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y“(n)-Verteilung vertafelt. Bei n > 30 ergeben sich die a-Fraktile x, der y“(n)- Verteilung näherungsweise gemäß Wo, F (F. + V2n – 1)“, wobei F, das a-Fraktil der. wo c eine Größe ist, die nicht von N oder E abhängt. Im Falle der BoseEinstein- Statistik!? ist dann stets M2p = 1 und M2 gleich der Zahl der Sätze N, welche. N (beziehungsweise n) ist ein Buchstabe des lateinischen Alphabets, siehe N. Darüber hinaus ist das Symbol für die Menge der natürlichen Zahlen. Statistik: N die Größe der Grundgesamtheit; n die Anzahl der Merkmalsausprägungen.

Een belangrijk begrippenpaar in de statistiek is populatie en steekproef. Men dient steeds goed te onderscheiden of men over de populatie verdeling spreekt dan wel over de steekproef.

De populatie is over het algemeen slechts in formele zin gegeven in termen van een kansverdeling met enkele onbekende parameters.

Het zijn deze parameters die men graag zou kennen, maar om uiteenlopende redenen niet kent. Een steekproef verschaft informatie over de parameters, door het geven van een schatting , het toetsen van een hypothese over een parameter, e.

Zo is er het populatiegemiddelde, meestal onbekend, en als schatting daarvan het steekproefgemiddelde. Evenzo is de steekproefvariantie een schatting van de populatievariantie, enzovoorts.

Doordat de uitkomst van een steekproef meestal sterk door het toeval bepaald wordt, maakt de statistiek veel gebruik van de kansrekening. Door middel van statistisch onderzoek probeert men deze waarde te benaderen via schattingen , toetsen en betrouwbaarheidsintervallen.

De Bayesianen geloven niet in een "ware" waarde en staan toe dat de parameters zelf stochastische variabelen zijn, met een meestal onbekende verdeling.

Wel wordt tevoren een veronderstelling over de verdeling gemaakt; de veronderstelde verdeling heet a-prioriverdeling. Hierdoor kan het theorema van Bayes toegepast worden.

Gevolgen hiervan zijn onder meer dat informatie, ook subjectieve informatie, van buiten de steekproef ingebracht kan worden. Verder betekent het dat de interpretatie van de uitkomsten fundamenteel wijzigt.

Een centraal begrip in de statistiek is dat van de stochastische variabele. Deze grootheid vertegenwoordigt in feite de populatieverdeling of de betrokken modelmatige kansverdeling.

De steekproefuitkomsten vat men op als waarnemingen aan deze grootheid. De basisveronderstelling bij een statistische analyse over de betrokken verdeling, is daarmee een veronderstelling omtrent de verdeling van de betrokken stochastische variabele; de veronderstelde verdeling wordt het "model" genoemd.

But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented.

Other categorizations have been proposed. For example, Mosteller and Tukey [18] distinguished grades, ranks, counted fractions, counts, amounts, and balances.

Nelder [19] described continuous counts, continuous ratios, count ratios, and categorical modes of data.

See also Chrisman , [20] van den Berg 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.

Whether or not a transformation is sensible to contemplate depends on the question one is trying to answer" Hand, , p.

Consider independent identically distributed IID random variables with a given probability distribution: A statistic is a random variable that is a function of the random sample, but not a function of unknown parameters.

The probability distribution of the statistic, though, may have unknown parameters. Consider now a function of the unknown parameter: Commonly used estimators include sample mean , unbiased sample variance and sample covariance.

A random variable that is a function of the random sample and of the unknown parameter, but whose probability distribution does not depend on the unknown parameter is called a pivotal quantity or pivot.

Widely used pivots include the z-score , the chi square statistic and Student's t-value. Between two estimators of a given parameter, the one with lower mean squared error is said to be more efficient.

Furthermore, an estimator is said to be unbiased if its expected value is equal to the true value of the unknown parameter being estimated, and asymptotically unbiased if its expected value converges at the limit to the true value of such parameter.

Other desirable properties for estimators include: UMVUE estimators 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 consistent estimators which converges in probability to the true value of such parameter.

This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed: Interpretation of statistical information can often involve the development of a null hypothesis which is usually but not necessarily that no relationship exists among variables or that no change occurred over time.

The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H 0 , asserts that the defendant is innocent, whereas the alternative hypothesis, H 1 , asserts that the defendant is guilty.

The indictment comes because of suspicion of the guilt. The H 0 status quo stands in opposition to H 1 and is maintained unless H 1 is supported by evidence "beyond a reasonable doubt".

However, "failure to reject H 0 " in this case does not imply innocence, but merely that the evidence was insufficient to convict.

So the jury does not necessarily accept H 0 but fails to reject H 0. While one can not "prove" a null hypothesis, one can test how close it is to being true with a power test , which tests for type II errors.

What statisticians call an alternative hypothesis is simply a hypothesis that contradicts the null hypothesis. Working from a null hypothesis , two basic forms of error are recognized:.

Standard deviation refers to the extent to which individual observations in a sample differ from a central value, such as the sample or population mean, while Standard error refers to an estimate of difference between sample mean and population mean.

A statistical error is the amount by which an observation differs from its expected value , a residual is the amount an observation differs from the value the estimator of the expected value assumes on a given sample also called prediction.

Mean squared error is used for obtaining efficient estimators , a widely used class of estimators. Root mean square error is simply the square root of mean squared error.

Many statistical methods seek to minimize the residual sum of squares , and these are called " methods of least squares " in contrast to Least absolute deviations.

The latter gives equal weight to small and big errors, while the former gives more weight to large errors. Residual sum of squares is also differentiable , which provides a handy property for doing regression.

Least squares applied to linear regression is called ordinary least squares method and least squares applied to nonlinear regression is called non-linear least squares.

Also in a linear regression model the non deterministic part of the model is called error term, disturbance or more simply noise.

Both linear regression and non-linear regression are addressed in polynomial least squares , 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.

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

Confidence intervals allow statisticians to express how closely the sample estimate matches the true value in the whole population.

From the frequentist perspective, such a claim does not even make sense, as the true value is not a random variable. Either the true value is or is not within the given interval.

One approach that does yield an interval that can be interpreted as having a given probability of containing the true value is to use a credible interval from Bayesian statistics: In principle confidence intervals can be symmetrical or asymmetrical.

An interval can be asymmetrical because it works as lower or upper bound for a parameter left-sided interval or right sided interval , but it can also be asymmetrical because the two sided interval is built violating symmetry around the estimate.

Sometimes the bounds for a confidence interval are reached asymptotically and these are used to approximate the true bounds. Interpretation often comes down to the level of statistical significance applied to the numbers and often refers to the probability of a value accurately rejecting the null hypothesis sometimes referred to as the p-value.

The standard approach [23] is to test a null hypothesis against an alternative hypothesis. A critical region 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 statistical significance and the probability of type II error is the probability that the estimator doesn't belong to the critical region given that the alternative hypothesis is true.

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

Referring to statistical significance does not necessarily mean that the overall result is significant in real world terms.

For example, in a large study of a drug it may be shown that the drug has a statistically significant but very small beneficial effect, such that the drug is unlikely to help the patient noticeably.

Although in principle the acceptable level of statistical significance may be subject to debate, the p-value is the smallest significance level 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 test statistic.

Therefore, the smaller the p-value, the lower the probability of committing type I error. Some problems are usually associated with this framework See criticism of hypothesis testing:.

Some well-known statistical tests and procedures are:. Misuse of statistics can produce subtle, but serious errors in description and interpretation—subtle in the sense that even experienced professionals make such errors, and serious in the sense that they can lead to devastating decision errors.

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

Even when statistical techniques are correctly applied, the results can be difficult to interpret for those lacking expertise. The statistical significance of a trend in the data—which measures the extent to which a trend could be caused by random variation in the sample—may or may not agree with an intuitive sense of its significance.

The set of basic statistical skills and skepticism that people need to deal with information in their everyday lives properly is referred to as statistical literacy.

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

Misuse of statistics can be both inadvertent and intentional, and the book How to Lie with Statistics [28] 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.

Warne, Lazo, Ramos, and Ritter Ways to avoid misuse of statistics include using proper diagrams and avoiding bias. Thus, people may often believe that something is true even if it is not well represented.

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

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

For example, a study of annual income that also looks at age of death might find that poor people tend to have shorter lives than affluent people.

The two variables are said to be correlated; however, they may or may not be the cause of one another. The correlation phenomena could be caused by a third, previously unconsidered phenomenon, called a lurking variable or confounding variable.

For this reason, there is no way to immediately infer the existence of a causal relationship between the two variables. See Correlation does not imply causation.

Some scholars pinpoint the origin of statistics to , with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt.

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

Today, statistics is widely employed in government, business, and natural and social sciences. Its mathematical foundations were laid in the 17th century with the development of the probability theory by Gerolamo Cardano , Blaise Pascal and Pierre de Fermat.

Mathematical probability theory arose from the study of games of chance, although the concept of probability was already examined in medieval law and by philosophers such as Juan Caramuel.

The modern field of statistics emerged in the late 19th and early 20th century in three stages. Galton's contributions included introducing the concepts of standard deviation , correlation , regression analysis and the application of these methods to the study of the variety of human characteristics—height, weight, eyelash length among others.

Ronald Fisher coined the term null hypothesis during the Lady tasting tea experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation".

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

Fisher's most important publications were his seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance , which was the first to use the statistical term, variance , his classic work Statistical Methods for Research Workers and his The Design of Experiments , [44] [45] [46] [47] where he developed rigorous design of experiments models.

He originated the concepts of sufficiency , ancillary statistics , Fisher's linear discriminator and Fisher information. Edwards has remarked that it is "probably the most celebrated argument in evolutionary biology ".

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

They introduced the concepts of " Type II " error, power of a test and confidence intervals. Jerzy Neyman in showed that stratified random sampling was in general a better method of estimation than purposive quota sampling.

Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a collated body of data and for making decisions in the face of uncertainty based on statistical methodology.

The use of modern computers has expedited large-scale statistical computations, and has also made possible new methods that are impractical to perform manually.

Statistics continues to be an area of active research, for example on the problem of how to analyze Big data.

Applied statistics comprises descriptive statistics and the application of inferential statistics. Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to methods of estimation and inference, but also various aspects of computational statistics and the design of experiments.

There are two applications for machine learning and data mining: Statistics tools are necessary for the data analysis.

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

Statistical consultants can help organizations and companies that don't have in-house expertise relevant to their particular questions. The rapid and sustained increases in computing power starting from the second half of the 20th century have had a substantial impact on the practice of statistical science.

Early statistical models were almost always from the class of linear models , but powerful computers, coupled with suitable numerical algorithms , caused an increased interest in nonlinear models such as neural networks as well as the creation of new types, such as generalized linear models and multilevel models.

Increased computing power has also led to the growing popularity of computationally intensive methods based on resampling , such as permutation tests and the bootstrap , while techniques such as Gibbs sampling have made use of Bayesian models more feasible.

The computer revolution has implications for the future of statistics with new emphasis on "experimental" and "empirical" statistics. A large number of both general and special purpose statistical software are now available.

Traditionally, statistics was concerned with drawing inferences using a semi-standardized methodology that was "required learning" in most sciences.

What was once considered a dry subject, taken in many fields as a degree-requirement, is now viewed enthusiastically.

Statistical techniques are used in a wide range of types of scientific and social research, including: Some fields of inquiry use applied statistics so extensively that they have specialized terminology.

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

Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systems variability, control processes as in statistical process control or SPC , for summarizing data, and to make data-driven decisions.

In these roles, it is a key tool, and perhaps the only reliable tool. From Wikipedia, the free encyclopedia.

For other uses, see Statistics disambiguation. Statistical data type and Levels of measurement. History of statistics and Founders of statistics.

List of fields of application of statistics. Actuarial science assesses risk in the insurance and finance industries Applied information economics Astrostatistics statistical evaluation of astronomical data Biostatistics Business statistics Chemometrics for analysis of data from chemistry Data mining applying statistics and pattern recognition to discover knowledge from data Data science Demography statistical study of populations Econometrics statistical analysis of economic data Energy statistics Engineering statistics Epidemiology statistical analysis of disease Geography and geographic information systems , specifically in spatial analysis Image processing Medical statistics Political science Psychological statistics Reliability engineering Social statistics Statistical mechanics.

Abundance estimation Data science Glossary of probability and statistics List of academic statistical associations List of important publications in statistics List of national and international statistical services List of statistical packages software List of statistics articles List of university statistical consulting centers Notation in probability and statistics.

Foundations of statistics List of statisticians Official statistics Multivariate analysis of variance. Stanford Encyclopedia of Philosophy. Meaning and Definition of Statistics".

Statistics for the Twenty-First Century. The Mathematical Association of America. Handbook of stochastic analysis and applications.

Theory of statistics Corr. A New Kind of Science. Theory and Practice , Cambridge University Press. Modern Epidemiology 3rd ed.

Data analysis and regression.

statistik n -

Anzahl befragte Personen oder aber eben auch Zeit in Tagen oder Monaten anderes. Die Berechnung der Quartile ist nicht ganz einheitlich; hier wurde offensichtlich nach einer etwas anderen Vorschrift gerechnet. Darüber hinaus hat das Zeichen und seine Abwandlungen folgende Bedeutungen:. Bei mir wäre es wahrscheinlich die Anzahl. Aus diesen Daten möchte ich jetzt ein Diagramm erstellen, das klappt auch ganz gut siehe Bild aber dennoch nicht ganz so wie ich es brauche. Bei mir wäre es wahrscheinlich die Anzahl. Umfang der Stichprobe x 1 , x 2 , Die Elemente der Stichprobe werden auf ein bestimmtes Merkmal untersucht, das in verschiedenen Ausprägungen auftreten kann. Die so erhaltene Zahl hat die Eigenschaft, dass die Hälfte der Werte darunter, die Hälfte darüber liegt. Durch die Nutzung dieser Website erklären Sie sich mit den Nutzungsbedingungen und der Datenschutzrichtlinie einverstanden.

N Statistik Video

Gruppering af talværdier - excel & N-spire (statistik) A hypothesis is proposed for vikingdirect statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship Beste Spielothek in Goslitz finden two data sets. Type I errors null hypothesis is falsely rejected giving casino seefled "false positive" and Type II errors null hypothesis fails to be rejected and an actual difference between populations is missed giving a "false negative". Population of capital cities and cities ofand more inhabitants Population of Beste Spielothek in Goslitz finden proper urban agglomeration, more Launch of the SDG Report 20 June - The Sustainable Development Goals Report reviews progress in the third year of implementation of the Agenda presenting an overview with charts and infographics of highlights of the 17 Goals, followed by chapters that focus in more depth on the Goals under review at the high-level political forum in July Even when statistical techniques are correctly applied, the results can be difficult to interpret for those lacking expertise. See Correlation does not imply causation. Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to methods of estimation and inference, but also various aspects of computational statistics and the design of experiments. A New Kind of Science. Population and Vital Statistics on Internet Quarterly report on the golden star casino no deposit census and mid-year population; latest vital statistics of births, deaths and infant deaths, more Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures. The dependability of a sample can be destroyed by [bias] The use of modern computers has expedited large-scale statistical computations, and has also made possible new methods that are impractical to perform manually. Deze pagina is voor het laatst bewerkt op 17 sep om Statistici trachten informatie over een populatie al dan niet abstract te krijgen uit de waarneming van een meestal beperkt aantal elementen van die populatie, de steekproef in sumertime geval dat de steekproef de gehele populatie omvat, spreekt men van volledige telling census, volkstelling.

N statistik -

In manchen Büchern findet sich für die Varianz folgende Formel: Also nicht wirklich genau so, aber bei den eher Waagerechten bei der oberen Linie nach oben und bei der unteren nach unten gebogen oder bei den eher Senkrechtendie linke Linie nach links und die rechte nach rechts gebogen. Hierzu liegen Daten seit vor, welche natürlich mit Reichsmark hinterlegt sind. Aber die Kaufkraft vor 5 Jahren o. Darauf möchte ich die Grafik erstellen. Und das ist halt nicht das was ich gerne hätte. N beziehungsweise n ist ein Buchstabe des lateinischen Alphabets , siehe N.

Other categorizations have been proposed. For example, Mosteller and Tukey [18] distinguished grades, ranks, counted fractions, counts, amounts, and balances.

Nelder [19] described continuous counts, continuous ratios, count ratios, and categorical modes of data. See also Chrisman , [20] van den Berg 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.

Whether or not a transformation is sensible to contemplate depends on the question one is trying to answer" Hand, , p.

Consider independent identically distributed IID random variables with a given probability distribution: A statistic is a random variable that is a function of the random sample, but not a function of unknown parameters.

The probability distribution of the statistic, though, may have unknown parameters. Consider now a function of the unknown parameter: Commonly used estimators include sample mean , unbiased sample variance and sample covariance.

A random variable that is a function of the random sample and of the unknown parameter, but whose probability distribution does not depend on the unknown parameter is called a pivotal quantity or pivot.

Widely used pivots include the z-score , the chi square statistic and Student's t-value. Between two estimators of a given parameter, the one with lower mean squared error is said to be more efficient.

Furthermore, an estimator is said to be unbiased if its expected value is equal to the true value of the unknown parameter being estimated, and asymptotically unbiased if its expected value converges at the limit to the true value of such parameter.

Other desirable properties for estimators include: UMVUE estimators 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 consistent estimators which converges in probability to the true value of such parameter.

This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed: Interpretation of statistical information can often involve the development of a null hypothesis which is usually but not necessarily that no relationship exists among variables or that no change occurred over time.

The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H 0 , asserts that the defendant is innocent, whereas the alternative hypothesis, H 1 , asserts that the defendant is guilty.

The indictment comes because of suspicion of the guilt. The H 0 status quo stands in opposition to H 1 and is maintained unless H 1 is supported by evidence "beyond a reasonable doubt".

However, "failure to reject H 0 " in this case does not imply innocence, but merely that the evidence was insufficient to convict.

So the jury does not necessarily accept H 0 but fails to reject H 0. While one can not "prove" a null hypothesis, one can test how close it is to being true with a power test , which tests for type II errors.

What statisticians call an alternative hypothesis is simply a hypothesis that contradicts the null hypothesis. Working from a null hypothesis , two basic forms of error are recognized:.

Standard deviation refers to the extent to which individual observations in a sample differ from a central value, such as the sample or population mean, while Standard error refers to an estimate of difference between sample mean and population mean.

A statistical error is the amount by which an observation differs from its expected value , a residual is the amount an observation differs from the value the estimator of the expected value assumes on a given sample also called prediction.

Mean squared error is used for obtaining efficient estimators , a widely used class of estimators.

Root mean square error is simply the square root of mean squared error. Many statistical methods seek to minimize the residual sum of squares , and these are called " methods of least squares " in contrast to Least absolute deviations.

The latter gives equal weight to small and big errors, while the former gives more weight to large errors. Residual sum of squares is also differentiable , which provides a handy property for doing regression.

Least squares applied to linear regression is called ordinary least squares method and least squares applied to nonlinear regression is called non-linear least squares.

Also in a linear regression model the non deterministic part of the model is called error term, disturbance or more simply noise. Both linear regression and non-linear regression are addressed in polynomial least squares , 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.

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

Confidence intervals allow statisticians to express how closely the sample estimate matches the true value in the whole population.

From the frequentist perspective, such a claim does not even make sense, as the true value is not a random variable. Either the true value is or is not within the given interval.

One approach that does yield an interval that can be interpreted as having a given probability of containing the true value is to use a credible interval from Bayesian statistics: In principle confidence intervals can be symmetrical or asymmetrical.

An interval can be asymmetrical because it works as lower or upper bound for a parameter left-sided interval or right sided interval , but it can also be asymmetrical because the two sided interval is built violating symmetry around the estimate.

Sometimes the bounds for a confidence interval are reached asymptotically and these are used to approximate the true bounds. Interpretation often comes down to the level of statistical significance applied to the numbers and often refers to the probability of a value accurately rejecting the null hypothesis sometimes referred to as the p-value.

The standard approach [23] is to test a null hypothesis against an alternative hypothesis. A critical region 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 statistical significance and the probability of type II error is the probability that the estimator doesn't belong to the critical region given that the alternative hypothesis is true.

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

Referring to statistical significance does not necessarily mean that the overall result is significant in real world terms. For example, in a large study of a drug it may be shown that the drug has a statistically significant but very small beneficial effect, such that the drug is unlikely to help the patient noticeably.

Although in principle the acceptable level of statistical significance may be subject to debate, the p-value is the smallest significance level 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 test statistic.

Therefore, the smaller the p-value, the lower the probability of committing type I error. Some problems are usually associated with this framework See criticism of hypothesis testing:.

Some well-known statistical tests and procedures are:. Misuse of statistics can produce subtle, but serious errors in description and interpretation—subtle in the sense that even experienced professionals make such errors, and serious in the sense that they can lead to devastating decision errors.

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

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

The statistical significance of a trend in the data—which measures the extent to which a trend could be caused by random variation in the sample—may or may not agree with an intuitive sense of its significance.

The set of basic statistical skills and skepticism that people need to deal with information in their everyday lives properly is referred to as statistical literacy.

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

Misuse of statistics can be both inadvertent and intentional, and the book How to Lie with Statistics [28] 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.

Warne, Lazo, Ramos, and Ritter Ways to avoid misuse of statistics include using proper diagrams and avoiding bias. Thus, people may often believe that something is true even if it is not well represented.

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

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

For example, a study of annual income that also looks at age of death might find that poor people tend to have shorter lives than affluent people.

The two variables are said to be correlated; however, they may or may not be the cause of one another. The correlation phenomena could be caused by a third, previously unconsidered phenomenon, called a lurking variable or confounding variable.

For this reason, there is no way to immediately infer the existence of a causal relationship between the two variables.

See Correlation does not imply causation. Some scholars pinpoint the origin of statistics to , with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt.

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

Today, statistics is widely employed in government, business, and natural and social sciences. Its mathematical foundations were laid in the 17th century with the development of the probability theory by Gerolamo Cardano , Blaise Pascal and Pierre de Fermat.

Mathematical probability theory arose from the study of games of chance, although the concept of probability was already examined in medieval law and by philosophers such as Juan Caramuel.

The modern field of statistics emerged in the late 19th and early 20th century in three stages. Galton's contributions included introducing the concepts of standard deviation , correlation , regression analysis and the application of these methods to the study of the variety of human characteristics—height, weight, eyelash length among others.

Ronald Fisher coined the term null hypothesis during the Lady tasting tea experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation".

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

Fisher's most important publications were his seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance , which was the first to use the statistical term, variance , his classic work Statistical Methods for Research Workers and his The Design of Experiments , [44] [45] [46] [47] where he developed rigorous design of experiments models.

He originated the concepts of sufficiency , ancillary statistics , Fisher's linear discriminator and Fisher information. Edwards has remarked that it is "probably the most celebrated argument in evolutionary biology ".

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

They introduced the concepts of " Type II " error, power of a test and confidence intervals. Jerzy Neyman in showed that stratified random sampling was in general a better method of estimation than purposive quota sampling.

Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a collated body of data and for making decisions in the face of uncertainty based on statistical methodology.

The use of modern computers has expedited large-scale statistical computations, and has also made possible new methods that are impractical to perform manually.

Statistics continues to be an area of active research, for example on the problem of how to analyze Big data.

Applied statistics comprises descriptive statistics and the application of inferential statistics. Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to methods of estimation and inference, but also various aspects of computational statistics and the design of experiments.

There are two applications for machine learning and data mining: Statistics tools are necessary for the data analysis.

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

Statistical consultants can help organizations and companies that don't have in-house expertise relevant to their particular questions.

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

Early statistical models were almost always from the class of linear models , but powerful computers, coupled with suitable numerical algorithms , caused an increased interest in nonlinear models such as neural networks as well as the creation of new types, such as generalized linear models and multilevel models.

Increased computing power has also led to the growing popularity of computationally intensive methods based on resampling , such as permutation tests and the bootstrap , while techniques such as Gibbs sampling have made use of Bayesian models more feasible.

The computer revolution has implications for the future of statistics with new emphasis on "experimental" and "empirical" statistics.

A large number of both general and special purpose statistical software are now available. Traditionally, statistics was concerned with drawing inferences using a semi-standardized methodology that was "required learning" in most sciences.

What was once considered a dry subject, taken in many fields as a degree-requirement, is now viewed enthusiastically. Statistical techniques are used in a wide range of types of scientific and social research, including: Some fields of inquiry use applied statistics so extensively that they have specialized terminology.

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

Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systems variability, control processes as in statistical process control or SPC , for summarizing data, and to make data-driven decisions.

In these roles, it is a key tool, and perhaps the only reliable tool. From Wikipedia, the free encyclopedia.

For other uses, see Statistics disambiguation. Statistical data type and Levels of measurement. History of statistics and Founders of statistics. List of fields of application of statistics.

Actuarial science assesses risk in the insurance and finance industries Applied information economics Astrostatistics statistical evaluation of astronomical data Biostatistics Business statistics Chemometrics for analysis of data from chemistry Data mining applying statistics and pattern recognition to discover knowledge from data Data science Demography statistical study of populations Econometrics statistical analysis of economic data Energy statistics Engineering statistics Epidemiology statistical analysis of disease Geography and geographic information systems , specifically in spatial analysis Image processing Medical statistics Political science Psychological statistics Reliability engineering Social statistics Statistical mechanics.

Abundance estimation Data science Glossary of probability and statistics List of academic statistical associations List of important publications in statistics List of national and international statistical services List of statistical packages software List of statistics articles List of university statistical consulting centers Notation in probability and statistics.

Foundations of statistics List of statisticians Official statistics Multivariate analysis of variance. Stanford Encyclopedia of Philosophy.

Meaning and Definition of Statistics". Statistics for the Twenty-First Century. The Mathematical Association of America.

Handbook of stochastic analysis and applications. Theory of statistics Corr. A New Kind of Science. Theory and Practice , Cambridge University Press.

Modern Epidemiology 3rd ed. Data analysis and regression. The knowledge needed to computerise the analysis and interpretation of statistical information.

Hier is vervolgens weer het Italiaanse woord statista van afgeleid, dat "staatsman" of "politicus" betekent - vergelijk ons woord status - evenals het Duitse Statistik , dat oorspronkelijk de analyse van staatsgegevens betekende, opgezet door Hermann Conring en bekend geworden door Gottfried Achenwall.

Een belangrijk begrippenpaar in de statistiek is populatie en steekproef. Men dient steeds goed te onderscheiden of men over de populatie verdeling spreekt dan wel over de steekproef.

De populatie is over het algemeen slechts in formele zin gegeven in termen van een kansverdeling met enkele onbekende parameters.

Het zijn deze parameters die men graag zou kennen, maar om uiteenlopende redenen niet kent. Een steekproef verschaft informatie over de parameters, door het geven van een schatting , het toetsen van een hypothese over een parameter, e.

Zo is er het populatiegemiddelde, meestal onbekend, en als schatting daarvan het steekproefgemiddelde. Evenzo is de steekproefvariantie een schatting van de populatievariantie, enzovoorts.

Doordat de uitkomst van een steekproef meestal sterk door het toeval bepaald wordt, maakt de statistiek veel gebruik van de kansrekening.

Door middel van statistisch onderzoek probeert men deze waarde te benaderen via schattingen , toetsen en betrouwbaarheidsintervallen.

De Bayesianen geloven niet in een "ware" waarde en staan toe dat de parameters zelf stochastische variabelen zijn, met een meestal onbekende verdeling.

Wel wordt tevoren een veronderstelling over de verdeling gemaakt; de veronderstelde verdeling heet a-prioriverdeling.

Hierdoor kan het theorema van Bayes toegepast worden. Gevolgen hiervan zijn onder meer dat informatie, ook subjectieve informatie, van buiten de steekproef ingebracht kan worden.

Verder betekent het dat de interpretatie van de uitkomsten fundamenteel wijzigt. Een centraal begrip in de statistiek is dat van de stochastische variabele.

Deze grootheid vertegenwoordigt in feite de populatieverdeling of de betrokken modelmatige kansverdeling. De steekproefuitkomsten vat men op als waarnemingen aan deze grootheid.

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