In
statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
and
research
Research is creative and systematic work undertaken to increase the stock of knowledge. It involves the collection, organization, and analysis of evidence to increase understanding of a topic, characterized by a particular attentiveness to ...
, internal consistency is typically a measure based on the
correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...
s between different items on the same test (or the same subscale on a larger test). It measures whether several items that propose to measure the same general
construct produce similar scores. For example, if a respondent expressed agreement with the statements "I like to ride bicycles" and "I've enjoyed riding bicycles in the past", and disagreement with the statement "I hate bicycles", this would be indicative of good internal consistency of the test.
Cronbach's alpha
Internal consistency is usually measured with Cronbach's alpha, a
statistic
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypot ...
calculated from the pairwise correlations between items. Internal consistency ranges between negative infinity and one. Coefficient alpha will be negative whenever there is greater within-subject variability than between-subject variability.
A commonly accepted rule of thumb for describing internal consistency is as follows:
Very high reliabilities (0.95 or higher) are not necessarily desirable, as this indicates that the items may be redundant. The goal in designing a reliable instrument is for scores on similar items to be related (internally consistent), but for each to contribute some unique information as well. Note further that Cronbach's alpha is necessarily higher for tests measuring more narrow constructs, and lower when more generic, broad constructs are measured. This phenomenon, along with a number of other reasons, argue against using objective cut-off values for internal consistency measures. Alpha is also a
function of the number of items, so shorter scales will often have lower reliability estimates yet still be preferable in many situations because they are lower burden. It is also worth noting that, unlike
Item Response Theory (IRT) based perspectives on reliability, Cronbach's alpha only provides a single summary value which may not accurately represent the variability of reliability across different points of the score distribution (e.g., it may overstate the reliability of measurement at extremes of the score distribution).
An alternative way of thinking about internal consistency is that it is the extent to which all of the items of a test measure the same
latent variable
In statistics, latent variables (from Latin: present participle of ) are variables that can only be inferred indirectly through a mathematical model from other observable variables that can be directly observed or measured. Such '' latent va ...
. The advantage of this perspective over the notion of a high average correlation among the items of a test – the perspective underlying Cronbach's alpha – is that the average item correlation is affected by
skewness (in the distribution of item correlations) just as any other
average
In colloquial, ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean the sum of the numbers divided by ...
is. Thus, whereas the
modal item correlation is zero when the items of a test measure several unrelated latent variables, the average item correlation in such cases will be greater than zero. Thus, whereas the ideal of measurement is for all items of a test to measure the same latent variable, alpha has been demonstrated many times to attain quite high values even when the set of items measures several unrelated latent variables.
The hierarchical "coefficient omega" may be a more appropriate index of the extent to which all of the items in a test measure the same latent variable. Several different measures of internal consistency are reviewed by Revelle & Zinbarg (2009).
See also
*
Consistency (statistics) In statistics, consistency of procedures, such as computing confidence intervals or conducting hypothesis tests, is a desired property of their behaviour as the number of items in the data set to which they are applied increases indefinitely. In p ...
*
Cronbach's alpha
Cronbach's alpha (Cronbach's \alpha), also known as tau-equivalent reliability (\rho_T) or coefficient alpha (coefficient \alpha), is a reliability coefficient and a measure of the internal consistency of tests and measures. It was named after ...
*
Reliability (statistics)
In statistics and psychometrics, reliability is the overall consistency of a measure. A measure is said to have a high reliability if it produces similar results under consistent conditions:It is the characteristic of a set of test scores that ...
References
External links
* {{cite web , title=Essentials of a Good Psychological Test , url=http://wilderdom.com/personality/L3-2EssentialsGoodPsychologicalTest.html , archive-url=https://web.archive.org/web/20090805095348/http://wilderdom.com/personality/L3-2EssentialsGoodPsychologicalTest.html , archive-date=5 August 2009, url-status=dead
Comparison of assessments
Statistical reliability