1.
Sociology
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Sociology is the study of social behaviour or society, including its origins, development, organisation, networks, and institutions. It is a science that uses various methods of empirical investigation and critical analysis to develop a body of knowledge about social order, disorder. Many sociologists aim to research that may be applied directly to social policy and welfare. Subject matter ranges from the level of individual agency and interaction to the macro level of systems. The traditional focuses of sociology include social stratification, social class, social mobility, religion, secularization, law, sexuality, the range of social scientific methods has also expanded. Social researchers draw upon a variety of qualitative and quantitative techniques, the linguistic and cultural turns of the mid-twentieth century led to increasingly interpretative, hermeneutic, and philosophic approaches towards the analysis of society. There is often a great deal of crossover between social research, market research, and other statistical fields, Sociology is distinguished from various general social studies courses, which bear little relation to sociological theory or to social-science research-methodology. The US National Science Foundation classifies sociology as a STEM field, Sociological reasoning pre-dates the foundation of the discipline. Social analysis has origins in the stock of Western knowledge and philosophy. The origin of the survey, i. e, there is evidence of early sociology in medieval Arab writings. The word sociology is derived from both Latin and Greek origins, the Latin word, socius, companion, the suffix -logy, the study of from Greek -λογία from λόγος, lógos, word, knowledge. It was first coined in 1780 by the French essayist Emmanuel-Joseph Sieyès in an unpublished manuscript, Sociology was later defined independently by the French philosopher of science, Auguste Comte, in 1838. Comte used this term to describe a new way of looking at society, Comte had earlier used the term social physics, but that had subsequently been appropriated by others, most notably the Belgian statistician Adolphe Quetelet. Comte endeavoured to unify history, psychology and economics through the understanding of the social realm. Comte believed a positivist stage would mark the final era, after conjectural theological and metaphysical phases, Comte gave a powerful impetus to the development of sociology, an impetus which bore fruit in the later decades of the nineteenth century. To say this is not to claim that French sociologists such as Durkheim were devoted disciples of the high priest of positivism. To be sure, beginnings can be traced back well beyond Montesquieu, for example, Marx rejected Comtean positivism but in attempting to develop a science of society nevertheless came to be recognized as a founder of sociology as the word gained wider meaning. For Isaiah Berlin, Marx may be regarded as the father of modern sociology
2.
Doctor of Philosophy
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A Doctor of Philosophy is a type of doctoral degree awarded by universities in many countries. Ph. D. s are awarded for a range of programs in the sciences, engineering. The Ph. D. is a degree in many fields. The completion of a Ph. D. is often a requirement for employment as a university professor, researcher, individuals with an earned doctorate can use the title of Doctor with their name and use the post-nominal letters Ph. D. The requirements to earn a Ph. D. degree vary considerably according to the country, institution, a person who attains a doctorate of philosophy is automatically awarded the academic title of doctor. A student attaining this level may be granted a Candidate of Philosophy degree at some institutions. A Ph. D. candidate must submit a project, thesis or dissertation often consisting of a body of academic research. In many countries, a candidate must defend this work before a panel of examiners appointed by the university. Universities award other types of doctorates besides the Ph. D. such as the Doctor of Musical Arts, a degree for music performers and the Doctor of Education, in 2016, ELIA launched The Florence Principles on the Doctorate in the Arts. The Florence Principles have been endorsed are supported also by AEC, CILECT, CUMULUS, the degree is abbreviated PhD, from the Latin Philosophiae Doctor, pronounced as three separate letters. In the universities of Medieval Europe, study was organized in four faculties, the faculty of arts. All of these faculties awarded intermediate degrees and final degrees, the doctorates in the higher faculties were quite different from the current Ph. D. degree in that they were awarded for advanced scholarship, not original research. No dissertation or original work was required, only lengthy residency requirements, besides these degrees, there was the licentiate. According to Keith Allan Noble, the first doctoral degree was awarded in medieval Paris around 1150, the doctorate of philosophy developed in Germany as the terminal Teachers credential in the 17th century. Typically, upon completion, the candidate undergoes an oral examination, always public, starting in 2016, in Ukraine Doctor of Philosophy is the highest education level and the first science degree. PhD is awarded in recognition of a contribution to scientific knowledge. A PhD degree is a prerequisite for heading a university department in Ukraine, upon completion of a PhD, a PhD holder can elect to continue his studies and get a post-doctoral degree called Doctor of Sciences, which is the second and the highest science degree in Ukraine. Scandinavian countries were among the early adopters of a known as a doctorate of philosophy
3.
History of statistics
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The history of statistics can be said to start around 1749 although, over time, there have been changes to the interpretation of the word statistics. In early times, the meaning was restricted to information about states and this was later extended to include all collections of information of all types, and later still it was extended to include the analysis and interpretation of such data. In modern terms, statistics means both sets of collected information, as in national accounts and temperature records, and analytical work which requires statistical inference. Statistical activities are associated with models expressed using probabilities, and require probability theory for them to be put on a firm theoretical basis. A number of concepts have an important impact on a wide range of sciences. By the 18th century, the term designated the systematic collection of demographic and economic data by states. For at least two millennia, these data were mainly tabulations of human and material resources that might be taxed or put to military use. In the early 19th century, collection intensified, and the meaning of statistics broadened to include the discipline concerned with the collection, summary, and analysis of data. Today, data are collected and statistics are computed and widely distributed in government, business, most of the sciences and sports, electronic computers have expedited more elaborate statistical computation even as they have facilitated the collection and aggregation of data. A single data analyst may have available a set of data-files with millions of records and these were collected over time from computer activity or from computerized sensors, point-of-sale registers, and so on. The term mathematical statistics designates the mathematical theories of probability and statistical inference, the relation between statistics and probability theory developed rather late, however. In the 19th century, statistics increasingly used probability theory, whose results were found in the 17th and 18th centuries. By 1800, astronomy used probability models and statistical theories, particularly the method of least squares, much of the theoretical work was readily available by the time computers were available to exploit them. By the 1970s, Johnson and Kotz produced a four-volume Compendium on Statistical Distributions, applied statistics can be regarded as not a field of mathematics but an autonomous mathematical science, like computer science and operations research. Unlike mathematics, statistics had its origins in public administration, Applications arose early in demography and economics, large areas of micro- and macro-economics today are statistics with an emphasis on time-series analyses. With its emphasis on learning from data and making best predictions, statistics also has been shaped by areas of research including psychological testing, medicine. The ideas of testing have considerable overlap with decision science. With its concerns with searching and effectively presenting data, statistics has overlap with information science, look up statistics in Wiktionary, the free dictionary
4.
Quantitative psychology
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Quantitative psychologists research traditional and novel methods of psychometrics, a field of study concerned with the theory and technique of psychological measurement. At a general level, quantitative psychologists help create methods for all psychologists to test their hypotheses, Psychological research has a long history of contributing to statistical applications and theory. Quantitative psychologists have traditionally been in demand in industry, government. Their combined training in social science and quantitative methodology provides a unique skill set for solving both applied and theoretical problems in a variety of areas. Quantitative psychology has its roots in experimental psychology when, in the nineteenth century. Wilhelm Wundt is often called the founder of experimental psychology, because he called himself a psychologist, intelligence testing has long been an important branch of quantitative psychology. He established the worlds first mental testing center in 1882 in the year he published his observations and theories in Inquiries into Human Faculty. Statistical methods are the tools most used by psychologists. Pearson introduced the correlation coefficient and the chi-squared test, the 1900–1920 period saw the t-test, the ANOVA and a non-parametric correlation coefficient. A large number of tests were developed in the half of the 20th century. In 1946, psychologist Stanley Smith Stevens organized levels of measurement into four scales, Nominal, Ordinal, Ratio and he gave his name to Cohens kappa and Cohens d. In 1990, a paper titled Graduate Training in Statistics, Methodology. This article discussed the need for increased and up-to-date training in methods for psychology graduate programs in the United States. There have been critiques about the use of methods in psychological research. Notably, Professor Joel Michell from the University of Sydney has written extensively on the use and misuse of psychometric techniques, Training for quantitative psychology can begin informally at the undergraduate level. Many graduate schools recommend that students have coursework in psychology and complete the full college sequence of calculus. Quantitative coursework in other such as economics and research methods. Historically, however, students without all these courses have been accepted if other aspects of their application show promise, some schools also offer formal minors in areas related to quantitative psychology
5.
Statistics
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Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e. g. a scientific, industrial, or social problem, populations can be diverse topics such as all people living in a country or every atom composing a crystal. Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys, statistician Sir Arthur Lyon Bowley defines statistics as Numerical statements of facts in any department of inquiry placed in relation to each other. When census data cannot be collected, statisticians collect data by developing specific experiment designs, representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. In contrast, an observational study does not involve experimental manipulation, inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena. A standard statistical procedure involves the test of the relationship between two data sets, or a data set and a synthetic data drawn from idealized model. A hypothesis is proposed for the relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the hypothesis is done using statistical tests that quantify the sense in which the null can be proven false. Working from a hypothesis, two basic forms of error are recognized, Type I errors and Type II errors. Multiple problems have come to be associated with this framework, ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis, measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random or systematic, the presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems. Statistics continues to be an area of research, for example on the problem of how to analyze Big data. Statistics is a body of science that pertains to the collection, analysis, interpretation or explanation. Some consider statistics to be a mathematical science rather than a branch of mathematics. While many scientific investigations make use of data, statistics is concerned with the use of data in the context of uncertainty, mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory. In applying statistics to a problem, it is practice to start with a population or process to be studied. Populations can be diverse topics such as all living in a country or every atom composing a crystal. Ideally, statisticians compile data about the entire population and this may be organized by governmental statistical institutes
6.
Biplot
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Biplots are a type of exploratory graph used in statistics, a generalization of the simple two-variable scatterplot. A biplot allows information on both samples and variables of a matrix to be displayed graphically. Samples are displayed as points while variables are displayed either as vectors, in the case of categorical variables, category level points may be used to represent the levels of a categorical variable. A generalised biplot displays information on both continuous and categorical variables, the biplot was introduced by K. Ruben Gabriel. Gower and Hand wrote a monograph on biplots, Yan and Kang described various methods which can be used in order to visualize and interpret a biplot. The transformed data matrix Y is obtained from the original matrix X by centering and optionally standardizing the columns. Using the SVD, we can write Y = ∑k=1. pdkukvkT, where the uk are n-dimensional column vectors, the vk are p-dimensional column vectors, the biplot is formed from two scatterplots that share a common set of axes and have a between-set scalar product interpretation. The first scatterplot is formed from the points, for i =1. n, the second plot is formed from the points, for j =1. p. This is the biplot formed by the dominant two terms of the SVD, which can then be represented in a two-dimensional display, typical choices of α are 1 and 0, and in some rare cases α=1/2 to obtain a symmetrically scaled biplot. Available for free download ISBN 978-84-923846-8-6, with materials, the biplot graphic display of matrices with application to principal component analysis. Gower, J. C. Lubbe, S. and le Roux, ISBN 978-0-470-01255-0 Gower, J. C. and Hand, D. J. ISBN 0-412-71630-5 Yan, W. and Kang, M. S, ISBN 0-8493-1338-4 Demey, J. R. Vicente-Villardón, J. L. Galindo-Villardón, M. P. and Zambrano, A. Y. Identifying molecular markers associated with classification of genotypes by External Logistic Biplots
7.
Actuary
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An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the profession is actuarial science. These risks can affect both sides of the sheet, and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, Actuaries of the 21st century require analytical skills, business knowledge, and an understanding of human behavior and information systems to design and manage programs that control risk. The actual steps needed to become an actuary are usually country-specific, however, almost all processes share a rigorous schooling or examination structure, the profession has consistently been ranked as one of the most desirable. In various studies, being an actuary was ranked number one or two times since 2010. Actuaries use skills primarily in mathematics, particularly calculus-based probability and mathematical statistics, but also economics, computer science, finance, and business. Actuaries assemble and analyze data to estimate the probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, most traditional actuarial disciplines fall into two main categories, life and non-life. Life actuaries, which include health and pension actuaries, primarily deal with mortality risk, morbidity risk, products prominent in their work include life insurance, annuities, pensions, short and long term disability insurance, health insurance, health savings accounts, and long-term care insurance. Non-life actuaries, also known as property and casualty or general insurance actuaries, Actuaries are also called upon for their expertise in enterprise risk management. This can involve dynamic financial analysis, stress testing, the formulation of corporate policy. Actuaries are also involved in areas of the financial services industry. On both the life and casualty sides, the function of actuaries is to calculate premiums. On the casualty side, this often involves quantifying the probability of a loss event, called the frequency. The amount of time that occurs before the event is important. On the life side, the analysis often involves quantifying how much a potential sum of money or a liability will be worth at different points in the future. Forecasting interest yields and currency movements also plays a role in determining future costs, Actuaries do not always attempt to predict aggregate future events. Often, their work may relate to determining the cost of financial liabilities that have occurred, called retrospective reinsurance
8.
Central limit theorem
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If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to the normal distribution. The central limit theorem has a number of variants, in its common form, the random variables must be identically distributed. In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, in more general usage, a central limit theorem is any of a set of weak-convergence theorems in probability theory. When the variance of the i. i. d, Variables is finite, the attractor distribution is the normal distribution. In contrast, the sum of a number of i. i. d, Random variables with power law tail distributions decreasing as | x |−α −1 where 0 < α <2 will tend to an alpha-stable distribution with stability parameter of α as the number of variables grows. Suppose we are interested in the sample average S n, = X1 + ⋯ + X n n of these random variables, by the law of large numbers, the sample averages converge in probability and almost surely to the expected value µ as n → ∞. The classical central limit theorem describes the size and the form of the stochastic fluctuations around the deterministic number µ during this convergence. For large enough n, the distribution of Sn is close to the distribution with mean µ. The usefulness of the theorem is that the distribution of √n approaches normality regardless of the shape of the distribution of the individual Xi, formally, the theorem can be stated as follows, Lindeberg–Lévy CLT. Suppose is a sequence of i. i. d, Random variables with E = µ and Var = σ2 < ∞. Then as n approaches infinity, the random variables √n converge in distribution to a normal N, n → d N. Note that the convergence is uniform in z in the sense that lim n → ∞ sup z ∈ R | Pr − Φ | =0, the theorem is named after Russian mathematician Aleksandr Lyapunov. In this variant of the limit theorem the random variables Xi have to be independent. The theorem also requires that random variables | Xi | have moments of order. Suppose is a sequence of independent random variables, each with finite expected value μi, in practice it is usually easiest to check Lyapunov’s condition for δ =1. If a sequence of random variables satisfies Lyapunov’s condition, then it also satisfies Lindeberg’s condition, the converse implication, however, does not hold. In the same setting and with the notation as above. Suppose that for every ε >0 lim n → ∞1 s n 2 ∑ i =1 n E =0 where 1 is the indicator function
9.
Kurtosis
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In probability theory and statistics, kurtosis is a measure of the tailedness of the probability distribution of a real-valued random variable. Depending on the measure of kurtosis that is used, there are various interpretations of kurtosis. The standard measure of kurtosis, originating with Karl Pearson, is based on a version of the fourth moment of the data or population. This number is related to the tails of the distribution, not its peak, hence, for this measure, higher kurtosis is the result of infrequent extreme deviations, as opposed to frequent modestly sized deviations. The kurtosis of any normal distribution is 3. It is common to compare the kurtosis of a distribution to this value, distributions with kurtosis less than 3 are said to be platykurtic, although this does not imply the distribution is flat-topped as sometimes reported. Rather, it means the distribution produces fewer and less extreme outliers than does the normal distribution, an example of a platykurtic distribution is the uniform distribution, which does not produce outliers. Distributions with kurtosis greater than 3 are said to be leptokurtic and it is also common practice to use an adjusted version of Pearsons kurtosis, the excess kurtosis, which is the kurtosis minus 3, to provide the comparison to the normal distribution. Some authors use kurtosis by itself to refer to the excess kurtosis, for the reason of clarity and generality, however, this article follows the non-excess convention and explicitly indicates where excess kurtosis is meant. Alternative measures of kurtosis are, the L-kurtosis, which is a version of the fourth L-moment. These are analogous to the measures of skewness that are not based on ordinary moments. The kurtosis is the fourth standardized moment, defined as Kurt = μ4 σ4 = E 2, several letters are used in the literature to denote the kurtosis. A very common choice is κ, which is fine as long as it is clear that it does not refer to a cumulant, other choices include γ2, to be similar to the notation for skewness, although sometimes this is instead reserved for the excess kurtosis. The kurtosis is bounded below by the squared skewness plus 1, μ4 σ4 ≥2 +1, the lower bound is realized by the Bernoulli distribution. There is no limit to the excess kurtosis of a general probability distribution. A reason why some authors favor the excess kurtosis is that cumulants are extensive, formulas related to the extensive property are more naturally expressed in terms of the excess kurtosis. Xn be independent random variables for which the fourth moment exists, the excess kurtosis of Y is Kurt −3 =12 ∑ i =1 n σ i 4 ⋅, where σ i is the standard deviation of X i. In particular if all of the Xi have the same variance, the reason not to subtract off 3 is that the bare fourth moment better generalizes to multivariate distributions, especially when independence is not assumed
10.
Scatter plot
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A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are color-coded, one variable can be displayed. A scatter plot can be used either one continuous variable that is under the control of the experimenter. The measured or dependent variable is plotted along the vertical axis. If no dependent variable exists, either type of variable can be plotted on either axis, a scatter plot can suggest various kinds of correlations between variables with a certain confidence interval. For example, weight and height, weight would be on y axis, correlations may be positive, negative, or null. If the pattern of dots slopes from lower left to upper right, if the pattern of dots slopes from upper left to lower right, it indicates a negative correlation. A line of best fit can be drawn in order to study the relationship between the variables, an equation for the correlation between the variables can be determined by established best-fit procedures. For a linear correlation, the procedure is known as linear regression and is guaranteed to generate a correct solution in a finite time. No universal best-fit procedure is guaranteed to generate a solution for arbitrary relationships. A scatter plot is very useful when we wish to see how two comparable data sets agree with each other. In this case, an identity line, i. e. a y=x line, one of the most powerful aspects of a scatter plot, however, is its ability to show nonlinear relationships between variables. The ability to do this can be enhanced by adding a line such as LOESS. Furthermore, if the data are represented by a model of simple relationships. The scatter diagram is one of the seven basic tools of quality control, scatter charts can be built in the form of bubble, marker, or/and line charts. The researcher would then plot the data in a plot, assigning lung capacity to the horizontal axis. A person with a capacity of 400 cl who held his/her breath for 21.7 seconds would be represented by a single dot on the scatter plot at the point in the Cartesian coordinates. For a set of data variables X1, X2, xk, the scatter plot matrix shows all the pairwise scatter plots of the variables on a single view with multiple scatterplots in a matrix format
11.
Economist
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An economist is a practitioner in the social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy. A generally accepted interpretation in academia is that an economist is one who has attained a Ph. D. in economics, teaches economic science, the professionalization of economics, reflected in academia, has been described as the main change in economics since around 1900. Economists debate the path they believe their profession should take, surveys among economists indicate a preference for a shift toward the latter. Most major universities have a faculty, school or department. However, many prominent economists come from a background in mathematics, business, political science, law, sociology, getting a PhD in economics takes six years, on average, with a median of 5.3 years. The Nobel Memorial Prize in Economics, established by Sveriges Riksbank in 1968, is a prize awarded to each year for outstanding intellectual contributions in the field of economics. The prize winners are announced in October every year and they receive their awards on December 10, the anniversary of Alfred Nobels death. In contrast to regulated professions such as engineering, law or medicine, in academia, to be called an economist requires a Ph. D. degree in Economics. A professional working inside of one of many fields of economics or having a degree in this subject is often considered to be an economist. In addition to government and academia, economists are employed in banking, finance, accountancy, commerce, marketing, business administration, lobbying. Politicians often consult economists before enacting economic policy, many statesmen have academic degrees in economics. Economics graduates are employable in varying degrees depending on the regional economic scenario, small numbers go on to undertake postgraduate studies, either in economics, research, teacher training or further qualifications in specialist areas. Nearly 135 colleges and universities grant around 900 new Ph. D. s every year, incomes are highest for those in the private sector, followed by the federal government, with academia paying the lowest incomes. As of January 2013, PayScale. com showed Ph. D. economists salary ranges as follows, all Ph. D. economists, $61,000 to $160,000, Ph. D. The largest single grouping of economists in the UK are the more than 1000 members of the Government Economic Service. This figure compares very favourably with the picture, with 64 percent of economics graduates in employment. Some current well-known economists include, Ben Bernanke, Chairman of the Federal Reserve from 2006 to 2014, milton Friedman, Nobel Memorial Prize in Economic Sciences laureate in Economics
12.
Statistical graphics
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Statistical graphics, also known as graphical techniques, are graphics in the field of statistics used to visualize quantitative data. Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form and they include plots such as scatter plots, histograms, probability plots, spaghetti plots, residual plots, box plots, block plots and biplots. Exploratory data analysis relies heavily on such techniques, in addition, the choice of appropriate statistical graphics can provide a convincing means of communicating the underlying message that is present in the data to others. If one is not using statistical graphics, then one is forfeiting insight into one or more aspects of the structure of the data. Statistical graphics have been central to the development of science and date to the earliest attempts to analyse data, many familiar forms, including bivariate plots, statistical maps, bar charts, and coordinate paper were used in the 18th century. Since the 1970s statistical graphics have been re-emerging as an important analytic tool with the revitalisation of computer graphics, famous graphics were designed by, William Playfair who produced what could be called the first line, bar, pie, and area charts. See the plots page for more examples of statistical graphics. nist. gov. The Visual Display of Quantitative Information, trend Compass Alphabetic gallery of graphical techniques DataScope a website devoted to data visualization and statistical graphics
