Validity (statistics)Validity is the main extent to which a concept, conclusion or measurement is well-founded and likely corresponds accurately to the real world. The word "valid" is derived from the Latin validus, meaning strong. The validity of a measurement tool (for example, a test in education) is the degree to which the tool measures what it claims to measure. Validity is based on the strength of a collection of different types of evidence (e.g. face validity, construct validity, etc.) described in greater detail below.
External validityExternal validity is the validity of applying the conclusions of a scientific study outside the context of that study. In other words, it is the extent to which the results of a study can be generalized to and across other situations, people, stimuli, and times. In contrast, internal validity is the validity of conclusions drawn within the context of a particular study. Because general conclusions are almost always a goal in research, external validity is an important property of any study.
Concurrent validityConcurrent validity is a type of evidence that can be gathered to defend the use of a test for predicting other outcomes. It is a parameter used in sociology, psychology, and other psychometric or behavioral sciences. Concurrent validity is demonstrated when a test correlates well with a measure that has previously been validated. The two measures may be for the same construct, but more often used for different, but presumably related, constructs. The two measures in the study are taken at the same time.
Internal validityInternal validity is the extent to which a piece of evidence supports a claim about cause and effect, within the context of a particular study. It is one of the most important properties of scientific studies and is an important concept in reasoning about evidence more generally. Internal validity is determined by how well a study can rule out alternative explanations for its findings (usually, sources of systematic error or 'bias').
Predictive validityIn psychometrics, predictive validity is the extent to which a score on a scale or test predicts scores on some criterion measure. For example, the validity of a cognitive test for job performance is the correlation between test scores and, for example, supervisor performance ratings. Such a cognitive test would have predictive validity if the observed correlation were statistically significant. Predictive validity shares similarities with concurrent validity in that both are generally measured as correlations between a test and some criterion measure.
Criterion validityIn psychometrics, criterion validity, or criterion-related validity, is the extent to which an operationalization of a construct, such as a test, relates to, or predicts, a theoretical representation of the construct—the criterion. Criterion validity is often divided into concurrent and predictive validity based on the timing of measurement for the "predictor" and outcome. Concurrent validity refers to a comparison between the measure in question and an outcome assessed at the same time.
Construct validityConstruct validity concerns how well a set of indicators represent or reflect a concept that is not directly measurable. Construct validation is the accumulation of evidence to support the interpretation of what a measure reflects. Modern validity theory defines construct validity as the overarching concern of validity research, subsuming all other types of validity evidence such as content validity and criterion validity.
Algebraic stackIn mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli spaces are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of pointed algebraic curves and the moduli stack of elliptic curves. Originally, they were introduced by Grothendieck to keep track of automorphisms on moduli spaces, a technique which allows for treating these moduli spaces as if their underlying schemes or algebraic spaces are smooth.
Marginal utilityIn economics, utility refers to the satisfaction or benefit that consumers derive from consuming a product or service. Marginal utility, on the other hand, describes the change in pleasure or satisfaction resulting from an increase or decrease in consumption of one unit of a good or service. Marginal utility can be positive, negative, or zero. For example, when eating pizza, the second piece brings more satisfaction than the first, indicating positive marginal utility.
Decision tree learningDecision tree learning is a supervised learning approach used in statistics, data mining and machine learning. In this formalism, a classification or regression decision tree is used as a predictive model to draw conclusions about a set of observations. Tree models where the target variable can take a discrete set of values are called classification trees; in these tree structures, leaves represent class labels and branches represent conjunctions of features that lead to those class labels.
