A least squares fit: in red the points to be fitted, in blue the fitted line.

1853:

refers to an estimate of difference between sample mean and population mean.

1810: 1803: 1736: 1629: 1625: 1621: 1572: 1318: 1313: 975:

The Correlation between Relatives on the Supposition of Mendelian Inheritance

969: 954: 872: 860: 660: 656: 529: 453: 178: 5626: 5050: 3955: 3938: 3708: 3691: 592:

can be used to summarize the population data. Numerical descriptors include

8308: 8303: 8207: 7925: 7858: 7835: 7750: 7080: 6376: 6274: 6209: 6151: 6136: 6073: 6028: 5695: 5468: 5370: 5180: 4855: 4498: 4479: 4461:

McCarney R, Warner J, Iliffe S, van Haselen R, Griffin M, Fisher P (2007).

4256: 3668: 3105: 2990: 2974: 2955: 2935: 2822: 2811: 2723: 2607: 2507: 2331: 1949: 1937: 1340: 1322: 1064: 1060: 920: 908: 577:

In applying statistics to a problem, it is common practice to start with a

540: 525: 490:) seeks to characterize the distribution's central or typical value, while 433: 364: 16:

Study of the collection, analysis, interpretation, and presentation of data

8065: 5263: 5127: 2749:, description, analysis, and summary of data), probability (typically the 2373: 1974: 1885: 1308:

examined changes to the working environment at the Hawthorne plant of the

611:

When a census is not feasible, a chosen subset of the population called a

8715: 8510: 8174: 8097: 7968: 7930: 7613: 7514: 7376: 7189: 7156: 6648: 6565: 6560: 6204: 6161: 6141: 6121: 6111: 5880: 4566: 4071:

Yates, F (June 1964). "Sir Ronald Fisher and the Design of Experiments".

3553: 3014: 2945: 2833: 2818: 2766: 2762: 2659: 2449:

concerns the logical arguments underlying justification of approaches to

2413: 2360:

How does he/she know? (Does he/she have the resources to know the facts?)

2194: 2121: 1836:

where the null hypothesis is falsely rejected, giving a "false positive".

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that will guide the performance of the experiment and which specifies the

1140: 928: 827: 805: 770: 766: 672: 664: 648: 566: 216: 142: 4512:

Rothman, Kenneth J; Greenland, Sander; Lash, Timothy, eds. (2008). "7".

1587:

from a larger population. Inferential statistics can be contrasted with

1530:

that quantitatively describes or summarizes features of a collection of

1343:, and then look for the number of cases of lung cancer in each group. A 847:

made major contributions to probabilistic methods leading to statistics.

8374: 8169: 6814: 6294: 5994: 5925: 5875: 5850: 5716: 5503: 5066: 5034: 4549: 4395: 4129: 4094: 4057: 3765: 2968: 2722:

formalizes the use of statistics, and other mathematics, in business. (

2611: 1960:

and specific techniques have been developed to address these problems.

1702: 1523: 1479: in this section. Unsourced material may be challenged and removed. 1387: 1188: 949: 652: 616: 368: 211: 5718:

Online Statistics Education: An Interactive Multimedia Course of Study

2434:

Applied statistics, theoretical statistics and mathematical statistics

2279:

to summarize their main characteristics, often with visual methods. A

6967: 6819: 6439: 6234: 6146: 6131: 6126: 6091: 5507: 5039:

Journal of the Royal Statistical Society. Series D (The Statistician)

3922: 3897: 2996: 2939: 2899: 2162: 1644: 1539: 1410: 1375: 1180: 1053: 904: 801: 789: 4387: 4086: 4049: 3971: 3528:. Washington, DC: The Mathematical Association of America. pp. 1454: 811:

Although the term 'statistic' was introduced by the Italian scholar

8399: 8318: 8245: 6483: 6101: 5978: 5973: 5968: 4248: 3321: 2715: 2585: 2511: 2417: 2276: 1594: 1179:

A common goal for a statistical research project is to investigate

1089: 1084: 979: 778: 193: 183: 5311:

Applied Business Statistics: Methods and Excel-Based Applications,

4632:

Measurement theory and practice: The world through quantification.

3120:

or SPC), for summarizing data, and to make data-driven decisions.

2301:

structures like bridges all rely on the proper use of statistics.

1397:, whereas ratio and interval measurements are grouped together as 727: 643:), and modeling relationships within the data (for example, using 436:

collect data by developing specific experiment designs and survey

360: 8711: 8184: 7988: 7689: 5515: 5492: 3726:

States and the Masters of Capital: Sovereign Lending, Old and New

2114: 2061: 2052:

In this graph the black line is probability distribution for the

2042: 1671: 1418: 1383: 1029: 586:). This may be organized by governmental statistical institutes. 188: 4719:"Basic Inferential Statistics - Purdue OWL® - Purdue University" 2796: 2457:. Mathematical statistics includes not only the manipulation of 2322:

There are three kinds of lies: lies, damned lies, and statistics

1685:

Between two estimators of a given parameter, the one with lower

1599: 1304:

Experiments on human behavior have special concerns. The famous

1171:

from samples to the parameters of a larger or total population.

7910: 6891: 6865: 6845: 6096: 5887: 4460: 4410:"Science in a Complex World – Big Data: Opportunity or Threat?" 804:(1187–1268) later made an important contribution on the use of 583: 429: 5491:, vol. 321, no. 4 (October 2019), pp. 62–67. "The use of 5414: 5090:

Nikoletseas, M.M. (2014) "Statistics: Concepts and Examples."

2100:

Some problems are usually associated with this framework (See

823:

Natural and Political Observations upon the Bills of Mortality

5739: 5545:"Introductory Statistics: Concepts, Models, and Applications" 3565:

Investigating Statistical Concepts, Applications, and Methods

2589: 1817:

is simply a hypothesis that contradicts the null hypothesis.

1746: 1713: 1417:, polytomous categorical variables with arbitrarily assigned 4990: 4929: 4927: 5830: 4520:(3rd ed.). Lippincott Williams & Wilkins. p. 2667: 1945: 1187:. There are two major types of causal statistical studies: 797: 593: 562: 465: 405: 5521: 4970:

Cohen, Jerome B. (December 1938). "Misuse of Statistics".

3939:"Francis Galton's Account of the Invention of Correlation" 2610:, but powerful computers, coupled with suitable numerical 1606:

independent identically distributed (IID) random variables

1579:. Inferential statistical analysis infers properties of a 8709: 4924: 3963: 3018: 2363:

What's missing? (Does he/she give us a complete picture?)

1365:

Various attempts have been made to produce a taxonomy of

1174: 5579:

Statistics in Psychology: Explanations without Equations

4150: 4965: 4963: 3552: 3181:

List of national and international statistical services

2918:(assesses risk in the insurance and finance industries) 2737:

A typical "Business Statistics" course is intended for

1860:

is the amount by which an observation differs from its

4760:. Cambridge, UK New York: Cambridge University Press. 4463:"The Hawthorne Effect: a randomised, controlled trial" 964:

The second wave of the 1910s and 20s was initiated by

947:, among many other things. Galton and Pearson founded 8992: 5108:

Introduction to Statistics: Concepts and Applications

5106:

Anderson, D.R.; Sweeney, D.J.; Williams, T.A. (1994)

4744:

Piazza Elio, Probabilità e Statistica, Esculapio 2007

631:), estimating numerical characteristics of the data ( 508:, which deals with the analysis of random phenomena. 7652:

Autoregressive conditional heteroskedasticity (ARCH)

5162:"Which statistics should tropical biologists learn?" 4960: 4511: 3753:

Willcox, Walter (1938) "The Founder of Statistics".

3601: 3286: 1300:

Documenting and presenting the results of the study.

1207:, they are also applied to other kinds of data—like 953:

as the first journal of mathematical statistics and

943:

for the fitting of distributions to samples and the

901:

presumably made use of it a decade earlier in 1795.

4573:. Library Association Report, London, March, 23–27. 3791:

Landmark writings in Western Mathematics, 1640-1940

2844:Methods of statistics may be used predicatively in 2761:, and correlation; (follow-on) courses may include 2478: 1712:Other desirable properties for estimators include: 7114: 5709:(Electronic Version): TIBCO Software Inc. (2020). 4645: 4153:"Bayesian Inference for Categorical Data Analysis" 3287: 1052:about a positive feedback runaway effect found in 978:(which was the first to use the statistical term, 9045:Mathematical and quantitative methods (economics) 5573:, 3rd edition by Diez, Barr, and Cetinkaya-Rundel 3854: 3631:(Corr. 2nd print. ed.). New York: Springer. 3448: 3446: 3197:List of university statistical consulting centers 2401: 1882:is simply the square root of mean squared error. 1554:that the sample of data is thought to represent. 1235:The basic steps of a statistical experiment are: 1040:called "probably the most celebrated argument in 968:, and reached its culmination in the insights of 9016: 5660:"Why most published research findings are false" 4895: 4820:"Why Most Published Research Findings Are False" 3604:Handbook of stochastic analysis and applications 2757:), test of hypotheses and confidence intervals, 2622:) as well as the creation of new types, such as 2357:Who says so? (Does he/she have an axe to grind?) 1829:, two broad categories of error are recognized: 1595:Terminology and theory of inferential statistics 1339:both smokers and non-smokers, perhaps through a 782:Manuscript on Deciphering Cryptographic Messages 7200:Multivariate adaptive regression splines (MARS) 5264:"Journal of Business & Economic Statistics" 5128:"Journal of Business & Economic Statistics" 5014: 4972:Journal of the American Statistical Association 4674:"Descriptive Statistics | Research Connections" 2569:, test of hypotheses and confidence intervals, 1067:in the 1930s. They introduced the concepts of " 4782:"Cohen (1994) The Earth Is Round (p < .05)" 4585:Cartography and Geographic Information Science 4544: 3832:"Gauss, Least Squares, and the Missing Planet" 3802: 3522:"Teaching Statistics as a Respectable Subject" 3452: 3443: 2494:Statistics is applicable to a wide variety of 2219:Pearson product-moment correlation coefficient 2161:it relies on sample size, and therefore under 2014:: this approach depends on a different way of 1893:Many statistical methods seek to minimize the 1550:, rather than use the data to learn about the 937:Pearson product-moment correlation coefficient 8695: 8081: 5755: 5637:Gigerenzer, G (2004). "Mindless statistics". 5268:Journal of Business & Economic Statistics 5238:Journal of Business & Economic Statistics 5132:Journal of Business & Economic Statistics 4808: 2927:(statistical evaluation of astronomical data) 2797:Statistics applied to mathematics or the arts 2726:is the application of statistical methods to 1600:Statistics, estimators and pivotal quantities 745:Formal discussions on inference date back to 321: 115: 5330:Holmes, L., Illowsky, B., Dean, S. (2017). 4879:, WW Norton & Company, Inc. New York. 4454: 3861:Studies in the history of statistical method 3176:List of important publications in statistics 2783:Business mathematics § University level 2254: 1909:, which provides a handy property for doing 1185:independent variables on dependent variables 569:. Some consider statistics to be a distinct 449:does not involve experimental manipulation. 8095: 4015:. Department of Statistical Science – 3689: 3100:Statistics in various sports, particularly 2874:List of fields of application of statistics 2682:In business, "statistics" is a widely used 2135:Fallacy of the transposed conditional, aka 2016:interpreting what is meant by "probability" 460:, which summarize data from a sample using 8702: 8688: 8088: 8074: 5800: 5762: 5748: 5636: 5506:results has contributed to an illusion of 3889: 3654: 3431:The Oxford Dictionary of Statistical Terms 3326:Digitales Wörterbuch der deutschen Sprache 2867: 1747:Null hypothesis and alternative hypothesis 1693:. Furthermore, an estimator is said to be 784:gave a detailed description of how to use 765:, which contains one of the first uses of 678: 328: 314: 122: 108: 36: 6413: 5685: 5675: 5657: 5458: 5440: 5372:Nonparametric Statistical Methods Using R 4845: 4835: 4814: 4740: 4738: 4488: 4478: 4315: 4288:The Genetical Theory of Natural Selection 4228: 4151:Agresti, Alan; David B. Hichcock (2005). 3954: 3921: 3707: 3626: 3343:. Oxford University Press. January 2008. 3229:Foundations and major areas of statistics 3171:List of academic statistical associations 2489: 1670:or pivot. Widely used pivots include the 1557: 1507: 1495:Learn how and when to remove this message 1025:The Genetical Theory of Natural Selection 452:Two main statistical methods are used in 5035:"From Statistics to Statistical Science" 5000:(1988). "Modern Elementary Statistics". 4582: 4375:Journal of the Royal Statistical Society 4280: 4271: 4070: 3455:"Descriptive and Inferential Statistics" 2584: 2580: 2372: 2341:. Misuse can occur when conclusions are 2047: 1973: 1884: 1664:does not depend on the unknown parameter 1286:Performing the experiment following the 985:Statistical Methods for Research Workers 903: 839: 792:messages, providing an early example of 726: 359: 339: 5542: 4933: 4869: 4867: 4865: 4753: 4442:Statistical Models: Theory and Practice 4356: 4347: 4309: 4234: 4107: 4033: 3969: 3936: 3803:Sylla, E. D.; Bernoulli, Jacob (2006). 3785:Schneider, I. (2005). Jakob Bernoulli, 3722: 3602:Lakshmikantham, D.; Kannan, V. (2002). 3526:Statistics for the Twenty-First Century 2977:(statistical analysis of economic data) 2962:Data science#Relationship to statistics 2556:Spearman's rank correlation coefficient 2229:Spearman's rank correlation coefficient 2165:p-values may be seriously mis-computed. 1159:and, more generally, the properties of 9017: 8817:Electrical and electronics engineering 8802:Developmental and reproductive biology 7726:Kaplan–Meier estimator (product limit) 5032: 4996: 4757:The Cambridge Dictionary of Statistics 4735: 4690: 4371: 4300: 4160:Statistical Methods & Applications 3895: 3789:(1713). In I. Grattan-Guinness (Ed.), 3692:"The emergence of statistical science" 3503:, Holt, Rinehart and Winston, p. xii, 3374: 3202:Notation in probability and statistics 3166:Glossary of probability and statistics 2793:, often include topics in statistics. 2730:in order to give empirical content to 2677: 2147:, although it requires establishing a 1963: 1770:(status quo) stands in opposition to H 1575:to deduce properties of an underlying 1333: 1175:Experimental and observational studies 998:models. He originated the concepts of 911:, a founder of mathematical statistics 8683: 8069: 7799: 7366: 7113: 6412: 6182: 5799: 5743: 5593: 5522:Barbara Illowsky; Susan Dean (2014). 5368: 5207: 5155: 5153: 4969: 4110:American Educational Research Journal 3650: 3648: 3519: 2710:. Statistics is also heavily used in 1878:, a widely used class of estimators. 1739:method and the more recent method of 1724:to the true value of such parameter. 1709:to the true value of such parameter. 8650: 8036: 7736:Accelerated failure time (AFT) model 5725:UCLA Statistical Computing Resources 4862: 4643: 3423: 3308:participating institution membership 2817:Predictive methods of statistics in 2690:tool. It is particularly applied in 2408:Correlation does not imply causation 1921:method and least squares applied to 1641:not a function of unknown parameters 1477:adding citations to reliable sources 1448: 1425:, and continuous variables with the 1294:following the experimental protocol. 1217:difference in differences estimation 757:between the 8th and 13th centuries. 707:measure-theoretic probability theory 8662: 8048: 7331:Analysis of variance (ANOVA, anova) 6183: 5735:Stanford Encyclopedia of Philosophy 5498:for nearly a century to determine 5015:Huff, Darrell; Irving Geis (1954). 4200: 3829: 3757:International Statistical Institute 3381:Stanford Encyclopedia of Philosophy 2787:Professional certification programs 1269:of treatments to subjects to allow 1095: 1028:, he applied statistics to various 939:, defined as a product-moment, the 737:was the first work that dealt with 13: 7426:Cochran–Mantel–Haenszel statistics 6052:Pearson product-moment correlation 5553:(3rd Web ed.). Archived from 5479: 5150: 3645: 3524:. In F. Gordon; S. Gordon (eds.). 3501:Statistics for the Social Sciences 2971:(statistical study of populations) 2829:can be used to create video works. 2614:, caused an increased interest in 1223:, among many others) that produce 1197:measurements with different levels 1106: 397: 14: 9066: 8847:Genetics and evolutionary biology 5703: 5348:Principles of Business Statistics 5274:from the original on 27 July 2020 5244:from the original on 23 June 2021 5210:The Manager's Guide to Statistics 5138:from the original on 27 July 2020 3480:Think and Explain with Statistics 3330: 3261:Multivariate analysis of variance 2993:(statistical analysis of disease) 2532:Pearson's correlation coefficient 2064:is represented by the green area. 9002: 8661: 8649: 8638: 8637: 8625: 8047: 8035: 8023: 8010: 8009: 7800: 5596:"Things I have learned (so far)" 5333:Introductory Business Statistics 2952:to discover knowledge from data) 2848:, as in a card trick based on a 2479:Machine learning and data mining 1453: 1350: 298: 89: 8851:Cellular and molecular biology 8546:Computational complexity theory 7685:Least-squares spectral analysis 5408: 5397:from the original on 2022-05-15 5362: 5286: 5256: 5226: 5201: 5190:from the original on 2020-10-19 5120: 5100: 5084: 5073:from the original on 2022-01-15 5026: 5008: 4889: 4799: 4788:from the original on 2015-09-05 4774: 4747: 4711: 4698:Oxford Dictionary of Statistics 4666: 4637: 4624: 4611: 4576: 4560: 4538: 4505: 4431: 4420:from the original on 2016-05-30 4402: 4365: 4336:from the original on 2019-12-25 4219: 4189:from the original on 2013-12-19 4144: 4101: 4064: 4027: 4005: 3994:from the original on 2020-08-18 3930: 3878:from the original on 2020-07-27 3848: 3823: 3796: 3779: 3770: 3747: 3716: 3683: 3620: 3595: 3584:from the original on 2020-11-22 3546: 3513: 3461:from the original on 2020-10-26 3412:from the original on 2020-11-22 3387:from the original on 2021-10-19 3357:from the original on 2020-09-03 2594:open source statistical package 2428: 2397:is called a confounding factor. 2102:criticism of hypothesis testing 2029: 1464:needs additional citations for 1139:Sampling theory is part of the 777:words with and without vowels. 647:). Inference can extend to the 550: 6666:Mean-unbiased minimum-variance 5769: 4984:10.1080/01621459.1938.10502344 4444:, Cambridge University Press. 4322:. Princeton University Press. 3493: 3472: 3398: 3368: 3314: 3280: 3001:geographic information systems 2402:Misinterpretation: correlation 2213:Mean square weighted deviation 1230: 994:, where he developed rigorous 763:Book of Cryptographic Messages 1: 7979:Geographic information system 7195:Simultaneous equations models 3690:Ostasiewicz, Walenty (2014). 3273: 3086:Structural equation modelling 2921:Applied information economics 2910:. These disciplines include: 1008:Fisher's linear discriminator 855:among mathematicians such as 7162:Coefficient of determination 6773:Uniformly most powerful test 5677:10.1371/journal.pmed.0040168 5615:10.1037/0003-066x.45.12.1304 5442:10.1371/journal.pone.0223706 5169:Revista de Biología Tropical 4837:10.1371/journal.pmed.0020124 4554:Data analysis and regression 3696:Śląski Przegląd Statystyczny 3556:; Rossman, Allan J. (2005). 3186:List of statistical packages 2560:principal component analysis 2174:Some well-known statistical 1632:of these IID variables. The 7: 7731:Proportional hazards models 7675:Spectral density estimation 7657:Vector autoregression (VAR) 7091:Maximum posterior estimator 6323:Randomized controlled trial 5651:10.1016/j.socec.2004.09.033 4938:Encyclopedia of Archaeology 4696:Upton, G., Cook, I. (2008) 4678:www.researchconnections.org 4619:Choosing an analysis method 3627:Schervish, Mark J. (1995). 3433:, Oxford University Press. 3375:Romijn, Jan-Willem (2014). 3241:Probability interpretations 3192:List of statistics articles 3123: 3118:statistical process control 2959: 2938:(for analysis of data from 2645:, while techniques such as 2309:properly is referred to as 2169: 1913:. Least squares applied to 1261:to reduce the influence of 1111: 21:Statistics (disambiguation) 10: 9071: 8952:Probability and statistics 8596:Films about mathematicians 7491:Multivariate distributions 5911:Average absolute deviation 5658:Ioannidis, J.P.A. (2005). 5639:Journal of Socio-Economics 5017:How to Lie with Statistics 4876:How to Lie with Statistics 4605:10.1559/152304098782383043 4013:"Karl Pearson (1857–1936)" 3898:"Typical laws of heredity" 3499:Hays, William Lee, (1973) 3377:"Philosophy of statistics" 3151: 3076:Statistical classification 2871: 2775:multiple linear regression 2598: 2453:, as well as encompassing 2405: 2327:How to Lie with Statistics 2290: 2258: 2033: 1967: 1774:and is maintained unless H 1561: 1511: 1444: 1354: 1099: 1014:. He also coined the term 716: 712: 682: 554: 432:data cannot be collected, 238:Relationship with sciences 18: 8722: 8619: 8569: 8526: 8436: 8398: 8365: 8317: 8289: 8236: 8183: 8165:Philosophy of mathematics 8140: 8105: 8005: 7959: 7896: 7849: 7812: 7808: 7795: 7767: 7749: 7716: 7707: 7665: 7612: 7573: 7522: 7513: 7479:Structural equation model 7434: 7391: 7387: 7362: 7321: 7287: 7241: 7208: 7170: 7137: 7133: 7109: 7049: 6958: 6877: 6841: 6832: 6815:Score/Lagrange multiplier 6800: 6753: 6698: 6624: 6615: 6425: 6421: 6408: 6367: 6341: 6293: 6248: 6230:Sample size determination 6195: 6191: 6178: 6082: 6037: 6011: 5993: 5949: 5901: 5821: 5812: 5808: 5795: 5777: 5550:Missouri State University 4942:. Elsevier Inc. pp. 4617:van den Berg, G. (1991). 4556:. Boston: Addison-Wesley. 4316:Andersson, Malte (1994). 4213:The Design of Experiments 4172:10.1007/s10260-005-0121-y 4122:10.3102/00028312003003223 4037:The American Statistician 4017:University College London 3988:10.1080/14786440009463897 3731:Columbia University Press 3723:Bruneau, Quentin (2022). 3657:The American Statistician 3478:Moses, Lincoln E. (1986) 3295:Oxford English Dictionary 3246:Foundations of statistics 3144:Resources in your library 2948:(applying statistics and 2781:more generally. See also 2624:generalized linear models 2544:Shannon's diversity index 2459:probability distributions 2441:sometimes referred to as 2286: 2266:Exploratory data analysis 2261:Exploratory data analysis 2255:Exploratory data analysis 1903:Least absolute deviations 1431:floating-point arithmetic 1283:of the experimental data. 1201:experimental manipulation 1147:. Probability is used in 991:The Design of Experiments 982:), his classic 1925 work 959:University College London 352:, is used extensively in 8601:Recreational mathematics 7974:Environmental statistics 7496:Elliptical distributions 7289:Generalized linear model 7218:Simple linear regression 6988:Hodges–Lehmann estimator 6445:Probability distribution 6354:Stochastic approximation 5916:Coefficient of variation 5731:Philosophy of Statistics 5500:statistical significance 5270:. Taylor & Francis. 5240:. Taylor & Francis. 5134:. Taylor & Francis. 5033:Nelder, John A. (1999). 4910:10.1177/0016986212444122 3457:. statistics.laerd.com. 3236:Philosophy of statistics 3081:Structured data analysis 3035:Psychological statistics 2777:, and other topics from 2601:Computational statistics 2575:free statistics software 2463:computational statistics 2306:statistical significance 2085:the patient noticeably. 2075:statistical significance 2036:Statistical significance 1931:polynomial least squares 1927:non-linear least squares 1899:methods of least squares 1897:, and these are called " 1820: 1722:converges in probability 1610:probability distribution 1577:probability distribution 1571:is the process of using 1310:Western Electric Company 1249:experimental variability 741:as currently understood. 513:test of the relationship 504:employ the framework of 480:(sample or population): 8747:Artificial intelligence 8486:Mathematical statistics 8476:Mathematical psychology 8446:Engineering mathematics 8380:Algebraic number theory 7634:Cross-correlation (XCF) 7242:Non-standard predictors 6676:Lehmann–Scheffé theorem 6349:Adaptive clinical trial 5727:(archived 17 July 2006) 5525:Introductory Statistics 5369:Cline, Graysen (2019). 5110:, pp. 5–9. West Group. 5051:10.1111/1467-9884.00187 4978:(204). JSTOR: 657–674. 4754:Everitt, Brian (1998). 4652:(2nd ed.). Wiley. 4648:Introductory Statistics 3709:10.15611/sps.2014.12.04 3606:. New York: M. Dekker. 3300:Oxford University Press 3071:Multivariate statistics 3040:Reliability engineering 2908:specialized terminology 2888:computational sociology 2868:Specialized disciplines 2473:Statistical consultants 2455:mathematical statistics 1895:residual sum of squares 1149:mathematical statistics 1141:mathematical discipline 893:was first described by 891:method of least squares 808:in frequency analysis. 773:, to list all possible 685:Mathematical statistics 679:Mathematical statistics 502:mathematical statistics 8977:Structural engineering 8917:Mechanical engineering 8890:Western and South Asia 8632:Mathematics portal 8481:Mathematical sociology 8461:Mathematical economics 8456:Mathematical chemistry 8385:Analytic number theory 8266:Differential equations 8030:Mathematics portal 7851:Engineering statistics 7759:Nelson–Aalen estimator 7336:Analysis of covariance 7223:Ordinary least squares 7147:Pearson product-moment 6551:Statistical functional 6462:Empirical distribution 6295:Controlled experiments 6024:Frequency distribution 5802:Descriptive statistics 5582:. Palgrave Macmillan. 5543:Stockburger, David W. 5512:reproducibility crises 4898:Gifted Child Quarterly 4644:Mann, Prem S. (1995). 4480:10.1186/1471-2288-7-30 3976:Philosophical Magazine 3937:Stigler, S.M. (1989). 3669:10.1198/tas.2011.10191 3406:"Cambridge Dictionary" 2986:Engineering statistics 2743:descriptive statistics 2732:economic relationships 2596: 2490:Statistics in academia 2447:Theoretical statistics 2398: 2159:inferential statistics 2065: 1982: 1919:ordinary least squares 1890: 1880:Root mean square error 1874:is used for obtaining 1815:alternative hypothesis 1589:descriptive statistics 1558:Inferential statistics 1544:inferential statistics 1536:descriptive statistics 1514:Descriptive statistics 1508:Descriptive statistics 1401:, which can be either 1399:quantitative variables 1369:. The psychophysicist 1245:alternative hypotheses 1221:instrumental variables 1161:statistical procedures 1153:sampling distributions 912: 848: 742: 723:Founders of statistics 703:differential equations 623:inferential statistics 589:Descriptive statistics 474:inferential statistics 458:descriptive statistics 410:statistical population 380: 373:descriptive statistics 357: 354:inferential statistics 96:Mathematics portal 8842:Environmental science 8727:Aerospace engineering 8611:Mathematics education 8541:Theory of computation 8261:Hypercomplex analysis 7946:Population statistics 7888:System identification 7622:Autocorrelation (ACF) 7550:Exponential smoothing 7464:Discriminant analysis 7459:Canonical correlation 7323:Partition of variance 7185:Regression validation 7029:(Jonckheere–Terpstra) 6928:Likelihood-ratio test 6617:Frequentist inference 6529:Location–scale family 6450:Sampling distribution 6415:Statistical inference 6382:Cross-sectional study 6369:Observational studies 6328:Randomized experiment 6157:Stem-and-leaf display 5959:Central limit theorem 5711:Data Science Textbook 5603:American Psychologist 5576:Stephen Jones, 2010. 4873:Huff, Darrell (1954) 4784:. YourStatsGuru.com. 3956:10.1214/ss/1177012580 3520:Moore, David (1992). 3251:List of statisticians 3154:Outline of statistics 3050:Statistical mechanics 2884:computational biology 2712:management accounting 2708:operations management 2588: 2581:Statistical computing 2467:design of experiments 2451:statistical inference 2376: 2051: 1977: 1888: 1718:consistent estimators 1614:statistical inference 1569:Statistical inference 1564:Statistical inference 1520:descriptive statistic 1395:categorical variables 1371:Stanley Smith Stevens 1367:levels of measurement 1361:Levels of measurement 1357:Statistical data type 1288:experimental protocol 1276:experimental protocol 1267:randomized assignment 1263:confounding variables 1255:Design of experiments 1225:consistent estimators 1213:observational studies 1193:observational studies 1169:inductively inferring 996:design of experiments 907: 895:Adrien-Marie Legendre 843: 794:statistical inference 730: 719:History of statistics 691:mathematical analysis 557:Outline of statistics 363: 343: 8591:Informal mathematics 8471:Mathematical physics 8466:Mathematical finance 8451:Mathematical biology 8390:Diophantine geometry 7869:Probabilistic design 7454:Principal components 7297:Exponential families 7249:Nonlinear regression 7228:General linear model 7190:Mixed effects models 7180:Errors and residuals 7157:Confounding variable 7059:Bayesian probability 7037:Van der Waerden test 7027:Ordered alternative 6792:Multiple comparisons 6671:Rao–Blackwellization 6634:Estimating equations 6590:Statistical distance 6308:Factorial experiment 5841:Arithmetic-Geometric 5563:OpenIntro Statistics 5208:Pekoz, Erol (2009). 5019:. New York: Norton. 4621:. Leiden: DSWO Press 4467:BMC Med Res Methodol 4286:Fisher, R.A. (1930) 3970:Pearson, K. (1900). 3629:Theory of statistics 3217:World Statistics Day 3212:Knowledge Statistics 3207:Statistics education 3161:Abundance estimation 3066:jackknife resampling 2755:normal distributions 2718:. The discipline of 2696:marketing management 2692:financial management 2656:statistical software 2567:normal distributions 2516:analysis of variance 2496:academic disciplines 2443:Statistical science, 2423:confounding variable 2379:confounding variable 2311:statistical literacy 2298:Misuse of statistics 2293:Misuse of statistics 2272:) is an approach to 2243:Time series analysis 2184:Analysis of variance 2178:and procedures are: 2137:prosecutor's fallacy 2126:confidence intervals 2020:Bayesian probability 1987:Confidence intervals 1979:Confidence intervals 1923:nonlinear regression 1876:efficient estimators 1741:estimating equations 1676:chi square statistic 1473:improve this article 1247:, and the estimated 1189:experimental studies 1077:confidence intervals 1042:evolutionary biology 1004:ancillary statistics 966:William Sealy Gosset 945:Pearson distribution 899:Carl Friedrich Gauss 845:Carl Friedrich Gauss 761:(717–786) wrote the 571:mathematical science 565:, or as a branch of 377:Iris flower data set 203:Discrete mathematics 19:For other uses, see 8606:Mathematics and art 8516:Operations research 8271:Functional analysis 7941:Official statistics 7864:Methods engineering 7545:Seasonal adjustment 7313:Poisson regressions 7233:Bayesian regression 7172:Regression analysis 7152:Partial correlation 7124:Regression analysis 6723:Prediction interval 6718:Likelihood interval 6708:Confidence interval 6700:Interval estimation 6661:Unbiased estimators 6479:Model specification 6359:Up-and-down designs 6047:Partial correlation 6003:Index of dispersion 5921:Interquartile range 5488:Scientific American 5433:2019PLoSO..1423706P 5309:Wegner, T. (2010). 5297:Business Statistics 5295:Sharpe, N. (2014). 4630:Hand, D.J. (2004). 4597:1998CGISy..25..231C 4516:Modern Epidemiology 4416:. 2 December 2013. 4237:American Naturalist 3943:Statistical Science 3914:1877Natur..15..492. 3453:Lund Research Ltd. 3298:(Online ed.). 3256:Official statistics 2950:pattern recognition 2678:Business statistics 2592:, an example of an 2540:Kruskal-Wallis test 2536:Mann-Whitney U test 2439:Applied statistics, 2224:Regression analysis 2012:Bayesian statistics 1970:Interval estimation 1964:Interval estimation 1689:is said to be more 1334:Observational study 1209:natural experiments 933:regression analysis 817:Gottfried Achenwall 747:Arab mathematicians 699:stochastic analysis 645:regression analysis 447:observational study 350:probability density 346:normal distribution 137:Part of a series on 8551:Numerical analysis 8160:Mathematical logic 8155:Information theory 7961:Spatial statistics 7841:Medical statistics 7741:First hitting time 7695:Whittle likelihood 7346:Degrees of freedom 7341:Multivariate ANOVA 7274:Heteroscedasticity 7086:Bayesian estimator 7051:Bayesian inference 6900:Kolmogorov–Smirnov 6785:Randomization test 6755:Testing hypotheses 6728:Tolerance interval 6639:Maximum likelihood 6534:Exponential family 6467:Density estimation 6427:Statistical theory 6387:Natural experiment 6333:Scientific control 6250:Survey methodology 5936:Standard deviation 5569:2019-06-16 at the 5354:2021-05-18 at the 5339:2021-06-16 at the 4414:Santa Fe Institute 3896:Galton, F (1877). 3482:, Addison-Wesley, 3091:Survey methodology 3025:Medical statistics 3003:, specifically in 2779:business analytics 2720:Management Science 2597: 2548:Tukey's range test 2399: 2145:Bayesian inference 2111:significance level 2090:significance level 2066: 1983: 1891: 1872:Mean squared error 1847:Standard deviation 1802:, which tests for 1733:maximum likelihood 1687:mean squared error 1437:den Berg (1991).) 1423:integral data type 1345:case-control study 1292:analyzing the data 1271:unbiased estimates 1205:randomized studies 1145:probability theory 1126:statistical models 1118:experiment designs 1034:Fisher's principle 1012:Fisher information 925:standard deviation 913: 877:probability theory 869:Christiaan Huygens 849: 786:frequency analysis 755:Islamic Golden Age 743: 739:probability theory 629:hypothesis testing 608:(like education). 598:standard deviation 506:probability theory 470:standard deviation 442:experimental study 400:"description of a 381: 358: 304:Mathematics Portal 8990: 8989: 8972:Scientific naming 8962:Quantum computing 8792:Computer hardware 8787:Clinical research 8782:Civil engineering 8677: 8676: 8276:Harmonic analysis 8063: 8062: 8001: 8000: 7997: 7996: 7936:National accounts 7906:Actuarial science 7898:Social statistics 7791: 7790: 7787: 7786: 7783: 7782: 7718:Survival function 7703: 7702: 7565:Granger causality 7406:Contingency table 7381:Survival analysis 7358: 7357: 7354: 7353: 7210:Linear regression 7105: 7104: 7101: 7100: 7076:Credible interval 7045: 7044: 6828: 6827: 6644:Method of moments 6513:Parametric family 6474:Statistical model 6404: 6403: 6400: 6399: 6318:Random assignment 6240:Statistical power 6174: 6173: 6170: 6169: 6019:Contingency table 5989: 5988: 5856:Generalized/power 5609:(12): 1304–1312. 5594:Cohen, J (1990). 5516:scientific fields 5382:978-1-83947-325-8 5345:Nica, M. (2013). 5116:978-0-314-03309-3 4953:978-0-12-373962-9 4816:Ioannidis, J.P.A. 4706:978-0-19-954145-4 4450:978-0-521-67105-7 3856:Helen Mary Walker 3836:Actuaries Digital 3816:978-0-8018-8235-7 3574:978-0-495-05064-3 3567:. Duxbury Press. 3539:978-0-88385-078-7 3509:978-0-03-077945-9 3488:978-0-201-15619-5 3429:Dodge, Y. (2006) 3350:978-0-19-954145-4 3306:(Subscription or 3222:Robust statistics 3130:Library resources 3096:Survival analysis 3045:Social statistics 3030:Political science 2981:Energy statistics 2916:Actuarial science 2759:linear regression 2649:have made use of 2639:permutation tests 2628:multilevel models 2571:linear regression 2528:linear regression 2281:statistical model 2248:Conjoint Analysis 2157:As everything in 2149:prior probability 2079:statistical power 2008:credible interval 1915:linear regression 1901:" in contrast to 1858:statistical error 1729:method of moments 1657:sample covariance 1618:estimation theory 1528:summary statistic 1505: 1504: 1497: 1415:Boolean data type 1241:treatment effects 1157:sample statistics 1046:Fisherian runaway 1032:concepts such as 941:method of moments 881:Jacob Bernoulli's 639:within the data ( 414:statistical model 338: 337: 293: 292: 132: 131: 9062: 9050:Research methods 9007: 9006: 8998: 8797:Computer science 8704: 8697: 8690: 8681: 8680: 8665: 8664: 8653: 8652: 8641: 8640: 8630: 8629: 8561:Computer algebra 8536:Computer science 8256:Complex analysis 8090: 8083: 8076: 8067: 8066: 8051: 8050: 8039: 8038: 8028: 8027: 8013: 8012: 7916:Crime statistics 7810: 7809: 7797: 7796: 7714: 7713: 7680:Fourier analysis 7667:Frequency domain 7647: 7594: 7560:Structural break 7520: 7519: 7469:Cluster analysis 7416:Log-linear model 7389: 7388: 7364: 7363: 7305: 7279:Homoscedasticity 7135: 7134: 7111: 7110: 7030: 7022: 7014: 7013:(Kruskal–Wallis) 6998: 6983: 6938:Cross validation 6923: 6905:Anderson–Darling 6852: 6839: 6838: 6810:Likelihood-ratio 6802:Parametric tests 6780:Permutation test 6763:1- & 2-tails 6654:Minimum distance 6626:Point estimation 6622: 6621: 6573:Optimal decision 6524: 6423: 6422: 6410: 6409: 6392:Quasi-experiment 6342:Adaptive designs 6193: 6192: 6180: 6179: 6057:Rank correlation 5819: 5818: 5810: 5809: 5797: 5796: 5764: 5757: 5750: 5741: 5740: 5699: 5689: 5679: 5654: 5633: 5631: 5625:. 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Edwards 1020:Lady tasting tea 897:in 1805, though 883:posthumous work 865:Pierre de Fermat 857:Gerolamo Cardano 813:Girolamo Ghilini 606:categorical data 519:to an idealized 483:central tendency 399: 348:, a very common 330: 323: 316: 302: 166: 165: 134: 133: 124: 117: 110: 94: 93: 40: 26: 25: 9070: 9069: 9065: 9064: 9063: 9061: 9060: 9059: 9055:Arab inventions 9035:Formal sciences 9015: 9014: 9013: 9001: 8993: 8991: 8986: 8885:Hebrew toponyms 8880:Arabic toponyms 8718: 8708: 8678: 8673: 8624: 8615: 8565: 8522: 8501:Systems science 8432: 8428:Homotopy theory 8394: 8361: 8313: 8285: 8232: 8179: 8150:Category theory 8136: 8101: 8094: 8064: 8059: 8022: 7993: 7955: 7892: 7878:quality control 7845: 7827:Clinical trials 7804: 7779: 7763: 7751:Hazard function 7745: 7699: 7661: 7645: 7608: 7604:Breusch–Godfrey 7592: 7569: 7509: 7484:Factor analysis 7430: 7411:Graphical model 7383: 7350: 7317: 7303: 7283: 7237: 7204: 7166: 7129: 7128: 7097: 7041: 7028: 7020: 7012: 6996: 6981: 6960:Rank statistics 6954: 6933:Model selection 6921: 6879:Goodness of fit 6873: 6850: 6824: 6796: 6749: 6694: 6683:Median unbiased 6611: 6522: 6455:Order statistic 6417: 6396: 6363: 6337: 6289: 6244: 6187: 6185:Data collection 6166: 6078: 6033: 6007: 5985: 5945: 5897: 5814:Continuous data 5804: 5791: 5773: 5768: 5706: 5629: 5598: 5571:Wayback Machine 5557:on 28 May 2020. 5536: 5482: 5480:Further reading 5477: 5476: 5413: 5409: 5400: 5398: 5383: 5367: 5363: 5356:Wayback Machine 5341:Wayback Machine 5313:Juta Academic. 5291: 5287: 5277: 5275: 5262: 5261: 5257: 5247: 5245: 5232: 5231: 5227: 5220: 5206: 5202: 5193: 5191: 5187: 5164: 5158: 5151: 5141: 5139: 5126: 5125: 5121: 5105: 5101: 5089: 5085: 5076: 5074: 5031: 5027: 5013: 5009: 5002:Credo Reference 4995: 4991: 4968: 4961: 4954: 4932: 4925: 4894: 4890: 4872: 4863: 4813: 4809: 4804: 4800: 4791: 4789: 4780: 4779: 4775: 4768: 4752: 4748: 4743: 4736: 4727: 4725: 4717: 4716: 4712: 4695: 4691: 4682: 4680: 4672: 4671: 4667: 4660: 4642: 4638: 4634:London: Arnold. 4629: 4625: 4616: 4612: 4581: 4577: 4565: 4561: 4543: 4539: 4532: 4510: 4506: 4459: 4455: 4436: 4432: 4423: 4421: 4408: 4407: 4403: 4388:10.2307/2342192 4370: 4366: 4361: 4357: 4352: 4348: 4339: 4337: 4330: 4314: 4310: 4305: 4301: 4285: 4281: 4276: 4272: 4233: 4229: 4224: 4220: 4205: 4201: 4192: 4190: 4186: 4155: 4149: 4145: 4106: 4102: 4087:10.2307/2528399 4069: 4065: 4050:10.2307/2682986 4032: 4028: 4011: 4010: 4006: 3997: 3995: 3968: 3964: 3935: 3931: 3894: 3890: 3881: 3879: 3872: 3853: 3849: 3840: 3838: 3828: 3824: 3817: 3801: 3797: 3787:Ars Conjectandi 3784: 3780: 3775: 3771: 3760:5(4): 321–328. 3752: 3748: 3741: 3721: 3717: 3688: 3684: 3653: 3646: 3639: 3625: 3621: 3614: 3600: 3596: 3587: 3585: 3581: 3575: 3560: 3554:Chance, Beth L. 3551: 3547: 3540: 3518: 3514: 3498: 3494: 3477: 3473: 3464: 3462: 3451: 3444: 3428: 3424: 3415: 3413: 3404: 3403: 3399: 3390: 3388: 3373: 3369: 3360: 3358: 3351: 3336: 3335: 3331: 3319: 3315: 3305: 3285: 3281: 3276: 3271: 3226: 3156: 3150: 3149: 3148: 3138: 3137: 3133: 3126: 3114: 3054: 2925:Astrostatistics 2904:social research 2892:network biology 2876: 2870: 2846:performance art 2838:Jackson Pollock 2799: 2739:business majors 2680: 2651:Bayesian models 2620:neural networks 2603: 2583: 2504:social sciences 2492: 2481: 2436: 2431: 2412:The concept of 2410: 2404: 2343:overgeneralized 2295: 2289: 2263: 2257: 2252: 2200:Factor analysis 2172: 2141:null hypothesis 2113:to include the 2070:critical region 2058:critical region 2038: 2032: 2018:, that is as a 2000:random variable 1972: 1966: 1827:null hypothesis 1825:Working from a 1823: 1797: 1792:fails to reject 1789: 1781: 1777: 1773: 1769: 1765: 1761: 1753:null hypothesis 1749: 1653:sample variance 1602: 1597: 1566: 1560: 1516: 1510: 1501: 1490: 1484: 1481: 1470: 1458: 1447: 1363: 1355:Main articles: 1353: 1336: 1306:Hawthorne study 1233: 1177: 1114: 1109: 1107:Data collection 1104: 1098: 1073:power of a test 1048:, a concept in 1016:null hypothesis 886:Ars Conjectandi 853:games of chance 734:Ars Conjectandi 725: 717:Main articles: 715: 687: 681: 602:continuous data 559: 553: 521:null hypothesis 334: 289: 288: 239: 231: 230: 226:Decision theory 174: 128: 88: 87: 73:Lists of topics 24: 17: 12: 11: 5: 9068: 9058: 9057: 9052: 9047: 9042: 9037: 9032: 9027: 9012: 9011: 8988: 8987: 8985: 8984: 8979: 8974: 8969: 8964: 8959: 8954: 8949: 8944: 8939: 8937:Nanotechnology 8934: 8929: 8924: 8919: 8914: 8909: 8907:Machine vision 8904: 8899: 8894: 8893: 8892: 8887: 8882: 8877: 8872: 8864: 8863: 8862: 8857: 8849: 8844: 8839: 8834: 8833: 8832: 8827: 8819: 8814: 8809: 8804: 8799: 8794: 8789: 8784: 8779: 8774: 8769: 8764: 8759: 8754: 8749: 8744: 8739: 8734: 8729: 8723: 8720: 8719: 8710:Glossaries of 8707: 8706: 8699: 8692: 8684: 8675: 8674: 8672: 8671: 8659: 8647: 8635: 8620: 8617: 8616: 8614: 8613: 8608: 8603: 8598: 8593: 8588: 8587: 8586: 8579:Mathematicians 8575: 8573: 8571:Related topics 8567: 8566: 8564: 8563: 8558: 8553: 8548: 8543: 8538: 8532: 8530: 8524: 8523: 8521: 8520: 8519: 8518: 8513: 8508: 8506:Control theory 8498: 8493: 8488: 8483: 8478: 8473: 8468: 8463: 8458: 8453: 8448: 8442: 8440: 8434: 8433: 8431: 8430: 8425: 8420: 8415: 8410: 8404: 8402: 8396: 8395: 8393: 8392: 8387: 8382: 8377: 8371: 8369: 8363: 8362: 8360: 8359: 8354: 8349: 8344: 8339: 8334: 8329: 8323: 8321: 8315: 8314: 8312: 8311: 8306: 8301: 8295: 8293: 8287: 8286: 8284: 8283: 8281:Measure theory 8278: 8273: 8268: 8263: 8258: 8253: 8248: 8242: 8240: 8234: 8233: 8231: 8230: 8225: 8220: 8215: 8210: 8205: 8200: 8195: 8189: 8187: 8181: 8180: 8178: 8177: 8172: 8167: 8162: 8157: 8152: 8146: 8144: 8138: 8137: 8135: 8134: 8129: 8124: 8123: 8122: 8117: 8106: 8103: 8102: 8093: 8092: 8085: 8078: 8070: 8061: 8060: 8058: 8057: 8045: 8033: 8019: 8006: 8003: 8002: 7999: 7998: 7995: 7994: 7992: 7991: 7986: 7981: 7976: 7971: 7965: 7963: 7957: 7956: 7954: 7953: 7948: 7943: 7938: 7933: 7928: 7923: 7918: 7913: 7908: 7902: 7900: 7894: 7893: 7891: 7890: 7885: 7880: 7871: 7866: 7861: 7855: 7853: 7847: 7846: 7844: 7843: 7838: 7833: 7824: 7822:Bioinformatics 7818: 7816: 7806: 7805: 7793: 7792: 7789: 7788: 7785: 7784: 7781: 7780: 7778: 7777: 7771: 7769: 7765: 7764: 7762: 7761: 7755: 7753: 7747: 7746: 7744: 7743: 7738: 7733: 7728: 7722: 7720: 7711: 7705: 7704: 7701: 7700: 7698: 7697: 7692: 7687: 7682: 7677: 7671: 7669: 7663: 7662: 7660: 7659: 7654: 7649: 7641: 7636: 7631: 7630: 7629: 7627:partial (PACF) 7618: 7616: 7610: 7609: 7607: 7606: 7601: 7596: 7588: 7583: 7577: 7575: 7574:Specific tests 7571: 7570: 7568: 7567: 7562: 7557: 7552: 7547: 7542: 7537: 7532: 7526: 7524: 7517: 7511: 7510: 7508: 7507: 7506: 7505: 7504: 7503: 7488: 7487: 7486: 7476: 7474:Classification 7471: 7466: 7461: 7456: 7451: 7446: 7440: 7438: 7432: 7431: 7429: 7428: 7423: 7421:McNemar's test 7418: 7413: 7408: 7403: 7397: 7395: 7385: 7384: 7360: 7359: 7356: 7355: 7352: 7351: 7349: 7348: 7343: 7338: 7333: 7327: 7325: 7319: 7318: 7316: 7315: 7299: 7293: 7291: 7285: 7284: 7282: 7281: 7276: 7271: 7266: 7261: 7259:Semiparametric 7256: 7251: 7245: 7243: 7239: 7238: 7236: 7235: 7230: 7225: 7220: 7214: 7212: 7206: 7205: 7203: 7202: 7197: 7192: 7187: 7182: 7176: 7174: 7168: 7167: 7165: 7164: 7159: 7154: 7149: 7143: 7141: 7131: 7130: 7127: 7126: 7121: 7115: 7107: 7106: 7103: 7102: 7099: 7098: 7096: 7095: 7094: 7093: 7083: 7078: 7073: 7072: 7071: 7066: 7055: 7053: 7047: 7046: 7043: 7042: 7040: 7039: 7034: 7033: 7032: 7024: 7016: 7000: 6997:(Mann–Whitney) 6992: 6991: 6990: 6977: 6976: 6975: 6964: 6962: 6956: 6955: 6953: 6952: 6951: 6950: 6945: 6940: 6930: 6925: 6922:(Shapiro–Wilk) 6917: 6912: 6907: 6902: 6897: 6889: 6883: 6881: 6875: 6874: 6872: 6871: 6863: 6854: 6842: 6836: 6834:Specific tests 6830: 6829: 6826: 6825: 6823: 6822: 6817: 6812: 6806: 6804: 6798: 6797: 6795: 6794: 6789: 6788: 6787: 6777: 6776: 6775: 6765: 6759: 6757: 6751: 6750: 6748: 6747: 6746: 6745: 6740: 6730: 6725: 6720: 6715: 6710: 6704: 6702: 6696: 6695: 6693: 6692: 6687: 6686: 6685: 6680: 6679: 6678: 6673: 6658: 6657: 6656: 6651: 6646: 6641: 6630: 6628: 6619: 6613: 6612: 6610: 6609: 6604: 6599: 6598: 6597: 6587: 6582: 6581: 6580: 6570: 6569: 6568: 6563: 6558: 6548: 6543: 6538: 6537: 6536: 6531: 6526: 6510: 6509: 6508: 6503: 6498: 6488: 6487: 6486: 6481: 6471: 6470: 6469: 6459: 6458: 6457: 6447: 6442: 6437: 6431: 6429: 6419: 6418: 6406: 6405: 6402: 6401: 6398: 6397: 6395: 6394: 6389: 6384: 6379: 6373: 6371: 6365: 6364: 6362: 6361: 6356: 6351: 6345: 6343: 6339: 6338: 6336: 6335: 6330: 6325: 6320: 6315: 6310: 6305: 6299: 6297: 6291: 6290: 6288: 6287: 6285:Standard error 6282: 6277: 6272: 6271: 6270: 6265: 6254: 6252: 6246: 6245: 6243: 6242: 6237: 6232: 6227: 6222: 6217: 6215:Optimal design 6212: 6207: 6201: 6199: 6189: 6188: 6176: 6175: 6172: 6171: 6168: 6167: 6165: 6164: 6159: 6154: 6149: 6144: 6139: 6134: 6129: 6124: 6119: 6114: 6109: 6104: 6099: 6094: 6088: 6086: 6080: 6079: 6077: 6076: 6071: 6070: 6069: 6064: 6054: 6049: 6043: 6041: 6035: 6034: 6032: 6031: 6026: 6021: 6015: 6013: 6012:Summary tables 6009: 6008: 6006: 6005: 5999: 5997: 5991: 5990: 5987: 5986: 5984: 5983: 5982: 5981: 5976: 5971: 5961: 5955: 5953: 5947: 5946: 5944: 5943: 5938: 5933: 5928: 5923: 5918: 5913: 5907: 5905: 5899: 5898: 5896: 5895: 5890: 5885: 5884: 5883: 5878: 5873: 5868: 5863: 5858: 5853: 5848: 5846:Contraharmonic 5843: 5838: 5827: 5825: 5816: 5806: 5805: 5793: 5792: 5790: 5789: 5784: 5778: 5775: 5774: 5767: 5766: 5759: 5752: 5744: 5738: 5737: 5728: 5722: 5714: 5705: 5704:External links 5702: 5701: 5700: 5670:(4): 696–701. 5655: 5645:(5): 587–606. 5634: 5632:on 2017-10-18. 5591: 5588:978-1137282392 5574: 5559: 5540: 5535:978-1938168208 5534: 5519: 5481: 5478: 5475: 5474: 5407: 5381: 5361: 5359: 5358: 5343: 5325:open textbooks 5322: 5321: 5307: 5305:978-0134705217 5285: 5255: 5225: 5219:978-0979570438 5218: 5212:. Erol Pekoz. 5200: 5175:(3): 983–992. 5149: 5119: 5099: 5096:978-1500815684 5083: 5045:(2): 257–269. 5025: 5007: 4989: 4959: 4952: 4923: 4904:(3): 134–149. 4888: 4861: 4807: 4798: 4773: 4766: 4746: 4734: 4723:owl.purdue.edu 4710: 4689: 4665: 4658: 4636: 4623: 4610: 4591:(4): 231–242. 4575: 4559: 4537: 4531:978-0781755641 4530: 4504: 4453: 4438:Freedman, D.A. 4430: 4401: 4382:(4): 557–625. 4364: 4355: 4346: 4328: 4308: 4299: 4279: 4270: 4249:10.1086/286141 4243:(6): 564–569. 4227: 4218: 4199: 4143: 4116:(3): 223–229. 4100: 4081:(2): 307–321. 4063: 4026: 4023:on 2008-09-25. 4004: 3962: 3929: 3888: 3871:978-0405066283 3870: 3864:. Arno Press. 3847: 3822: 3815: 3795: 3778: 3769: 3755:Review of the 3746: 3740:978-0231555647 3739: 3715: 3682: 3663:(4): 255–257. 3644: 3637: 3619: 3612: 3594: 3573: 3545: 3538: 3512: 3492: 3471: 3442: 3422: 3397: 3367: 3349: 3337:"Statistics". 3329: 3313: 3278: 3277: 3275: 3272: 3270: 3269: 3267: 3264: 3263: 3258: 3253: 3248: 3243: 3238: 3232: 3231: 3230: 3225: 3224: 3219: 3214: 3209: 3204: 3199: 3194: 3189: 3183: 3178: 3173: 3168: 3163: 3157: 3152:Main article: 3147: 3146: 3140: 3139: 3128: 3127: 3125: 3122: 3113: 3112: 3098: 3093: 3088: 3083: 3078: 3073: 3068: 3058: 3053: 3052: 3047: 3042: 3037: 3032: 3027: 3022: 3012: 3007: 2994: 2988: 2983: 2978: 2972: 2966: 2953: 2943: 2933: 2928: 2922: 2919: 2912: 2896:social science 2872:Main article: 2869: 2866: 2865: 2864: 2861:Iannis Xenakis 2853: 2850:Markov process 2842: 2830: 2815: 2798: 2795: 2789:, such as the 2771:decision trees 2741:, and covers 2679: 2676: 2647:Gibbs sampling 2599:Main article: 2582: 2579: 2491: 2488: 2480: 2477: 2435: 2432: 2430: 2427: 2403: 2400: 2371: 2370: 2367: 2364: 2361: 2358: 2291:Main article: 2288: 2285: 2259:Main article: 2256: 2253: 2251: 2250: 2245: 2240: 2231: 2226: 2221: 2216: 2210: 2202: 2197: 2192: 2187: 2180: 2171: 2168: 2167: 2166: 2155: 2152: 2133: 2095:test statistic 2054:test statistic 2034:Main article: 2031: 2028: 1968:Main article: 1965: 1962: 1956:may result in 1907:differentiable 1862:expected value 1851:Standard error 1844: 1843: 1840:Type II errors 1837: 1822: 1819: 1804:type II errors 1795: 1787: 1779: 1775: 1771: 1767: 1763: 1759: 1748: 1745: 1699:expected value 1678:and Student's 1642: 1601: 1598: 1596: 1593: 1562:Main article: 1559: 1556: 1512:Main article: 1509: 1506: 1503: 1502: 1461: 1459: 1452: 1446: 1443: 1427:real data type 1352: 1349: 1335: 1332: 1302: 1301: 1298: 1295: 1284: 1252: 1232: 1229: 1176: 1173: 1122:survey samples 1113: 1110: 1108: 1105: 1100:Main article: 1097: 1094: 917:Francis Galton 751:cryptographers 714: 711: 695:linear algebra 683:Main article: 680: 677: 635:), describing 555:Main article: 552: 549: 530:Type II errors 336: 335: 333: 332: 325: 318: 310: 307: 306: 295: 294: 291: 290: 287: 286: 281: 276: 271: 266: 261: 256: 251: 246: 240: 237: 236: 233: 232: 229: 228: 219: 214: 205: 200: 191: 186: 181: 175: 170: 169: 162: 161: 160: 159: 154: 146: 145: 139: 138: 130: 129: 127: 126: 119: 112: 104: 101: 100: 99: 98: 85: 80: 75: 70: 65: 60: 55: 50: 42: 41: 33: 32: 15: 9: 6: 4: 3: 2: 9067: 9056: 9053: 9051: 9048: 9046: 9043: 9041: 9038: 9036: 9033: 9031: 9028: 9026: 9023: 9022: 9020: 9010: 9005: 9000: 8999: 8996: 8983: 8980: 8978: 8975: 8973: 8970: 8968: 8965: 8963: 8960: 8958: 8955: 8953: 8950: 8948: 8945: 8943: 8940: 8938: 8935: 8933: 8930: 8928: 8925: 8923: 8920: 8918: 8915: 8913: 8910: 8908: 8905: 8903: 8900: 8898: 8895: 8891: 8888: 8886: 8883: 8881: 8878: 8876: 8873: 8871: 8868: 8867: 8865: 8861: 8858: 8856: 8853: 8852: 8850: 8848: 8845: 8843: 8840: 8838: 8835: 8831: 8828: 8826: 8823: 8822: 8820: 8818: 8815: 8813: 8810: 8808: 8805: 8803: 8800: 8798: 8795: 8793: 8790: 8788: 8785: 8783: 8780: 8778: 8775: 8773: 8770: 8768: 8765: 8763: 8760: 8758: 8755: 8753: 8750: 8748: 8745: 8743: 8740: 8738: 8735: 8733: 8730: 8728: 8725: 8724: 8721: 8717: 8713: 8705: 8700: 8698: 8693: 8691: 8686: 8685: 8682: 8670: 8669: 8660: 8658: 8657: 8648: 8646: 8645: 8636: 8634: 8633: 8628: 8622: 8621: 8618: 8612: 8609: 8607: 8604: 8602: 8599: 8597: 8594: 8592: 8589: 8585: 8582: 8581: 8580: 8577: 8576: 8574: 8572: 8568: 8562: 8559: 8557: 8554: 8552: 8549: 8547: 8544: 8542: 8539: 8537: 8534: 8533: 8531: 8529: 8528:Computational 8525: 8517: 8514: 8512: 8509: 8507: 8504: 8503: 8502: 8499: 8497: 8494: 8492: 8489: 8487: 8484: 8482: 8479: 8477: 8474: 8472: 8469: 8467: 8464: 8462: 8459: 8457: 8454: 8452: 8449: 8447: 8444: 8443: 8441: 8439: 8435: 8429: 8426: 8424: 8421: 8419: 8416: 8414: 8411: 8409: 8406: 8405: 8403: 8401: 8397: 8391: 8388: 8386: 8383: 8381: 8378: 8376: 8373: 8372: 8370: 8368: 8367:Number theory 8364: 8358: 8355: 8353: 8350: 8348: 8345: 8343: 8340: 8338: 8335: 8333: 8330: 8328: 8325: 8324: 8322: 8320: 8316: 8310: 8307: 8305: 8302: 8300: 8299:Combinatorics 8297: 8296: 8294: 8292: 8288: 8282: 8279: 8277: 8274: 8272: 8269: 8267: 8264: 8262: 8259: 8257: 8254: 8252: 8251:Real analysis 8249: 8247: 8244: 8243: 8241: 8239: 8235: 8229: 8226: 8224: 8221: 8219: 8216: 8214: 8211: 8209: 8206: 8204: 8201: 8199: 8196: 8194: 8191: 8190: 8188: 8186: 8182: 8176: 8173: 8171: 8168: 8166: 8163: 8161: 8158: 8156: 8153: 8151: 8148: 8147: 8145: 8143: 8139: 8133: 8130: 8128: 8125: 8121: 8118: 8116: 8113: 8112: 8111: 8108: 8107: 8104: 8099: 8091: 8086: 8084: 8079: 8077: 8072: 8071: 8068: 8056: 8055: 8046: 8044: 8043: 8034: 8032: 8031: 8026: 8020: 8018: 8017: 8008: 8007: 8004: 7990: 7987: 7985: 7984:Geostatistics 7982: 7980: 7977: 7975: 7972: 7970: 7967: 7966: 7964: 7962: 7958: 7952: 7951:Psychometrics 7949: 7947: 7944: 7942: 7939: 7937: 7934: 7932: 7929: 7927: 7924: 7922: 7919: 7917: 7914: 7912: 7909: 7907: 7904: 7903: 7901: 7899: 7895: 7889: 7886: 7884: 7881: 7879: 7875: 7872: 7870: 7867: 7865: 7862: 7860: 7857: 7856: 7854: 7852: 7848: 7842: 7839: 7837: 7834: 7832: 7828: 7825: 7823: 7820: 7819: 7817: 7815: 7814:Biostatistics 7811: 7807: 7803: 7798: 7794: 7776: 7775:Log-rank test 7773: 7772: 7770: 7766: 7760: 7757: 7756: 7754: 7752: 7748: 7742: 7739: 7737: 7734: 7732: 7729: 7727: 7724: 7723: 7721: 7719: 7715: 7712: 7710: 7706: 7696: 7693: 7691: 7688: 7686: 7683: 7681: 7678: 7676: 7673: 7672: 7670: 7668: 7664: 7658: 7655: 7653: 7650: 7648: 7646:(Box–Jenkins) 7642: 7640: 7637: 7635: 7632: 7628: 7625: 7624: 7623: 7620: 7619: 7617: 7615: 7611: 7605: 7602: 7600: 7599:Durbin–Watson 7597: 7595: 7589: 7587: 7584: 7582: 7581:Dickey–Fuller 7579: 7578: 7576: 7572: 7566: 7563: 7561: 7558: 7556: 7555:Cointegration 7553: 7551: 7548: 7546: 7543: 7541: 7538: 7536: 7533: 7531: 7530:Decomposition 7528: 7527: 7525: 7521: 7518: 7516: 7512: 7502: 7499: 7498: 7497: 7494: 7493: 7492: 7489: 7485: 7482: 7481: 7480: 7477: 7475: 7472: 7470: 7467: 7465: 7462: 7460: 7457: 7455: 7452: 7450: 7447: 7445: 7442: 7441: 7439: 7437: 7433: 7427: 7424: 7422: 7419: 7417: 7414: 7412: 7409: 7407: 7404: 7402: 7401:Cohen's kappa 7399: 7398: 7396: 7394: 7390: 7386: 7382: 7378: 7374: 7370: 7365: 7361: 7347: 7344: 7342: 7339: 7337: 7334: 7332: 7329: 7328: 7326: 7324: 7320: 7314: 7310: 7306: 7300: 7298: 7295: 7294: 7292: 7290: 7286: 7280: 7277: 7275: 7272: 7270: 7267: 7265: 7262: 7260: 7257: 7255: 7254:Nonparametric 7252: 7250: 7247: 7246: 7244: 7240: 7234: 7231: 7229: 7226: 7224: 7221: 7219: 7216: 7215: 7213: 7211: 7207: 7201: 7198: 7196: 7193: 7191: 7188: 7186: 7183: 7181: 7178: 7177: 7175: 7173: 7169: 7163: 7160: 7158: 7155: 7153: 7150: 7148: 7145: 7144: 7142: 7140: 7136: 7132: 7125: 7122: 7120: 7117: 7116: 7112: 7108: 7092: 7089: 7088: 7087: 7084: 7082: 7079: 7077: 7074: 7070: 7067: 7065: 7062: 7061: 7060: 7057: 7056: 7054: 7052: 7048: 7038: 7035: 7031: 7025: 7023: 7017: 7015: 7009: 7008: 7007: 7004: 7003:Nonparametric 7001: 6999: 6993: 6989: 6986: 6985: 6984: 6978: 6974: 6973:Sample median 6971: 6970: 6969: 6966: 6965: 6963: 6961: 6957: 6949: 6946: 6944: 6941: 6939: 6936: 6935: 6934: 6931: 6929: 6926: 6924: 6918: 6916: 6913: 6911: 6908: 6906: 6903: 6901: 6898: 6896: 6894: 6890: 6888: 6885: 6884: 6882: 6880: 6876: 6870: 6868: 6864: 6862: 6860: 6855: 6853: 6848: 6844: 6843: 6840: 6837: 6835: 6831: 6821: 6818: 6816: 6813: 6811: 6808: 6807: 6805: 6803: 6799: 6793: 6790: 6786: 6783: 6782: 6781: 6778: 6774: 6771: 6770: 6769: 6766: 6764: 6761: 6760: 6758: 6756: 6752: 6744: 6741: 6739: 6736: 6735: 6734: 6731: 6729: 6726: 6724: 6721: 6719: 6716: 6714: 6711: 6709: 6706: 6705: 6703: 6701: 6697: 6691: 6688: 6684: 6681: 6677: 6674: 6672: 6669: 6668: 6667: 6664: 6663: 6662: 6659: 6655: 6652: 6650: 6647: 6645: 6642: 6640: 6637: 6636: 6635: 6632: 6631: 6629: 6627: 6623: 6620: 6618: 6614: 6608: 6605: 6603: 6600: 6596: 6593: 6592: 6591: 6588: 6586: 6583: 6579: 6578:loss function 6576: 6575: 6574: 6571: 6567: 6564: 6562: 6559: 6557: 6554: 6553: 6552: 6549: 6547: 6544: 6542: 6539: 6535: 6532: 6530: 6527: 6525: 6519: 6516: 6515: 6514: 6511: 6507: 6504: 6502: 6499: 6497: 6494: 6493: 6492: 6489: 6485: 6482: 6480: 6477: 6476: 6475: 6472: 6468: 6465: 6464: 6463: 6460: 6456: 6453: 6452: 6451: 6448: 6446: 6443: 6441: 6438: 6436: 6433: 6432: 6430: 6428: 6424: 6420: 6416: 6411: 6407: 6393: 6390: 6388: 6385: 6383: 6380: 6378: 6375: 6374: 6372: 6370: 6366: 6360: 6357: 6355: 6352: 6350: 6347: 6346: 6344: 6340: 6334: 6331: 6329: 6326: 6324: 6321: 6319: 6316: 6314: 6311: 6309: 6306: 6304: 6301: 6300: 6298: 6296: 6292: 6286: 6283: 6281: 6280:Questionnaire 6278: 6276: 6273: 6269: 6266: 6264: 6261: 6260: 6259: 6256: 6255: 6253: 6251: 6247: 6241: 6238: 6236: 6233: 6231: 6228: 6226: 6223: 6221: 6218: 6216: 6213: 6211: 6208: 6206: 6203: 6202: 6200: 6198: 6194: 6190: 6186: 6181: 6177: 6163: 6160: 6158: 6155: 6153: 6150: 6148: 6145: 6143: 6140: 6138: 6135: 6133: 6130: 6128: 6125: 6123: 6120: 6118: 6115: 6113: 6110: 6108: 6107:Control chart 6105: 6103: 6100: 6098: 6095: 6093: 6090: 6089: 6087: 6085: 6081: 6075: 6072: 6068: 6065: 6063: 6060: 6059: 6058: 6055: 6053: 6050: 6048: 6045: 6044: 6042: 6040: 6036: 6030: 6027: 6025: 6022: 6020: 6017: 6016: 6014: 6010: 6004: 6001: 6000: 5998: 5996: 5992: 5980: 5977: 5975: 5972: 5970: 5967: 5966: 5965: 5962: 5960: 5957: 5956: 5954: 5952: 5948: 5942: 5939: 5937: 5934: 5932: 5929: 5927: 5924: 5922: 5919: 5917: 5914: 5912: 5909: 5908: 5906: 5904: 5900: 5894: 5891: 5889: 5886: 5882: 5879: 5877: 5874: 5872: 5869: 5867: 5864: 5862: 5859: 5857: 5854: 5852: 5849: 5847: 5844: 5842: 5839: 5837: 5834: 5833: 5832: 5829: 5828: 5826: 5824: 5820: 5817: 5815: 5811: 5807: 5803: 5798: 5794: 5788: 5785: 5783: 5780: 5779: 5776: 5772: 5765: 5760: 5758: 5753: 5751: 5746: 5745: 5742: 5736: 5732: 5729: 5726: 5723: 5720: 5719: 5715: 5712: 5708: 5707: 5697: 5693: 5688: 5683: 5678: 5673: 5669: 5665: 5664:PLOS Medicine 5661: 5656: 5652: 5648: 5644: 5640: 5635: 5628: 5624: 5620: 5616: 5612: 5608: 5604: 5597: 5592: 5589: 5585: 5581: 5580: 5575: 5572: 5568: 5565: 5564: 5560: 5556: 5552: 5551: 5546: 5541: 5537: 5531: 5527: 5526: 5520: 5517: 5513: 5509: 5505: 5501: 5497: 5495: 5490: 5489: 5484: 5483: 5470: 5466: 5461: 5456: 5452: 5448: 5443: 5438: 5434: 5430: 5426: 5422: 5418: 5411: 5396: 5392: 5388: 5384: 5378: 5374: 5373: 5365: 5357: 5353: 5350: 5349: 5344: 5342: 5338: 5335: 5334: 5329: 5328: 5326: 5320: 5316: 5312: 5308: 5306: 5302: 5298: 5294: 5293: 5289: 5273: 5269: 5265: 5259: 5243: 5239: 5235: 5229: 5221: 5215: 5211: 5204: 5186: 5182: 5178: 5174: 5170: 5163: 5156: 5154: 5137: 5133: 5129: 5123: 5117: 5113: 5109: 5103: 5097: 5093: 5087: 5072: 5068: 5064: 5060: 5056: 5052: 5048: 5044: 5040: 5036: 5029: 5022: 5018: 5011: 5003: 4999: 4993: 4985: 4981: 4977: 4973: 4966: 4964: 4955: 4949: 4945: 4940: 4939: 4930: 4928: 4919: 4915: 4911: 4907: 4903: 4899: 4892: 4886: 4885:0-393-31072-8 4882: 4878: 4877: 4870: 4868: 4866: 4857: 4853: 4848: 4843: 4838: 4833: 4829: 4825: 4824:PLOS Medicine 4821: 4817: 4811: 4802: 4787: 4783: 4777: 4769: 4763: 4759: 4758: 4750: 4741: 4739: 4724: 4720: 4714: 4707: 4703: 4699: 4693: 4679: 4675: 4669: 4661: 4659:0-471-31009-3 4655: 4650: 4649: 4640: 4633: 4627: 4620: 4614: 4606: 4602: 4598: 4594: 4590: 4586: 4579: 4572: 4568: 4563: 4555: 4551: 4547: 4546:Mosteller, F. 4541: 4533: 4527: 4523: 4518: 4517: 4508: 4500: 4496: 4491: 4486: 4481: 4476: 4472: 4468: 4464: 4457: 4451: 4447: 4443: 4439: 4434: 4419: 4415: 4411: 4405: 4397: 4393: 4389: 4385: 4381: 4377: 4376: 4368: 4359: 4350: 4335: 4331: 4329:0-691-00057-3 4325: 4321: 4320: 4312: 4303: 4297: 4296:0-19-850440-3 4293: 4289: 4283: 4274: 4266: 4262: 4258: 4254: 4250: 4246: 4242: 4238: 4231: 4222: 4215: 4214: 4210:R.A. Fisher, 4209: 4203: 4185: 4181: 4177: 4173: 4169: 4165: 4161: 4154: 4147: 4139: 4135: 4131: 4127: 4123: 4119: 4115: 4111: 4104: 4096: 4092: 4088: 4084: 4080: 4076: 4075: 4067: 4059: 4055: 4051: 4047: 4043: 4039: 4038: 4030: 4022: 4018: 4014: 4008: 3993: 3989: 3985: 3981: 3977: 3973: 3966: 3957: 3952: 3948: 3944: 3940: 3933: 3924: 3919: 3915: 3911: 3907: 3903: 3899: 3892: 3877: 3873: 3867: 3863: 3862: 3857: 3851: 3837: 3833: 3826: 3818: 3812: 3809:. JHU Press. 3808: 3807: 3799: 3793:(pp. 88-103). 3792: 3788: 3782: 3773: 3767: 3763: 3759: 3758: 3750: 3742: 3736: 3732: 3728: 3727: 3719: 3710: 3705: 3702:(18): 76–77. 3701: 3697: 3693: 3686: 3678: 3674: 3670: 3666: 3662: 3658: 3651: 3649: 3640: 3634: 3630: 3623: 3615: 3609: 3605: 3598: 3580: 3576: 3570: 3566: 3559: 3555: 3549: 3541: 3535: 3531: 3527: 3523: 3516: 3510: 3506: 3502: 3496: 3489: 3485: 3481: 3475: 3460: 3456: 3449: 3447: 3440: 3439:0-19-920613-9 3436: 3432: 3426: 3411: 3407: 3401: 3386: 3382: 3378: 3371: 3356: 3352: 3346: 3342: 3341: 3333: 3327: 3323: 3317: 3309: 3301: 3297: 3296: 3290: 3283: 3279: 3268: 3266: 3265: 3262: 3259: 3257: 3254: 3252: 3249: 3247: 3244: 3242: 3239: 3237: 3234: 3233: 3228: 3227: 3223: 3220: 3218: 3215: 3213: 3210: 3208: 3205: 3203: 3200: 3198: 3195: 3193: 3190: 3187: 3184: 3182: 3179: 3177: 3174: 3172: 3169: 3167: 3164: 3162: 3159: 3158: 3155: 3145: 3142: 3141: 3136: 3131: 3121: 3119: 3111: 3107: 3103: 3099: 3097: 3094: 3092: 3089: 3087: 3084: 3082: 3079: 3077: 3074: 3072: 3069: 3067: 3063: 3060: 3059: 3057: 3051: 3048: 3046: 3043: 3041: 3038: 3036: 3033: 3031: 3028: 3026: 3023: 3020: 3016: 3013: 3011: 3008: 3006: 3002: 2998: 2995: 2992: 2989: 2987: 2984: 2982: 2979: 2976: 2973: 2970: 2967: 2963: 2957: 2954: 2951: 2947: 2944: 2941: 2937: 2934: 2932: 2931:Biostatistics 2929: 2926: 2923: 2920: 2917: 2914: 2913: 2911: 2909: 2905: 2901: 2897: 2893: 2889: 2885: 2881: 2880:biostatistics 2875: 2862: 2858: 2854: 2851: 2847: 2843: 2839: 2835: 2831: 2828: 2824: 2820: 2816: 2813: 2812:scatter plots 2809: 2808:number theory 2805: 2804: 2803: 2794: 2792: 2788: 2784: 2780: 2776: 2772: 2768: 2764: 2760: 2756: 2752: 2748: 2744: 2740: 2735: 2733: 2729: 2728:economic data 2725: 2721: 2717: 2713: 2709: 2705: 2701: 2697: 2693: 2689: 2685: 2675: 2673: 2669: 2665: 2661: 2657: 2652: 2648: 2644: 2640: 2636: 2631: 2629: 2625: 2621: 2617: 2613: 2609: 2608:linear models 2602: 2595: 2591: 2587: 2578: 2576: 2572: 2568: 2563: 2561: 2557: 2553: 2549: 2545: 2541: 2537: 2533: 2529: 2525: 2521: 2517: 2513: 2509: 2505: 2501: 2497: 2487: 2485: 2476: 2474: 2470: 2468: 2464: 2460: 2456: 2452: 2448: 2444: 2440: 2426: 2424: 2419: 2415: 2409: 2396: 2392: 2388: 2384: 2380: 2375: 2368: 2365: 2362: 2359: 2356: 2355: 2354: 2351: 2349: 2344: 2340: 2335: 2333: 2329: 2328: 2323: 2319: 2314: 2312: 2307: 2302: 2299: 2294: 2284: 2282: 2278: 2275: 2271: 2267: 2262: 2249: 2246: 2244: 2241: 2239: 2237: 2232: 2230: 2227: 2225: 2222: 2220: 2217: 2214: 2211: 2209: 2208: 2205:Mann–Whitney 2203: 2201: 2198: 2196: 2193: 2191: 2188: 2185: 2182: 2181: 2179: 2177: 2164: 2160: 2156: 2153: 2150: 2146: 2142: 2138: 2134: 2131: 2127: 2123: 2119: 2117: 2112: 2107: 2106: 2105: 2103: 2098: 2096: 2091: 2086: 2082: 2080: 2076: 2071: 2063: 2059: 2055: 2050: 2046: 2044: 2037: 2027: 2023: 2021: 2017: 2013: 2009: 2005: 2001: 1997: 1993: 1988: 1980: 1976: 1971: 1961: 1959: 1955: 1951: 1947: 1943: 1939: 1934: 1932: 1928: 1924: 1920: 1916: 1912: 1908: 1904: 1900: 1896: 1887: 1883: 1881: 1877: 1873: 1869: 1867: 1863: 1859: 1854: 1852: 1848: 1841: 1838: 1835: 1834:Type I errors 1832: 1831: 1830: 1828: 1818: 1816: 1812: 1811:statisticians 1807: 1805: 1801: 1793: 1785: 1756: 1754: 1744: 1742: 1738: 1737:least squares 1734: 1730: 1725: 1723: 1719: 1715: 1710: 1708: 1704: 1700: 1696: 1692: 1688: 1683: 1681: 1677: 1673: 1669: 1665: 1660: 1658: 1654: 1650: 1646: 1640: 1637: 1635: 1631: 1630:column vector 1628:given by the 1627: 1626:random vector 1623: 1622:random sample 1619: 1615: 1611: 1608:with a given 1607: 1592: 1590: 1586: 1582: 1578: 1574: 1573:data analysis 1570: 1565: 1555: 1553: 1549: 1545: 1541: 1537: 1533: 1529: 1525: 1521: 1515: 1499: 1496: 1488: 1485:December 2020 1478: 1474: 1468: 1467: 1462:This section 1460: 1456: 1451: 1450: 1442: 1438: 1434: 1432: 1428: 1424: 1420: 1416: 1412: 1408: 1404: 1400: 1396: 1391: 1389: 1385: 1381: 1377: 1372: 1368: 1362: 1358: 1351:Types of data 1348: 1346: 1342: 1331: 1328: 1324: 1320: 1319:control group 1315: 1314:assembly line 1311: 1307: 1299: 1296: 1293: 1289: 1285: 1282: 1278: 1277: 1272: 1268: 1264: 1260: 1256: 1253: 1250: 1246: 1242: 1238: 1237: 1236: 1228: 1226: 1222: 1218: 1214: 1210: 1206: 1202: 1198: 1194: 1190: 1186: 1182: 1172: 1170: 1166: 1162: 1158: 1154: 1151:to study the 1150: 1146: 1142: 1137: 1134: 1129: 1127: 1123: 1119: 1103: 1093: 1091: 1086: 1080: 1078: 1074: 1070: 1066: 1062: 1057: 1055: 1051: 1047: 1043: 1039: 1035: 1031: 1027: 1026: 1021: 1017: 1013: 1009: 1005: 1001: 997: 993: 992: 988:and his 1935 987: 986: 981: 977: 976: 971: 970:Ronald Fisher 967: 962: 960: 956: 955:biostatistics 952: 951: 946: 942: 938: 934: 930: 926: 922: 918: 910: 906: 902: 900: 896: 892: 888: 887: 882: 878: 874: 873:Juan Caramuel 870: 866: 862: 861:Blaise Pascal 858: 854: 846: 842: 838: 836: 834: 829: 825: 824: 818: 814: 809: 807: 803: 799: 795: 791: 787: 783: 780: 776: 772: 768: 764: 760: 756: 753:, during the 752: 748: 740: 736: 735: 729: 724: 720: 710: 708: 704: 700: 696: 692: 686: 676: 674: 671:, as well as 670: 666: 662: 661:interpolation 658: 657:extrapolation 654: 650: 646: 642: 638: 634: 630: 625: 624: 618: 614: 609: 607: 603: 599: 595: 591: 590: 585: 580: 575: 572: 568: 564: 558: 548: 546: 542: 538: 533: 531: 527: 526:Type I errors 522: 518: 514: 509: 507: 503: 499: 495: 494: 489: 485: 484: 479: 475: 471: 467: 463: 459: 455: 454:data analysis 450: 448: 443: 439: 435: 434:statisticians 431: 426: 424: 420: 415: 411: 407: 403: 395: 394: 389: 385: 378: 374: 370: 366: 365:Scatter plots 362: 355: 351: 347: 342: 331: 326: 324: 319: 317: 312: 311: 309: 308: 305: 301: 297: 296: 285: 282: 280: 277: 275: 272: 270: 267: 265: 262: 260: 257: 255: 252: 250: 247: 245: 242: 241: 235: 234: 227: 223: 220: 218: 215: 213: 209: 206: 204: 201: 199: 195: 192: 190: 187: 185: 182: 180: 179:Number theory 177: 176: 173: 168: 167: 164: 163: 158: 155: 153: 150: 149: 148: 147: 144: 141: 140: 136: 135: 125: 120: 118: 113: 111: 106: 105: 103: 102: 97: 92: 86: 84: 81: 79: 76: 74: 71: 69: 66: 64: 61: 59: 56: 54: 53:Statisticians 51: 49: 46: 45: 44: 43: 39: 35: 34: 31: 28: 27: 22: 8821:Engineering 8772:Cell biology 8742:Architecture 8666: 8654: 8642: 8623: 8556:Optimization 8495: 8418:Differential 8342:Differential 8309:Order theory 8304:Graph theory 8208:Group theory 8052: 8040: 8021: 8014: 7926:Econometrics 7876: / 7859:Chemometrics 7836:Epidemiology 7829: / 7802:Applications 7644:ARIMA model 7591:Q-statistic 7540:Stationarity 7436:Multivariate 7379: / 7375: / 7373:Multivariate 7371: / 7311: / 7307: / 7081:Bayes factor 6980:Signed rank 6892: 6866: 6858: 6846: 6541:Completeness 6377:Cohort study 6275:Opinion poll 6210:Missing data 6197:Study design 6152:Scatter plot 6074:Scatter plot 6067:Spearman's ρ 6029:Grouped data 5770: 5717: 5667: 5663: 5642: 5638: 5627:the original 5606: 5602: 5578: 5562: 5555:the original 5548: 5524: 5504:experimental 5493: 5486: 5424: 5420: 5410: 5399:. Retrieved 5371: 5364: 5347: 5332: 5310: 5296: 5288: 5276:. Retrieved 5267: 5258: 5246:. Retrieved 5237: 5228: 5209: 5203: 5192:. Retrieved 5172: 5168: 5140:. Retrieved 5131: 5122: 5107: 5102: 5086: 5075:. Retrieved 5042: 5038: 5028: 5020: 5016: 5010: 5001: 4998:Freund, J.E. 4992: 4975: 4971: 4937: 4901: 4897: 4891: 4874: 4827: 4823: 4810: 4801: 4790:. Retrieved 4776: 4756: 4749: 4726:. Retrieved 4722: 4713: 4697: 4692: 4681:. Retrieved 4677: 4668: 4647: 4639: 4631: 4626: 4618: 4613: 4588: 4584: 4578: 4570: 4567:Nelder, J.A. 4562: 4553: 4540: 4515: 4507: 4470: 4466: 4456: 4441: 4433: 4422:. Retrieved 4413: 4404: 4379: 4373: 4367: 4358: 4349: 4338:. Retrieved 4318: 4311: 4302: 4282: 4273: 4240: 4236: 4230: 4221: 4211: 4207: 4202: 4191:. Retrieved 4163: 4159: 4146: 4113: 4109: 4103: 4078: 4072: 4066: 4041: 4035: 4029: 4021:the original 4007: 3996:. Retrieved 3979: 3978:. Series 5. 3975: 3965: 3949:(2): 73–79. 3946: 3942: 3932: 3905: 3901: 3891: 3880:. Retrieved 3860: 3850: 3839:. 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Retrieved 3339: 3332: 3325: 3316: 3293: 3289:"statistics" 3282: 3134: 3115: 3106:sabermetrics 3064: / 3055: 2991:Epidemiology 2975:Econometrics 2956:Data science 2936:Chemometrics 2877: 2859:invented by 2823:chaos theory 2800: 2736: 2724:Econometrics 2681: 2632: 2604: 2564: 2508:econometrics 2498:, including 2493: 2482: 2471: 2454: 2446: 2442: 2438: 2437: 2429:Applications 2411: 2394: 2390: 2386: 2382: 2352: 2336: 2332:Darrell Huff 2325: 2315: 2303: 2296: 2269: 2265: 2264: 2235: 2206: 2173: 2129: 2115: 2099: 2087: 2083: 2067: 2039: 2030:Significance 2024: 1991: 1984: 1950:missing data 1935: 1892: 1870: 1855: 1845: 1824: 1808: 1791: 1783: 1757: 1750: 1735:method, the 1726: 1711: 1684: 1666:is called a 1663: 1661: 1638: 1603: 1568: 1567: 1535: 1526:sense) is a 1519: 1517: 1491: 1482: 1471:Please help 1466:verification 1463: 1439: 1435: 1392: 1364: 1341:cohort study 1337: 1303: 1280: 1274: 1234: 1178: 1138: 1130: 1115: 1081: 1065:Jerzy Neyman 1061:Egon Pearson 1058: 1023: 989: 983: 973: 963: 948: 921:Karl Pearson 914: 909:Karl Pearson 884: 850: 832: 821: 810: 788:to decipher 781: 771:combinations 767:permutations 762: 744: 732: 731:Bernoulli's 688: 669:spatial data 637:associations 621: 617:experimental 610: 587: 576: 560: 551:Introduction 541:missing data 534: 510: 497: 491: 487: 481: 478:distribution 477: 464:such as the 451: 427: 391: 383: 382: 371:are used in 221: 29: 9040:Information 9009:Mathematics 8942:Ornithology 8927:Meteorology 8912:Mathematics 8902:Ichthyology 8737:Archaeology 8732:Agriculture 8716:engineering 8668:WikiProject 8511:Game theory 8491:Probability 8228:Homological 8218:Multilinear 8198:Commutative 8175:Type theory 8142:Foundations 8098:mathematics 8054:WikiProject 7969:Cartography 7931:Jurimetrics 7883:Reliability 7614:Time domain 7593:(Ljung–Box) 7515:Time-series 7393:Categorical 7377:Time-series 7369:Categorical 7304:(Bernoulli) 7139:Correlation 7119:Correlation 6915:Jarque–Bera 6887:Chi-squared 6649:M-estimator 6602:Asymptotics 6546:Sufficiency 6313:Interaction 6225:Replication 6205:Effect size 6162:Violin plot 6142:Radar chart 6122:Forest plot 6112:Correlogram 6062:Kendall's τ 5299:, Pearson. 4830:(8): e124. 4206:OED quote: 3104:– known as 3015:Jurimetrics 2946:Data mining 2834:process art 2819:forecasting 2767:time series 2763:forecasting 2684:management- 2660:Mathematica 2414:correlation 2348:represented 2195:Correlation 1996:frequentist 1940:(noise) or 1651:, unbiased 1649:sample mean 1612:: standard 1532:information 1380:temperature 1231:Experiments 1018:during the 1000:sufficiency 929:correlation 828:John Graunt 806:sample size 673:data mining 665:time series 649:forecasting 641:correlation 567:mathematics 517:alternative 498:variability 423:experiments 369:line charts 269:Linguistics 259:Computation 254:Geosciences 217:Probability 143:Mathematics 9025:Statistics 9019:Categories 8957:Psychiatry 8866:Geography 8837:Entomology 8496:Statistics 8375:Arithmetic 8337:Arithmetic 8203:Elementary 8170:Set theory 7921:Demography 7639:ARMA model 7444:Regression 7021:(Friedman) 6982:(Wilcoxon) 6920:Normality 6910:Lilliefors 6857:Student's 6733:Resampling 6607:Robustness 6595:divergence 6585:Efficiency 6523:(monotone) 6518:Likelihood 6435:Population 6268:Stratified 6220:Population 6039:Dependence 5995:Count data 5926:Percentile 5903:Dispersion 5836:Arithmetic 5771:Statistics 5401:2021-09-16 5391:1132348139 5375:. 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