Statistics

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https://en.wikipedia.org/wiki/Statistics

The normal distribution, a very common probability density, is used extensively in inferential statistics.

Scatter plots and line charts are used in descriptive statistics to show the observed relationships between different variables, here using the Iris flower data set.

Statistics (from German: Statistik, orig. "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model 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 surveys and experiments. Statistics is deeply related to subjects like physics, chemistry, geography, geopolitics, and especially mathematics.

When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Random sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.

Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, 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 distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences made using mathematical statistics employ the framework of probability theory, which deals with the analysis of random phenomena.

A standard statistical procedure involves the collection of data leading to a test of the relationship 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 alternative to an idealized null hypothesis 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: Type I errors (null hypothesis is rejected when it is in fact true, giving a "false positive") and Type II errors (null hypothesis fails to be rejected when 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.

Statistical measurement processes are also prone to error with regard to the data they generate. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of missing data or censoring may result in biased estimates, and specific techniques have been developed to address these problems.

Introduction

Main article: Outline of statistics

"Statistics is both the science of uncertainty and the technology of extracting information from data." - featured in the International Encyclopedia of Statistical Science.

Statistics is the discipline that deals with data, facts and figures with which meaningful information is inferred. Data may represent a numerical value, in form of quantitative data, or a label, as with qualitative data. Data may be collected, presented and summarised, in one of two methods called descriptive statistics. Two elementary summaries of data, singularly called a statistic, are the mean and dispersion. Whereas inferential statistics interprets data from a population sample to induce statements and predictions about a population.

Statistics is regarded as a body of science or a branch of mathematics. It is based on probability, a branch of mathematics that studies random events. Statistics is considered the science of uncertainty. This arises from the ways to cope with measurement and sampling error as well as dealing with uncertanties in modelling. Although probability and statistics were once paired together as a single subject, they are conceptually distinct from one another. The former is based on deducing answers to specific situations from a general theory of probability, meanwhile statistics induces statements about a population based on a data set. Statistics serves to bridge the gap between probability and applied mathematical fields.

Some consider statistics to be a distinct mathematical science 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. Statistics is indexed at 62, a subclass of probability theory and stochastic processes, in the Mathematics Subject Classification. Mathematical statistics is covered in the range 276-280 of subclass QA (science > mathematics) in the Library of Congress Classification.

The word statistics ultimately comes from the Latin word Status, meaning "situation" or "condition" in society, which in late Latin adopted the meaning "state". Derived from this, political scientist Gottfried Achenwall, coined the German word statistik (a summary of how things stand). In 1770, the term entered the English language through German and referred to the study of political arrangements. The term gained its modern meaning in the 1790s in John Sinclair's works. In modern German, the term statistik is synonymous with mathematical statistics. The term statistic, in singular form, is used to describe a function that returns its value of the same name.

Statistical data

Data collection

Sampling

When census data cannot be collected, statisticians collect sample data by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting through statistical models.

To use a sample as a guide to an entire population, it is important that it truly represents the overall population. Representative sampling ensures that inferences and conclusions can safely be extended from the sample to the population as a whole. A major problem lies in determining the extent to which the chosen sample is actually representative. Statistics offers methods to estimate and correct for any bias in the sample and data collection procedures. There are also methods of experimental design that can lessen these issues at the outset of a study, strengthening its ability to discern truths about the population.

Sampling theory is part of the mathematical discipline of probability theory. Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures. The use of any statistical method is valid only 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 with the given parameters of a total population to deduce probabilities that pertain to samples. Statistical inference, however, moves in the opposite direction—inductively inferring from samples to the parameters of a larger or total population.

Experimental and observational studies

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

Experiments

The basic steps of a statistical experiment are:

1. Planning the research, including finding the number of replicates of the study, using the following information: preliminary estimates regarding the size of treatment effects, alternative hypotheses, and the estimated experimental variability. Consideration of the selection of experimental subjects and the ethics of research is necessary. Statisticians recommend that experiments compare (at least) one new treatment with a standard treatment or control, to allow an unbiased estimate of the difference in treatment effects.
2. Design of experiments, using blocking to reduce the influence of confounding variables, and randomized assignment of treatments to subjects to allow unbiased estimates of treatment effects and experimental error. At this stage, the experimenters and statisticians write the experimental protocol that will guide the performance of the experiment and which specifies the primary analysis of the experimental data.
3. Performing the experiment following the experimental protocol and analyzing the data following the experimental protocol.
4. Further examining the data set in secondary analyses, to suggest new hypotheses for future study.
5. Documenting and presenting the results of the study.

Experiments on human behavior have special concerns. The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of the Western Electric Company. The researchers were interested in determining whether increased illumination would increase the productivity of the assembly line workers. The researchers first measured the productivity in the plant, then modified the illumination in an area of the plant and checked if the changes in illumination affected productivity. It turned out that productivity indeed improved (under the experimental conditions). However, the study is heavily criticized today for errors in experimental procedures, specifically for the lack of a control group and blindness. The Hawthorne effect refers to finding that an outcome (in this case, worker productivity) changed due to observation itself. Those in the Hawthorne study became more productive not because the lighting was changed but because they were being observed.

Observational study

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 both smokers and non-smokers, perhaps through a cohort study, and then look for the number of cases of lung cancer in each group. A case-control study 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.

Types of data

Main articles: Statistical data type and Levels of measurement

Various attempts have been made to produce a taxonomy of levels of measurement. The psychophysicist Stanley Smith Stevens defined nominal, ordinal, interval, and ratio scales. Nominal measurements do not have meaningful rank order among values, and permit any one-to-one (injective) transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and permit any order-preserving transformation. Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit), and permit any linear transformation. Ratio measurements have both a meaningful zero value and the distances between different measurements defined, and permit any rescaling transformation.

Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature. Such distinctions can often be loosely correlated with data type in computer science, in that dichotomous categorical variables may be represented with the Boolean data type, polytomous categorical variables with arbitrarily assigned integers in the integral data type, and continuous variables with the real data type involving floating-point arithmetic. But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented.

Other categorizations have been proposed. For example, Mosteller and Tukey (1977) 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 den Berg (1991).)

The issue of whether it is appropriate to apply different kinds of statistical methods to data obtained from different kinds of measurement procedures is complicated by issues concerning the transformation of variables and the precise interpretation of research questions. "The relationship between the data and what they describe merely reflects the fact that certain kinds of statistical statements may have truth values that are not invariant under some transformations. Whether a transformation is sensible to contemplate depends on the question one is trying to answer."

Methods

Descriptive statistics

Main article: Descriptive statistics

A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features of a collection of information, while descriptive statistics in the mass noun sense is the process of using and analyzing those statistics. Descriptive statistics is distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aims to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.

Inferential statistics

Main article: Statistical inference

Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. 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.

Terminology and theory of inferential statistics

Statistics, estimators and pivotal quantities

Consider independent identically distributed (IID) random variables with a given probability distribution: standard statistical inference and estimation theory defines a random sample as the random vector given by the column vector of these IID variables. The population being examined is described by a probability distribution that may have unknown parameters.

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: an estimator is a statistic used to estimate such function. Commonly used estimators include sample mean, unbiased sample variance and sample covariance.

A random variable 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: the method of moments, the maximum likelihood method, the least squares method and the more recent method of estimating equations.

Null hypothesis and alternative hypothesis

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

The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H₀, asserts that the defendant is innocent, whereas the alternative hypothesis, H₁, asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H₀ (the status quo) stands in opposition to H₁ and is maintained unless H₁ is supported by evidence "beyond a reasonable doubt". However, "failure to reject H₀" in this case does not imply innocence, but merely that the evidence was insufficient to convict. So the jury does not necessarily accept H₀ but fails to reject H₀. While one can not "prove" a null hypothesis, one can test how close it is to being true with a power test, which tests for type II errors. The null hypothesis cannot be proven true because it is already assumed to be true when the test is being conducted.

Error

Working from a null hypothesis, two broad categories of error are recognized:

• Type I errors where the null hypothesis is falsely rejected, giving a "false positive".
• Type II errors where the null hypothesis fails to be rejected and an actual difference between populations is missed, giving a "false negative".

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

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

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

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

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.

Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.

Interval estimation

Main article: Interval estimation

Confidence intervals: the red line is true value for the mean in this example, the blue lines are random confidence intervals for 100 realizations.

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. Confidence intervals allow statisticians to express how closely the sample estimate matches the true value in the whole population. Often they are expressed as 95% confidence intervals. Formally, a 95% confidence interval for a value is a range where, if the sampling and analysis were repeated under the same conditions (yielding a different dataset), the interval would include the true (population) value in 95% of all possible cases. This does not imply that the probability that the true value is in the confidence interval is 95%. From the frequentist perspective, such a claim does not even make sense, as the true value is not a random variable. Either the true value is or is not within the given interval. However, it is true that, before any data are sampled and given a plan for how to construct the confidence interval, the probability is 95% that the yet-to-be-calculated interval will cover the true value: at this point, the limits of the interval are yet-to-be-observed random variables. One approach that does yield an interval that can be interpreted as having a given probability of containing the true value is to use a credible interval from Bayesian statistics: this approach depends on a different way of interpreting what is meant by "probability", that is as a Bayesian probability.

In principle, confidence intervals can be symmetrical or asymmetrical. An interval can be asymmetrical because it works as a lower or upper bound for a parameter (left-sided interval or right sided interval), but it can also be asymmetrical if a two-sided interval is built violating symmetry around the estimate. Sometimes the bounds of a confidence interval are reached asymptotically, and these are used to approximate the true bounds.

Significance

Main article: Statistical significance

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 p-value).

In this graph the black line is probability distribution for the test statistic, the critical region is the set of values to the right of the observed data point (observed value of the test statistic) and the p-value is represented by the green area.

The standard approach 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 does not 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 it is unlikely to help the patient noticeably.

Although in principle the acceptable level of statistical significance may be subject to debate, the significance level 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 test statistic. Therefore, the smaller the significance level, the lower the probability of committing type I error.

Some problems are usually associated with this framework (See criticism of hypothesis testing):

• 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 significance level to include the p-value when reporting whether a hypothesis is rejected or accepted. The p-value, however, does not indicate the size 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 confidence intervals. Although these are produced from the same calculations as those of hypothesis tests or p-values, they describe both the size of the effect and the uncertainty surrounding it.
• Fallacy of the transposed conditional, aka prosecutor's fallacy: criticisms arise because the hypothesis testing approach forces one hypothesis (the null hypothesis) 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 Bayesian inference, although it requires establishing a prior probability.
• Rejecting the null hypothesis does not automatically prove the alternative hypothesis.
• As everything in inferential statistics it relies on sample size, and therefore under fat tails p-values may be seriously mis-computed.

Examples

Some well-known statistical tests and procedures are:

• Analysis of variance (ANOVA)
• Chi-squared test
• Correlation
• Factor analysis
• Mann–Whitney U
• Mean square weighted deviation (MSWD)
• Pearson product-moment correlation coefficient
• Regression analysis
• Spearman's rank correlation coefficient
• Student's t-test
• Time series analysis
• Conjoint Analysis

Bayesian statistics

Main article: Bayesian statistics

An alternative paradigm to the popular frequentist paradigm is to use Bayes' theorem to update the prior probability of the hypotheses in consideration based on the relative likelihood of the evidence gathered to obtain a posterior probability.

As an example, suppose that 1 in 1000 women in a population have breast cancer. Suppose that all (100%) of those with cancer will get a positive test result (detection of cancer), while 5% without breast cancer will also get a positive result (falsely detecting cancer) - that is, the test has a false positive rate of 5%

Suppose a woman in this population had a positive mammogram. By Bayes law, the chance that she actually has cancer is given by taking the prior odds of having cancer (around 1:1000) and multiplying by the likelihood ratio 20:1 (since a cancer patient is 20 times more likely to get a positive result than a healthy patient) to get the posterior odds 20:1000 = 1:50, which is around 2%. Many find this probability unintuitively small due to neglecting the low base rate of cancer. As an example, in one study only 18% of doctors got the correct answer, with 45% of them giving a probability of cancer of 95%, and the average probability being 56% (overestimating by a factor of 30).

The concept of using likelihood ratio can also be prominently seen in medical diagnostic testing.

For statistical modelling purposes, Bayesian models tend to be hierarchical. For example, one could model each YouTube channel as having video views distributed as a normal distribution with channel dependent mean and variance ${\displaystyle \mathcal{N}({\mu }_i,{\sigma }_i)}$, while modeling the channel means as themselves coming from a normal distribution representing the distribution of average video view counts per channel, and the variances as coming from another distribution.

Bayesian methods have been aided by the increase in available computing power to compute the posterior probability using numerical approximation techniques like Markov Chain Monte Carlo.

Exploratory data analysis

Main article: Exploratory data analysis

Exploratory data analysis (EDA) is an approach to analyzing data sets to summarize their main characteristics, often with visual methods. A statistical model 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.

Mathematical statistics

Main article: Mathematical statistics

Mathematical statistics is the application of mathematics to statistics. Mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory. All statistical analyses make use of at least some mathematics, and mathematical statistics can therefore be regarded as a fundamental component of general statistics.

History

Main articles: History of statistics and Founders of statistics

Bernoulli's Ars Conjectandi was the first work that dealt with probability theory as currently understood.

Formal discussions on inference date back to the mathematicians and cryptographers of the Islamic Golden Age between the 8th and 13th centuries. Al-Khalil (717–786) wrote the Book of Cryptographic Messages, which contains one of the first uses of permutations and combinations, to list all possible Arabic words with and without vowels. Al-Kindi's Manuscript on Deciphering Cryptographic Messages gave a detailed description of how to use frequency analysis to decipher encrypted messages, providing an early example of statistical inference for decoding. Ibn Adlan (1187–1268) later made an important contribution on the use of sample size in frequency analysis.

Although the term statistic was introduced by the Italian scholar Girolamo Ghilini in 1589 with reference to a collection of facts and information about a state, it was the German Gottfried Achenwall 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 Natural and Political Observations upon the Bills of Mortality by John Graunt.

Early applications of statistical thinking revolved around the needs of states to base policy on demographic and economic data, hence its stat- etymology. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in government, business, and natural and social sciences.

Carl Friedrich Gauss made major contributions to probabilistic methods leading to statistics.

The mathematical foundations of statistics developed from discussions concerning games of chance among mathematicians such as Gerolamo Cardano, Blaise Pascal, Pierre de Fermat, and Christiaan Huygens. Although the idea of probability was already examined in ancient and medieval law and philosophy (such as the work of Juan Caramuel), probability theory as a mathematical discipline only took shape at the very end of the 17th century, particularly in Jacob Bernoulli's posthumous work Ars Conjectandi. 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 method of least squares was first described by Adrien-Marie Legendre in 1805, though Carl Friedrich Gauss presumably made use of it a decade earlier in 1795.

Karl Pearson, a founder of mathematical statistics

In the 1830s-1850s, "statistical offices" and national "statistical societies" were founded in Europe and America, and in the mid-19th century, the idea arose of "organized contacts between the statisticians of different countries although informal contacts occurred earlier". In those days, the name "statistics" referred mainly to "matters of state", and British statisticians were often called "statists".

Belgian scientist Adolphe Quetelet (1796–1874) introduced the notion of the "average man" (l'homme moyen) as a means of understanding complex social phenomena such as crime rates, marriage rates, and suicide rates. In 1853 Quetelet organised in Brussels the First International Statistical Congress in order to unify measurement in statistical research.

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 Francis Galton and Karl Pearson, who transformed statistics into a rigorous mathematical discipline used for analysis, not just in science, but in industry and politics as well. Galton's contributions included introducing the concepts of standard deviation, correlation, regression analysis and the application of these methods to the study of the variety of human characteristics—height, weight and eyelash length among others. Pearson developed the Pearson product-moment correlation coefficient, defined as a product-moment, the method of moments for the fitting of distributions to samples and the Pearson distribution, among many other things. Galton and Pearson founded Biometrika as the first journal of mathematical statistics and biostatistics (then called biometry), and the latter founded the world's first university statistics department at University College London.

The second wave of the 1910s and 20s was initiated by William Sealy Gosset, and reached its culmination in the insights of Ronald Fisher, who wrote the textbooks that were to define the academic discipline in universities around the world. Fisher's most important publications were his 1918 seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance (which was the first to use the statistical term, variance), his classic 1925 work Statistical Methods for Research Workers and his 1935 The Design of Experiments, where he developed rigorous design of experiments models. He originated the concepts of sufficiency, ancillary statistics, Fisher's linear discriminator and Fisher information. He also coined the term null hypothesis during the Lady tasting tea experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation". In his 1930 book The Genetical Theory of Natural Selection, he applied statistics to various biological concepts such as Fisher's principle (which A. W. F. Edwards called "probably the most celebrated argument in evolutionary biology") and Fisherian runaway, a concept in sexual selection about a positive feedback runaway effect found in evolution.

The final wave, which mainly saw the refinement and expansion of earlier developments, emerged from the collaborative work between Egon Pearson and Jerzy Neyman in the 1930s. They introduced the concepts of "Type II" error, power of a test and confidence intervals. Jerzy Neyman in 1934 showed that stratified random sampling was in general a better method of estimation than purposive (quota) sampling.

Among the early attempts to measure national economic activity were those of William Petty in the 17th century. In the 20th century the uniform System of National Accounts was developed.

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.

Applications

Applied statistics, theoretical statistics and mathematical statistics

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

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

Machine learning and data mining

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

Statistics in academia

Statistics is applicable to a wide variety of academic disciplines, including natural and social sciences, government, and business. Business statistics applies statistical methods in econometrics, auditing 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: analysis of variance (ANOVA), chi-squared test, Student's t-test, linear regression, Pearson's correlation coefficient, Mann-Whitney U test, Kruskal-Wallis test, Shannon's diversity index, Tukey's range test, cluster analysis, Spearman's rank correlation coefficient and principal component analysis.

A typical statistics course covers descriptive statistics, probability, binomial and normal distributions, test of hypotheses and confidence intervals, linear regression, and correlation. Modern fundamental statistical courses for undergraduate students focus on correct test selection, results interpretation, and use of free statistics software.

Statistical computing

Main article: Computational statistics

gretl, an example of an open source statistical package

The rapid and sustained increases in computing power starting from the second half of the 20th century have had a substantial impact on the practice of statistical science. Early statistical models were almost always from the class of linear models, but powerful computers, coupled with suitable numerical algorithms, caused an increased interest in nonlinear models (such as neural networks) as well as the creation of new types, such as generalized linear models and multilevel models.

Increased computing power has also led to the growing popularity of computationally intensive methods based on resampling, such as permutation tests and the bootstrap, while techniques such as Gibbs sampling have made use of Bayesian models more feasible. The computer revolution has implications for the future of statistics with a new emphasis on "experimental" and "empirical" statistics. A large number of both general and special purpose statistical software are now available. Examples of available software capable of complex statistical computation include programs such as Mathematica, SAS, SPSS, and R.

Business statistics

See also: Business mathematics § University level

In business, "statistics" is a widely used management- and decision support tool. It is particularly applied in financial management, marketing management, and production, services and operations management. Statistics is also heavily used in management accounting and auditing. The discipline of Management Science formalizes the use of statistics, and other mathematics, in business. (Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships.)

A typical "Business Statistics" course is intended for business majors, and covers descriptive statistics (collection, description, analysis, and summary of data), probability (typically the binomial and normal distributions), test of hypotheses and confidence intervals, linear regression, and correlation; (follow-on) courses may include forecasting, time series, decision trees, multiple linear regression, and other topics from business analytics more generally. Professional certification programs, such as the CFA, often include topics in statistics.

Specialized disciplines

Main article: List of fields of application of statistics

Statistical techniques are used in a wide range of types of scientific and social research, including: biostatistics, computational biology, computational sociology, network biology, social science, sociology and social research. Some fields of inquiry use applied statistics so extensively that they have specialized terminology. These disciplines include:

• Actuarial science (assesses risk in the insurance and finance industries)
• Applied information economics
• Astrostatistics (statistical evaluation of astronomical data)
• Biostatistics
• 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
• Jurimetrics (law)
• Medical statistics
• Political science
• Psychological statistics
• Reliability engineering
• Social statistics
• Statistical mechanics

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

• Bootstrap / jackknife resampling
• Multivariate statistics
• Statistical classification
• Structured data analysis
• Structural equation modelling
• Survey methodology
• Survival analysis
• Statistics in various sports, particularly baseball – known as sabermetrics – and cricket

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.

Misuse

Main article: Misuse of statistics

Misuse of statistics can produce subtle but serious errors in description and interpretation—subtle in the sense that even experienced professionals make such errors, and serious in the sense that they can lead to devastating decision errors. For instance, social policy, medical practice, and the reliability of structures like bridges all rely on the proper use of statistics.

Even when statistical techniques are correctly applied, the results can be difficult to interpret for those lacking expertise. The statistical significance of a trend in the data—which measures the extent to which a trend could be caused by random variation in the sample—may or may not agree with an intuitive sense of its significance. The set of basic statistical skills (and skepticism) that people need to deal with information in their everyday lives properly is referred to as statistical literacy.

There is a general perception that statistical knowledge is all-too-frequently intentionally misused by finding ways to interpret only the data that are favorable to the presenter. A mistrust and misunderstanding of statistics is associated with the quotation, "There are three kinds of lies: lies, damned lies, and statistics". Misuse of statistics can be both inadvertent and intentional, and the book How to Lie with Statistics, by Darrell Huff, 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)).

Ways to avoid misuse of statistics include using proper diagrams and avoiding bias. Misuse can occur when conclusions are overgeneralized and claimed to be representative of more than they really are, often by either deliberately or unconsciously overlooking sampling bias. 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 bias or errors, so they are not noticed. Thus, people may often believe that something is true even if it is not well represented. 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 [bias]... allow yourself some degree of skepticism."

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

• Who says so? (Do they have an axe to grind?)
• How do they know? (Do they have the resources to know the facts?)
• What's missing? (Do they give us a complete picture?)
• Did someone change the subject? (Do they offer us the right answer to the wrong problem?)
• Does it make sense? (Is their conclusion logical and consistent with what we already know?)

Misinterpretation: correlation

See also: Correlation does not imply causation

The confounding variable problem: X and Y may be correlated, not because there is causal relationship between them, but because both depend on a third variable Z. Z is called a confounding factor.

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 could instead be produced by a third, previously unconsidered factor, called a lurking variable or confounding variable. For example, higher incomes may have a tendency to allow for more leisure time, which in turn allows for more time spent exercising. It may be that this higher level of activity causes the longer lifespans observed in the more affluent group. Raising income levels therefore does not in itself cause people to live longer. Rather, a confounding variable is responsible for the increase.

For this reason, correlation does not imply causation: a causal relationship between the two variables cannot be inferred from their correlation alone.

Academic freedom

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Academic_freedom

Worldwide state of academic freedom according to the Academic Freedom Index

Academic freedom is the right of a teacher to instruct and the right of a student to learn in an academic setting unhampered by interference. It may also include the right of academics to engage in social and political criticism.

Academic freedom is often premised on the conviction that freedom of inquiry by faculty members is essential to the mission of the academy as well as the principles of academia, and that scholars should have freedom to teach or communicate ideas or facts (including those that are inconvenient to external political groups or to authorities) without the fear of being repressed, losing their job or being imprisoned. While the core of academic freedom covers scholars acting in an academic capacity (as teachers or researchers expressing strictly scholarly viewpoints), an expansive interpretation extends these occupational safeguards to scholars' speech on matters outside their professional expertise.

Academic tenure protects academic freedom by ensuring that teachers can be fired only for causes such as gross professional incompetence or behavior that evokes condemnation from the academic community itself. The academic community pressuring scholars can reduce academic freedom.

Historically, academic freedom emerged tentatively, as academics in medieval and early modern Europe could face repression for acting in ways considered objectionable by religious authorities or by governments. Scholars tend to link the institutionalization of academic freedom to the rise of the modern research university and the Humboldtian model of higher education from the 19th century. By one estimate, academic freedom has substantially increased worldwide since the 1960s. Academic freedom is more likely in liberal democratic states, while it is more heavily constrained in authoritarian states, illiberal states, and states embroiled in military conflict. Since 2013, while some countries have seen improvements to academic freedom, the overall trend is towards reductions in freedom.

Definition

A minimal definition of academic freedom is that a teacher has a right to instruct, and a student has a right to learn in an academic setting unhampered by interference. Other definitions include the right of teachers to engage in social and political criticism.

A broader definition of academic freedom incorporates individual, extramural and institutional components. Under this broader definition, an academic has freedom of expression without government interference, but this freedom is circumscribed by academic expertise and position. Academic freedom of speech is therefore narrower than a general freedom of speech. For example, a non-academic has the freedom of speech to criticize the efficacy of vaccines, but only has academic freedom to do so if they possess the prerequisite academic qualifications to do so. Unlike public speech, academic speech is also subject to quality controls by academic peers, for example through peer review.

Universities UK has defined academic freedom as "protecting the intellectual independence of academics to question and test received views and wisdom, and to put forward new ideas and controversial or unpopular opinions, without placing themselves in danger of losing their jobs or privileges", while the American Federation of Teachers has seen it as "based on the idea that the free exchange of ideas on campus is essential to good education". Norwegian education sees it as a guarantee that research and teaching is "intellectually and morally independent of all political and economic interests", leading to openness, free enquiry and debate.

The laissez-faire approach of unaccountable academic freedom is contrasted with democratic accountability of academia.

Historical background

Historically, academic freedom emerged tentatively. However, Richard Hofstadter and Walter Metzger contend that academic freedom is "a modern term for an ancient idea" and "can be traced at least as far back as Socrates' eloquent defense of himself in 399 B.C. against the charge of corrupting the youth of Athens."

In 1155, the Holy Roman Emperor Frederick I Barbarossa issued the document Authentica habita which laid out rights and privileges of students and scholars, which included immunity from civil jurisdiction and freedom of movement for the purposes of studying and teaching. Similarly, civil disturbances, such as the St Scholastica Day riot of 1355 at the University of Oxford often led to great autonomy for universities. And even those scholars who committed theological heresy, such as John Wyclif and Jan Hus, has support due to their roles as faculty at a university.

19th century

The Humboldtian model of higher education from the 19th century enshrined the basic ideas of academic freedom and diffused them to other countries. Wilhelm von Humboldt was a philosopher and linguist who was given the authority to create a new university in Berlin in the early 19th century. In founding the Humboldt University of Berlin he created a university that adhered to two principles of academic freedom: freedom of scientific inquiry and the unity between research and teaching. According to Humboldt, the fundamental proposition underlying the principles of academic freedom was to uphold the view that science is not something that has already been found but as knowledge that will never be fully discovered and, yet, needs to be searched for unceasingly. The university he founded later became a model and inspiration for modern colleges in Germany and universities in the West.

During this period there was also a sense that universities must be insulated from the pressures of donors, boards of trustees and state governments. One notable instance was the case of the resignation of Brown University president Elisha Andrews, who advocated silver coinage to reduce the impact on Americans and farmers who owed larger and larger loans due to deflation. The board of Brown University, many of whom were creditors and landowners and benefited from deflation, told Andrews to cease his public advocacy. The dean of Yale Law School, Francis Wayland, argued that Andrews' free expression threatened donations to Brown, and that money was the life blood of universities. In 1897, Andrews was forced to offer his resignation, but there was a backlash by faculty and students who advocated that he should be protected under the principles of free speech. The board reversed its decision and refused Andrews' resignation. A year later, Andrews resigned anyway.

20th century

The concept of academic freedom was also formulated in response to the encroachments of the totalitarian state on science and academia in general for the furtherance of its own goals. For instance, in the Soviet Union, scientific research was brought under strict political control in the 1930s. A number of research areas were declared "bourgeois pseudoscience" and forbidden, notably genetics (see "Lysenkoism") and sociology. Marxist scientist John Desmond Bernal characterized this as part of the interdependence between "applied science" and "pure science".

Michael Polanyi argued that academic freedom was a fundamental necessity for the production of true knowledge.

Michael Polanyi argued that a structure of liberty is essential for the advancement of science. In 1936, as a consequence of an invitation to give lectures for the Ministry of Heavy Industry in the USSR, Polanyi met Bukharin, who told him that in socialist societies all scientific research is directed to accord with the needs of the latest five-year plan. Demands in Britain for centrally planned scientific research led Polanyi, together with John Baker, to found the Society for Freedom in Science. The society promoted a liberal conception of science as free enquiry against the instrumental view that science should exist primarily to serve the needs of society. In a series of articles, re-published in The Contempt of Freedom (1940) and The Logic of Liberty (1951), Polanyi claimed that co-operation among scientists is analogous to the way in which agents co-ordinate themselves within a free market. Just as consumers in a free market determine the value of products, science is a spontaneous order that arises as a consequence of open debate among specialists. Science can therefore only flourish when scientists have the liberty to pursue truth as an end in itself:

[S]cientists, freely making their own choice of problems and pursuing them in the light of their own personal judgment, are in fact co-operating as members of a closely knit organization.

Such self-co-ordination of independent initiatives leads to a joint result which is unpremeditated by any of those who bring it about.

Any attempt to organize the group ... under a single authority would eliminate their independent initiatives, and thus reduce their joint effectiveness to that of the single person directing them from the centre. It would, in effect, paralyse their co-operation.

Rationale

Proponents of academic freedom believe that the freedom of inquiry by students and faculty members is essential to the mission of the academy. They argue that academic communities are repeatedly targeted for repression due to their ability to shape and control the flow of information. When scholars attempt to teach or communicate ideas or facts that are inconvenient to external political groups or to authorities, they may find themselves targeted for public vilification, job loss, imprisonment, or even death. For example, in North Africa, a professor of public health discovered that his country's infant mortality rate was higher than government figures indicated. He lost his job and was imprisoned.

The fate of biology in the Soviet Union is cited by Jasper Becker as a reason why society has an interest in protecting academic freedom. Also it is important to make the distinction between science and pseudoscience, on the border of this lies the case of a Soviet biologist Trofim Lysenko rejected Western science – then focused primarily on making advances in theoretical genetics, based on research with the fruit fly (Drosophila melanogaster) – and proposed an approach to farming that was based on the collectivist principles of dialectical materialism. Lysenko called this "Michurinism", but it is more commonly known today as Lysenkoism, and named after him. Lysenko's ideas appealed to the Soviet leadership, in part because of their value as propaganda, and he was ultimately made director of the Soviet Academy of Agricultural Sciences. Subsequently, Lysenko directed a purge of scientists who professed "harmful ideas", resulting in the expulsion, imprisonment, or death of hundreds of Soviet scientists. Lysenko's ideas were then implemented on collectivized farms in the Soviet Union and China. Famines that resulted partly from Lysenko's influence are believed to have killed 30 million people in China alone during the Great Leap Forward.

Sociologist Ruth Pearce argued that the concept of academic freedom exists to protect scholarship from censure by state or religious authorities or others, and not to defend intolerance. Academic freedom can be reduced through scholars pressuring other scholars and resulting self-censorship or political bias.

A large-scale empirical study, covering more than 157 countries over the 1900-2015 period, links academic freedom to the quality and quantity of patents filed in a given country. David Audretsch and colleagues estimate that academic freedom has declined over the last decade for the first time over their century-long observation period, resulting in at least 4% fewer patents filed. The study claims to be the first to link academic freedom to economic growth through an innovation channel.

Academic freedom has also been identified as a leading indicator for whether a government will become more or less democratic.

Academic Freedom Index

In 2020, the V-Dem Institute partnered with Scholars at Risk to create the first index of Academic freedom. The index provides retroactive ratings for countries going back to 1900 that are also updated yearly. The index estimates academic freedom using five categories that follow the UNESCO definition:

• freedom to research and teach
• freedom of academic exchange and dissemination
• institutional autonomy
• campus integrity
• freedom of academic and cultural expression

As of 2025, academic freedom overall around the world has been in retreat since 2013. Causes cited have included authoritarianism as well as political polarization and populism.

Country-specific

See also: Academic freedom in the Middle East

The concept of academic freedom as a right of faculty members is an established part of most legal systems. While in the United States the constitutional protection of academic freedom derives from the guarantee of free speech under the First Amendment, the constitutions of other countries (particularly in civil law systems) typically grant a separate right to free learning, teaching, and research.

Academic freedom in China (1900–2023)

Australia

This section is an excerpt from Censorship in Australia § Universities.edit

Concerns have been expressed by Freedom House and others about protections for freedom of speech and academic freedom at Australia's universities. In 2018, the Australian Government asked former Chief Justice Robert French to conduct an independent review of freedom of speech and academic freedom in Australian higher education. While French disagreed that there was a "freedom of speech crisis" on campuses, he nonetheless noted the risks to freedom posed by the various and vaguely-worded protections then in place. Concerns include the influence of the People's Republic of China on university administrations; 'deplatforming' of controversial speakers and viewpoints; and demands that academics refrain from contesting one another's conclusions.

Chile

During the late 1950s and early 1960s, students and faculty began advocating for the democratization of university life in Chile. However, after the 1973 coup, academic freedom under the Pinochet military dictatorship was repressed. Nevertheless, during the 1980s, students and faculty, with support from members of the public, collaborated to protect academic freedom.

Since the transition to democracy after the end of the Pinochet regime in 1990, academic freedom in higher education in Chile has been strong. In 2025, Chile ranked in the top ten percent of countries on the Academic Freedom Index (AFI).

China

Self-censorship in a Chinese academic journal: an editor asks the article's author to remove a sentence about blocking of Wikipedia in mainland China as it could cause trouble with the "authorities".

Academic freedom is severely limited in China. Academics have noted an incentive not to express 'incorrect' opinions about issues sensitive to the Government of China and the ruling Chinese Communist Party (CCP). These efforts have been effective in causing academics to self-censor and shift academic discourse.

During the general secretaryship of Xi Jinping, universities in the country have increasingly been put under the direct management of a CCP committee secretary and have intensified ideological controls. In December 2020, the Associated Press reported that China was controlling scientific research into the origins of COVID-19 under direct orders from CCP general secretary Xi Jinping. According to the report, an order by China's State Council required all research to be approved by a task force under their management, saying scientific publication should be orchestrated like "a game of chess", warning that those who publish without permission will be held accountable.

According to National Public Radio, from 2013 to 2017, at least 109 universities in China issued their first charters affirming the CCP leadership. In 2020, Shanghai's Fudan University removed freedom of thought from its charter following the December 2019 revision of the school charter to emphasize loyalty to the CCP.

Hong Kong academia expressed concerns about the impact of the 2020 Hong Kong National Security Law on academic freedom in Hong Kong. As of 2025, it ranked in the bottom 20% worldwide for academic freedom according to the Academic Freedom Index.

In an August 2021 study, Jue Jiang from the University of London argued that academic freedom in China is impaired by the CCP's system of student informants, who are recruited and encouraged to watch and inform on their professors on university campuses.

Denmark

Danish law guarantees both institutional and individual academic freedom at universities, yet the country ranked 24th of 28 EU states in 2017 and 32nd of 179 countries in a 2024 study. Researchers and the academic union DM reported in 2024 that political pressure, insecure employment, competition for external funding and limited public awareness are weakening independence and discouraging basic research. In 2021, a political campaign against alleged “pseudo-research and activism” led to parliamentary resolution V137, with some politicians demanding interventions, lists of “dangerous” programmes and the closure of certain research fields. Over 3,000 academics signed a petition arguing the resolution threatened academic freedom and could increase self-censorship and harassment, including on social media. Earlier and ongoing controversies include the 1986 government-ordered closure of a sociology programme at Copenhagen University and recent proposals from Danish People's Party and Liberal Alliance to shut down Roskilde University for ideological reasons, including for being 'woke'.

Hungary

Central European University was forced to leave Hungary after its academic freedom deteriorated under Victor Orban. In 2020, students protested the overhauling by the government of the University of Theater and Film Arts.

India

As of 2025, India ranks in the bottom 10-20% of countries globally.

Ireland

Protections for academic freedom for research, teaching and other activity "to question and test received wisdom, to put forward new ideas and to state controversial or unpopular opinions" without being disadvantaged, are provided in Section 14 of the 1997 Universities Act.

Israel

Academic freedom in Israel is taken from "the Law of the Council for Higher Education". Paragraph 15 in which it states that "a recognized institution is free to all its academic and administrative matters, within the framework of its budget, as it sees fit. In this paragraph, 'academic and administrative matters' – includes: determining a research and teaching program, appointing the authorities of the institution, appointing teachers and promoting them, determining a teaching method and study, and any other scientific, educational or economic activity". It seems that the paragraph is worded in a clear and comprehensible way even for laymen. The body that is supposed to guard academic freedom, as well as maintain an adequate academic level in the higher education institutions, is the Council for Higher Education – hereinafter "The Council". This council consists of academics who serve as professors at universities, and public figures, with the Minister of Education as the head of the council.

At the disposal of "The Council" is an executive body called the "Committee for Planning and Budgeting", which mainly deals with the matter of universities budgeting and establishing relevant procedures and guidelines for budget and salary matters. Another body that is supposed to guard academic freedom is the "Committee of the Heads of the Universities", which is a voluntary body, but has an influence on the work of the Legislature and "The Council ". Through their employee committees, and through the personal activity of each of them, these bodies can try and influence the preservation of academic freedom.

In general, it can be said that the essential academic freedom, the one aimed at the freedom of teaching and research, was preserved, and the government neither interfered nor tried to interfere in these contents. Its way of influencing this matter is by providing incentives for teaching in this or that way, or for research in certain fields, and this is through grants. The fact that the government finances a significant percentage of the current budget of the universities (around 70% or more), also allows the government to decide what will be the tuition fee for a student at the budgeted universities in Israel. But, In 2021, an academic committee of the prestigious Israel Prize decided to award the Israel Prize in the field of mathematics and computer science to Professor Oded Goldreich from the Weizmann Institute of Science. The Minister of Education did not accept the committee's recommendation on the grounds that Goldreich signed a petition calling for an academic boycott of Ariel University, which is located in the territories of Judea and Samaria, which are occupied territory, as well as for appealing to the German government to revoke its decision that the BDS movement is an anti-Semitic movement. The award committee appealed to the Supreme Court for a violation of its academic freedom, and the court overturned the decision, and ordered the Minister of Education to award Goldreich the award. Godreich received the award a year later.

In recent years, a fierce debate has erupted on the issue of academic freedom, following extreme political statements by a number of university faculty members. The vast majority of the controversial statements were those that called for an academic boycott of Israel, or support for organizations that support an economic and academic boycott of Israel. The question that was at the center of the storm was whether an academic faculty member (hereafter referred to as a professor) is protected by the principle of freedom of speech, or is it forbidden, when he wears the guise of a professor, to express a political position that might identify the position with the institution he allegedly represents. All the more, is it permissible for the professor to express a political position during his teaching, and even to invite representatives of political bodies to lecture in his classes, and without maintaining a balance between those invited. Referring to that background, the Minister of Education at the time Naftali Bennett (in 2017) asked Prof. Asa Kasher to compile an academic Code of Ethics for universities, a code that was approved by "The Council" in March 2018. All the research universities (7 universities), with the exception of Ben-Gurion University of the Negev, which already had for an academic code of ethics that also included the issue of freedom of expression, refused to adopt this code on the grounds of infringing academic freedom.

All research universities in Israel have a Chief internal auditor, relatively independent. This issue of the interrelationship between the internal audit in universities and the principle of academic freedom is discussed in detail in an article that appeared in a book issued on behalf of the Ben-Gurion university of the Negev – the only one as mentioned that has a binding academic code of ethics.

Mauritius

In the Chapter II Constitution of Mauritius, academics have the right to: the protection of freedom of conscience, protection of freedom of expression, protection of freedom of assembly and association, protection of freedom to establish schools and the protection from discrimination. The institutional bureaucracy and the dependence on the state for funds has restricted the freedom of academics to criticize government policy. Dr. Kasenally, an educator at the University of Mauritius stated that in 1970s to 1980s the university was at the forefront of controversial debates, but in the 1990s the university stepped away after academic freedom was curtailed to not express views or ideas especially if they oppose those of the management or government. In a 2012 paper on the University of Mauritius the author states that although there are no records of abuse of human rights or freedom of the state "subtle threats to freedom of expression do exist, especially with regard to criticisms of ruling political parties and their leaders as well as religious groups." While there have been no cases of arrests or extreme detention of academics, there has been fear that it would hinder their career progress especially at the level of a promotion thus, the academics try to avoid participating in controversial debates. Academic freedom became a public issue in May 2009 when the university spoke out against the vice chancellor Professor I. Fagoonee, who had forwarded a circular sent by the Ministry of Education to academics. This circular targeted public officers and required them to consult their superiors before speaking to the press. The pushback resulted in the vice chancellor stepping down, with the author speculating the government used the vice chancellor as the scapegoat for its unpopular proposal to try to curtail academic freedom.

Netherlands

In the Netherlands the academic freedom is limited relative to other Western European countries. In November 1985 the Dutch Ministry of Education published a policy paper titled Higher Education: Autonomy and Quality. This paper had a proposal that steered away from traditional education and informed that the future of higher education sector should not be regulated by the central government. In 1992 the Law of Higher Education and Research (Wet op het hoger onderwijs en wetenschappelijk onderzoek, article 1.6) was published and became effective in 1993. However, this law governs only certain institutions.

New Zealand

The Education Act 1989 (s161(2)) defines Academic freedom as: a) The freedom of academic staff and students, within the law, to question and test received wisdom, to put forward new ideas and to state controversial or unpopular opinions; b) The freedom of academic staff and students to engage in research; c) The freedom of the university and its staff to regulate the subject matter of courses taught at the university; d) The freedom of the university and its staff to teach and assess students in the manner they consider best promotes learning; and e) The freedom of the university through its council and vice-chancellor to appoint its own staff.

Philippines

This section is an excerpt from Education in the Philippines § Academic freedom.edit

Academic freedom is protected by the 1987 Philippine Constitution, which states in Article XIV, Section 5 (2), "Academic freedom shall be enjoyed in all institutions of higher learning". Philippine Supreme Court Justice Estela Perlas-Bernabe wrote that "Academic freedom is anchored on the recognition that academic institutions perform a social function, and its business is conducted for the common good; that is, it is a necessary tool for critical inquiry of truth and its free exposition. Thus, the guarantee of academic freedom is complementary to the freedom of expression and the freedom of the mind."

Republic Act 8292 (Higher Education Modernization Act of 1997) states that "all institutions of higher learning, public or private, shall enjoy academic freedom and institutional autonomy". Implementing rules for this law state that "all SUCs shall enjoy academic freedom and institutional autonomy". Academic freedom is also enshrined in Republic Act 9500 (The University of the Philippines Charter of 2008), which states, "the national university has the right and responsibility to exercise academic freedom".

Threats to academic freedom include attempts to establish a military presence in campuses or corporations dictating that a school teach only "marketable courses". Other threats may come in the form of state-sponsored historical distortion and the red-tagging, surveillance, and harassment of students and faculty. In Freedom House's 2025 Academic Freedom Index, the Philippines scored 0.624 (out of 1, 1 is best), the country's lowest score in nearly 40 years.

South Africa

According to the FAU Academic Freedom Index, in 2025 South Africa scored a 0.83 on a scale of 0 to 1, which has been pretty constant between 2015 to 2025.

Academic freedom in the Constitution

Section 16(1) of the Constitution of the Republic of South Africa, established in 1996, guarantees everyone the right to freedom of expression, including “academic freedom and freedom of scientific research".

Higher education under apartheid South Africa

Under apartheid, universities were racially segregated, a legacy that influences the lives of students and academics in South Africa today. The Population Registration Act of 1950 classified South Africans by race, using categories of White, Indian, Coloured, and Black. Based on this legislation, the Extension of University Education Act 45 dictated that students of nonwhite descent were not permitted to register at traditionally white universities unless given expression permission by the minister. As a result, several non-white universities were established, including the University of Durban-Westville for Indians, and the University of the Western Cape at Belleville, open to the Coloured community. Fort Hare University, University of Zululand, and the University of the North at Turfloop were established or reformed as institutions for specific ethnic groups. The higher education system remained starkly segregated until 1988, when the National Party government, led by F.W. de Klerk, put forth a set of policies repealing various systematic segregationist laws.

Movements and controversies

As of 2007, there have been scandals over the restricted academic freedom at a number of universities in South Africa. The University of KwaZulu-Natal received fame over its restricted academic freedom and the scandal that occurred in 2007. Fazel Khan was fired in April 2007 for "bringing the university into disrepute" after releasing information to the news media about being airbrushed from a photograph in a campus publication because of his participation in a staff strike. The South African Council on Higher Education released a report stating that the state is influencing academic freedom. Public universities are more susceptible to political pressure because they receive funds from the public.

Among postdoctoral fellows, there exist sentiments of being taken advantage of, based on the personal testimonies of postdoctoral fellows at the University of Johannesburg. While these conversations occur in many postdoctoral settings, much of the conversation arises from South Africa, where fellows report that the unstable nature of postdoctoral contracts is lends itself to insufficient compensation disproportionate to the demand for fellows. Multiple accounts and reports from postdoctoral fellows have shown two conflicting ideas: one believing the postdoc system to be a reliable pathway for a future scholarly career and one perceiving the system as unreliable and exploitive.

Institutional capture and patronage networks, informal institutions intertwined with South Africa's academic landscape, Jonas Magedi argues, compromises the integrity of higher education. Specifically, pressure from external sources may suppress dissent and inhibit further growth, especially in the area of humanities.

Turkey

See also: List of educational institutions closed in the 2016 Turkish purges and Academic freedom in Turkey

In 2016, Erdogan was given the power to appoint professors by decree. This, along with firings, harassment and imprisonment of academics helped to drop Turkey to one of the countries with the lowest academic freedom in the world by 2021, leading to protests at institutions like Boğaziçi University.

United Kingdom

See also: Anthony D. Smith

The Robbins Report on Higher Education, commissioned by the British government and published in 1963, devoted a full chapter, Chapter XVI, to Academic freedom and its scope. This gives a detailed discussion of the importance attached both to freedom of individual academics and of the institution itself. In a world, both then and now, where illiberal governments are all too ready to attack freedom of expression, the Robbins committee saw the (then) statutory protection given to academic freedom as giving some protection for society as a whole from any temptation to mount such attacks.

When Margaret Thatcher's government sought to remove many of the statutory protections of academic freedom which Robbins had regarded as so important, she was partly frustrated by a hostile amendment to her bill in the House of Lords. This incorporated into what became the 1988 Education Reform Act, the legal right of academics in the UK 'to question and test received wisdom and to put forward new ideas and controversial or unpopular opinions without placing themselves in jeopardy of losing their jobs or the privileges they may have'. These principles of academic freedom are thus articulated in the statutes of most UK universities. Professor Kathleen Stock formerly of University of Sussex resigned from her role due to controversy from students and the media regarding her transphobic views. In response to such concerns, the Equality and Human Rights Commission has issued guidance. The Guidance provides detailed procedures for universities to consider in determining whether or not specific events can go ahead. It also provides ways to reduce any potential barriers for freedom of speech in regards to specific events. The guidance also makes clear the statutory requirement of universities to ensure they protect freedom of speech on campus however as well as compliance with the Prevent Strategy and the Equality Act 2010. In 2016 the Warden of Wadham College Oxford, a lawyer previously Director of Public Prosecutions, pointed out that the Conservative government's anti-terrorism "Prevent" strategy legislation has placed on universities 'a specific enforceable duty ... to prevent the expression of views that are otherwise entirely compatible with the criminal law'.

United States

Further information: Censorship of school curricula in the United States and Freedom of speech in schools in the United States

See also: Chicago principles and Academic Freedom Alliance

Academic freedom started in America after the Civil War disrupted the previously stagnating systems of higher education. The educational system that Germany had was analyzed by universities to progress fields of research. Johns Hopkins University was the first to use this education system.

Prior to the turn of the twentieth century, a professor by the name of Edward Ross published the free silver movement supporting document known as Honest Dollars. The document placed the professor in political disagreement with the founders of Stanford University. The Stanford family made their money from the railroad industry that the professor had publicly ridiculed. In 1900, the professor expressed politically charged statements that called for the expulsion of Japanese immigrants from the country which would lead to his termination from the university. This decision was followed by seven other professors resigning from the university and elevated the matter to national scrutiny. This event would set in motion the creation of the AAUP to provide monetary and legal security, filling the gaps in many of their contracts.

In the United States, academic freedom is generally taken as the notion of academic freedom defined by the "1940 Statement of Principles on Academic Freedom and Tenure", jointly authored by the American Association of University Professors (AAUP) and the Association of American Colleges and Universities. These principles state that "Teachers are entitled to freedom in the classroom in discussing their subject." The statement also permits institutions to impose "limitations of academic freedom because of religious or other aims", so long as they are "clearly stated in writing at the time of the appointment". The principle also refers to the ability of teachers, students, and educational institutions to pursue knowledge without unreasonable political or government interference. The Principles have only the character of private pronouncements, not that of binding law. In short the statement argues that professors have the privilege to search for truth and knowledge and the right to impart those truths and knowledge to others, including students, the academy, and the general public, unfettered by political or ideological pressure.

Since being drafted, this definition has undergone two revisions in 1970 and 1999 respectively. The 1970 revision declares that the protections of academic freedom "apply not only to the full-time probationary and the tenured teacher, but also to all others, such as part-time faculty and teaching assistants, who exercise teaching responsibilities". The 1999 revision places emphasis on the idea that post-tenure review should be conducted in a manner that respects academic freedom and due process.

In 1957, the U.S. Supreme Court began to take up the matter starting with the case of Sweezy v. New Hampshire. In Keyishian v. Board of Regents (1967), the Supreme Court made connections between the First Amendment and academic freedom as an especially important protection on the grounds that it was crucial to everyone. Such First Amendment protections only applied to public institutions, and academic freedom contains protections outside of the First Amendment as the Court never outright declared that it contained academic freedom.

Some accreditors work with American colleges and universities, including private and religious institutions, to support academic freedom in various forms, although this varies by accreditor. Additionally, the AAUP, which is not an accrediting body, works with these same institutions. The AAUP does not always agree with the accrediting bodies on the standards of protection of academic freedom and tenure. The AAUP censures those colleges and universities which it has found, after its own investigations, to violate these principles. By 2022, 88 percent of four-year colleges and universities will limit student free speech, reversing a 15-year trend, according to the College Speech Codes annual report. The Foundation for Individual Rights and Expression (FIRE) reported that 426 out of 486 institutions have at least one policy restricting student speech.

For institutions

A prominent feature of the English university concept is the freedom to appoint faculty, set standards and admit students. This ideal may be better described as institutional autonomy and is distinct from whatever freedom is granted to students and faculty by the institution.

The Supreme Court of the United States said that academic freedom means a university can "determine for itself on academic grounds:

1. who may teach,
2. what may be taught,
3. how it should be taught, and
4. who may be admitted to study."

In a 2008 case, a federal court in Virginia ruled that professors have no academic freedom; all academic freedom resides with the university or college. In that case, Stronach v. Virginia State University, a district court judge held "that no constitutional right to academic freedom exists that would prohibit senior (university) officials from changing a grade given by (a professor) to one of his students." The court relied on mandatory precedent of the U.S. Supreme Court case of Sweezy v. New Hampshire and a case from the fourth circuit court of appeals. The Stronach court also relied on persuasive cases from several circuits of the courts of appeals, including the first, third, and seventh circuits. That court distinguished the situation when a university attempts to coerce a professor into changing a grade, which is clearly in violation of the First Amendment, from when university officials may, in their discretionary authority, change the grade upon appeal by a student. The Stronach case has gotten significant attention in the academic community as an important precedent.

Relationship to freedom of speech

Academic freedom and free speech rights are not coextensive, although this widely accepted view has been challenged by an "institutionalist" perspective on the First Amendment. Academic freedom involves more than speech rights; for example, it includes the right to determine what is taught in the classroom. The AAUP gives teachers a set of guidelines to follow when their ideas are considered threatening to religious, political, or social agendas. When teachers speak or write in public, whether via social media or in academic journals, they are able to articulate their own opinions without the fear from institutional restriction or punishment, but they are encouraged to show restraint and clearly specify that they are not speaking for their institution. In practice, academic freedom is protected by institutional rules and regulations, letters of appointment, faculty handbooks, collective bargaining agreements, and academic custom.

In the U.S., the freedom of speech is guaranteed by the First Amendment, which states that "Congress shall make no law... abridging the freedom of speech, or of the press...." By extension, the First Amendment applies to all governmental institutions, including public universities. The U.S. Supreme Court has historically held that academic freedom is a First Amendment right at public institutions. However, the United States' First Amendment has generally been held to not apply to private institutions, including religious institutions. These private institutions may honor freedom of speech and academic freedom at their discretion.

Controversies

Evolution debate

See also: Scopes Monkey Trial

Academic freedom is also associated with a movement to introduce intelligent design as an alternative explanation to evolution in US public schools. Supporters claim that academic institutions need to fairly represent all possible explanations for the observed biodiversity on Earth, rather than implying no alternatives to evolutionary theory exist, although in practice are interested in possible explanations from only one of the world's religious traditions, the Abrahamic religions.

Critics of the movement claim intelligent design is religiously motivated pseudoscience and cannot be allowed into the curriculum of US public schools due to the First Amendment to the United States Constitution, often citing Kitzmiller v. Dover Area School District as legal precedent. They also reject the allegations of discrimination against proponents of intelligent design, of which investigation showed no evidence.

A number of "academic freedom bills" have been introduced in state legislatures in the United States between 2004 and 2008. The bills were based largely upon language drafted by the Discovery Institute, the hub of the Intelligent Design movement, and derive from language originally drafted for the Santorum Amendment in the United States Senate. According to The Wall Street Journal, the common goal of these bills is to expose more students to articles and videos that undercut evolution, most of which are produced by advocates of intelligent design or biblical creationism. The American Association of University Professors has reaffirmed its opposition to these bills, including any portrayal of creationism as a scientifically credible alternative and any misrepresentation of evolution as scientifically controversial. As of 2013, only the Louisiana bill has been successfully passed into law.

ALFP debate (2014)

In 2014, a debate was held by the Academic Leadership Fellows Program (ALFP), addressing the potential need to either further revise the text, overhaul it completely, or leave it as is. The argument that revision/overhaul is necessary asserts that due to rapid growth of technology in education, introduction of social media (which effectively blurs the line between existing as an academic and an individual with unique interests), increase in international students, and rise in student expectations for return on investment since 1999, the statement no longer applies to modernized academia and thus should be changed. The counterargument to revision/overhaul asserts that the AAUP's statement has aged well, and that overhauling the standard that has existed for decades would only stir up further confusion. Instead, it is necessary to "clearly articulate the statements' intended meaning through education, discussion, and by not supporting inappropriate behavior in the name of academic freedom". This debate took place in front of a live audience, who after hearing both arguments agreed overwhelmingly with keeping the statement as-is.

Communism

In the 20th century and particularly the 1950s during McCarthyism, there was much public date in print on Communism's role in academic freedom, e.g., Sidney Hook's Heresy, Yes–Conspiracy, No and Whittaker Chambers' "Is Academic Freedom in Danger?" among many other books and articles.

Diversity initiatives

Since 2014, Harvard Medical School Dean Jeffrey Flier, and American Mathematical Society Vice President Abigail Thompson have contended that academics are asked to support diversity initiatives, and are discouraged from voicing opposition to equity and inclusion through self-censorship, as well as explicit promotion, hiring, and firing.

Controversial opinions

While some controversies of academic freedom are reflected in proposed laws that would affect large numbers of students through entire regions, many cases involve individual academics that express unpopular opinions or share politically unfavorable information. These individual cases may receive widespread attention and periodically test the limits of, and support for, academic freedom. Several of these specific cases are also the foundations for later legislation.

In 1929, Experimental Psychology professor Max Friedrich Meyer and sociology assistant professor Harmon O. DeGraff were dismissed from their positions at the University of Missouri for advising student Orval Hobart Mowrer regarding distribution of a questionnaire which inquired about attitudes towards partners' sexual tendencies, modern views of marriage, divorce, extramarital sexual relations, and cohabitation. The university was subsequently censured by the American Association of University Professors in an early case regarding academic freedom due a tenured professor.

In 2006, Lawrence Summers, while president of Harvard University, led a discussion that was intended to identify the reasons why fewer women chose to study science and mathematics at advanced levels. He suggested that the possibility of intrinsic gender differences in terms of talent for science and mathematics should be explored. He became the target of considerable public backlash. His critics were, in turn, accused of attempting to suppress academic freedom. Due to the adverse reception to his comments, he resigned after a five-year tenure. Another significant factor of his resignation was several votes of no-confidence placed by the deans of schools, notably multiple professors in the Faculty of Arts and Sciences.

In 2009 Thio Li-ann withdrew from an appointment at New York University School of Law after controversy erupted about some anti-gay remarks she had made, prompting a discussion of academic freedom within the law school. Subsequently, Li-ann was asked to step down from her position in the NYU Law School.

In 2009 the University of California at Santa Barbara accused William I. Robinson of antisemitism after he circulated an email to his class containing photographs and paragraphs of the Holocaust juxtaposed to those of the Gaza Strip. Robinson was fired from the university, but later the accusations were dropped after a worldwide campaign against the management of the university.