Validity (statistics)

# Overview
In psychology, validity has two distinct fields of application. The first involves test validity, a concept that has evolved with the field of psychometrics but which textbooks still commonly gloss as the degree to which a test measures what it was designed to measure. The second involves research design. Here the term refers to the degree to which a study supports the intended conclusion drawn from the results. In the Campbellian tradition, this latter sense divides into four aspects: support for the conclusion that the causal variable caused the effect variable in the specific study (internal validity), support that the same effect generalizes to the statistical population from which the sample was drawn (statistical conclusion validity), support for the intended interpretation of the variables (construct validity), and support for the generalization of the results beyond the statistical population (external validity).

# Introduction to the concept
An early definition of test validity identified it with the degree of correlation between the test and a criterion. Under this definition, one can show that reliability of the test and the criterion places an upper limit on the possible correlation between them (the so-called validity coefficient). Intuitively, this reflects the fact that reliability involves freedom from random error and random errors do not correlate with one another. Thus, the less random error in the variables, the higher the possible correlation between them. Under these definitions, a test cannot have high validity unless it also has high reliability. However, the concept of validity has expanded substantially beyond this early definition and the classical relationship between reliability and validity need not hold for alternative conceptions of reliability and validity.
Within classical test theory, predictive or concurrent validity (correlation between the predictor and the predicted) cannot exceed the square root of the correlation between two versions of the same measure  that is, reliability limits validity.
Test validity can be assessed in a number of ways and thorough test validation typically involves more than one line of evidence in support of the validity of an assessment method (e.g. structured interview, personality survey, etc). The current Standards for Educational and Psychological Measurement follow Samuel Messick in discussing various types of validity evidence for a single summative validity judgment. These include construct related evidence, content related evidence, and criterion related evidence which breaks down into two subtypes (concurrent and predictive) according to the timing of the data collection.
Construct related evidence involves the empirical and theoretical support for the interpretation of the construct. Such lines of evidence include statistical analyses of the internal structure of the test including the relationships between responses to different test items. They also include relationships between the test and measures of other constructs. As currently understood, construct validity is not distinct from the support for the substantive theory of the construct that the test is designed to measure. As such, experiments designed to reveal aspects of the causal role of the construct also contribute to construct validity evidence.
Content related evidence involves the degree to which the content of the test matches a content domain associated with the construct. For example, a test of the ability to add two-digit numbers should cover the full range of combinations of digits. A test with only one-digit numbers, or only even numbers, would not have good coverage of the content domain. Content related evidence typically involves subject matter experts (SME's) evaluating test items against the test specifications.
Criterion related evidence involves the correlation between the test and a criterion variable (or variables) taken as representative of the construct. For example, employee selection tests are often validated against meaures of job performance. Measures of risk of recidivism among those convicted of a crime can be validated against measures of recidivism. If the test data and criterion data are collected at the same time, this is referred to as concurrent validity evidence. If the test data is collected first in order to predict criterion data collected at a later point in time, then this is referred to as predictive validity evidence.
Face validity is an estimate of whether a test appears to measure a certain criterion; it does not guarantee that the test actually measures phenomena in that domain. Indeed, when a test is subject to faking (malingering), low face validity might make the test more valid.
In contrast to test validity, assessment of the validity of a research design generally does not involve data collection or statistical analysis but rather evaluation of the design in relation to the desired conclusion on the basis of prevailing standards and theory of research design.

# Internal validity
Internal validity is an estimate of how much your measurement is based on clean experimental techniques, so that you can make clear-cut inferences about cause-consequence relations. If you choose experimental designs with random assignment of subjects or (if that isn't possible) you counterbalance for interfering variables then you get an experiment with high internal validity.

# External validity
The issue of external validity concerns the question to what extent one may safely generalize the conclusion derived from a statistical evaluation to the population outside the confines of the experimental situation.

## Ecological validity
This issue is closely related to internal validity and covers the question to which degree your experimental findings mirror what you can observe in the real world (ecology= science of interaction between organism and its environment).
Typically in science, you have two domains of research: Passive-observational and active-experimental. The purpose of experimental designs is to test causality, so that you can infer A causes B or  B causes A. 
But sometimes, ethical and/or methological restrictions prevent you from conducting an experiment (e.g. how does isolation influence a child's cognitive functioning?) Then you can still do research, but it's not causal, it's correlational, A occurs together with B. 
Both techniques have their strengths and weaknesses. To get an experimental design you have to control for all interfering variables. That's why you conduct your experiment in a laboratory setting. While gaining internal validity (excluding interfering variables by keeping them constant) you lose ecological validity because you establish an artificial lab setting.
On the other hand with observational research you can't control for interfering variables (low internal validity) but you can measure in the natural (ecological) environment, thus at the place where behavior occurs.

## Population validity

# Construct validity
Construct validity refers to the totality of evidence about whether a particular operationalization of a construct adequately represents what is intended by theoretical account of the construct being measured.

## Intentional validity

## Representation validity or translation validity

# Face validity
Face validity is very closely related to content validity, though it should not be confused with it.
While content validity depends on a theoretical basis for assuming if a test is assessing all domains of a certain criterion (e.g. does assessing addition skills yield in a good measure for mathematial skills? -  To answer this you have to know, what different kinds of arithmetic skills mathematical skills include ) face validity relates to whether a test appears to be a good measure or not. This judgment is made on the "face" of the test, thus it can also be judged by the amateur.

### Content validity
This is a non-statistical type of validity that involves the systematic examination of the test content to determine whether it covers a representative sample of the behaviour domain to be measured (Anatasi & Urbina, 1997 p114).
A test has content validity built into it by careful selection of which items to include (Anatasi & Urbina, 1997).  Items are chosen so that they comply with the test specification which is drawn up through a thorough examination of the subject domain.  Foxcraft et al (2004, p. 49) note that by using a panel of experts to review the test specifications and the selection of items the content validity of a test can be improved.  The experts will be able to review the items and comment on whether the items cover a representative sample of the behaviour domain.

## Observation validity

### Criterion-Related Validity
Criterion-related validity reflects the success of measures used for prediction or estimation. There are two types of criterion-related validity: Concurrent and predictive validity.
Concurrent validity refers to the degree to which the operationalization correlates with other measures of the same construct that are measured at the same time.
Predictive validity refers to the degree to which the operationalization can predict (or correlate with) with other measures of the same construct that are measured at some time in the future.

### Convergent validity
Convergent validity refers to the degree to which a measure is correlated with other measures that it is theoretically predicted to correlate with.

### Discriminant validity
Discriminant validity describes the degree to which the operationalization does not correlate with other operationalizations that it theoretically should not correlated with.

# Statistical conclusion

# Factors jeopardizing internal and external validity
Campbell and Stanley (1963) define internal validity as the basic requirements for an experiment to be interpretable - did the experiment make a difference in this instance?  External validity addresses the question of generalizability - to whom can we generalize this experiment's findings?
Eight extraneous variables can interfere with internal validity:
1. History, the specific events occurring between the first and second measurements in addition to the experimental variables
2. Maturation, processes within the participants as a function of the passage of time (not specific to particular events), e.g., growing older, hungrier, more tired, and so on.
3. Testing, the effects of taking a test upon the scores of a second testing.
4. Instrumentation, changes in calibration of a measurement tool or changes in the observers or scorers may produce changes in the obtained measurements.
5. Statistical regression, operating where groups have been selected on the basis of their extreme scores.
6. Selection, biases resulting from differential selection of respondents for the comparison groups.
7. Experimental mortality, or differential loss of respondents from the comparison groups.
8. Selection-maturation interaction, etc. e.g., in multiple-group quasi-experimental designs
Four factors jeopardizing external validity or representativeness are:
9. Reactive or interaction effect of testing, a pretest might increase
10. Interaction effects of selection biases and the experimental variable.
11. Reactive effects of experimental arrangements, which would preclude generalization about the effect of the experimental variable upon persons being exposed to it in non-experimental settings
12. Multiple-treatment interference, where effects of earlier treatments are not erasable.