Statistical assumptionStatistics, like all mathematical disciplines, does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions.
Statistical inferenceStatistical inference is the process of using data analysis to infer 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.
Statistical populationIn statistics, a population is a set of similar items which is of interest for some question or experiment. A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker).
ProbabilityProbability concerns events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin.
Statistical hypothesis testA statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a p-value computed from the test statistic. Roughly 100 specialized statistical tests are in use.
Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in many fields, including applied mathematics, natural sciences, social sciences and engineering. In particular, the field of operations research studies the use of mathematical modelling and related tools to solve problems in business or military operations.
Random variableVariable representing a random phenomenonA random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.Data generating processIn statistics and in empirical sciences, a data generating process is a process in the real world that "generates" the data one is interested in. This process encompasses the underlying mechanisms, factors, and randomness that contribute to the production of observed data. Usually, scholars do not know the real data generating model and instead rely on assumptions, approximations, or inferred models to analyze and interpret the observed data effectively.EstimatorIn statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results.Kenneth A. BollenKenneth Alan Bollen (born 1951) is the Henry Rudolf Immerwahr Distinguished Professor of Sociology at the University of North Carolina at Chapel Hill. Bollen joined UNC-Chapel Hill in 1985. He is also a member of the faculty in the Quantitative Psychology Program housed in the L. L. Thurstone Psychometric Laboratory. He is a fellow at the Carolina Population Center, the American Statistical Association and the American Association for the Advancement of Science.
Herman J. AdèrHermanus Johannes "Herman J." Adèr (born May 20, 1940) is a Dutch statistician/methodologist and consultant at the Vrije Universiteit, the VU University Medical Center and the University of Stavanger, known for work on Methodological Modelling and Social Research Methodology.
Sampling (statistics)In statistics, quality assurance, and survey methodology, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. The subset, called a statistical sample (or sample, for short), is meant to reflect the whole population, and statisticians attempt to collect samples that are representative of the population.*As an Amazon Associate I earn from qualifying purchases.