Kuder-Richardson Formula 20
Encyclopedia
In statistics
, the Kuder-Richardson Formula 20 (KR-20) first published in 1937 is a measure of internal consistency reliability
for measures with dichotomous choices. It is analogous to Cronbach's α
, except Cronbach's α is also used for non-dichotomous (continuous) measures. A high KR-20 coefficient (e.g., >0.90) indicates a homogeneous test.
Values can range from 0.00 to 1.00 (sometimes expressed as 0 to 100), with high values indicating that the examination is likely to correlate with alternate forms (a desirable characteristic). The KR20 may be affected by difficulty of the test, the spread in scores and the length of the examination.
In the case when scores are not tau-equivalent (for example when there is not homogeneous but rather examination items of increasing difficulty) then the KR-20 is an indication of the lower bound of internal consistency (reliability).
where K is the length of the test and
where the variance for the denominator is
.
If it is important to use unbiased operators then the Sum of Squares should be divided by degrees of freedom (N − 1) and the probabilities are multiplied by
Since Cronbach's α
was published in 1951, there has been no known advantage to KR-20 over Cronbach. KR-20 is seen as a derivative of the Cronbach formula, with the advantage to Cronbach that it can handle both dichotomous and continuous variables.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, the Kuder-Richardson Formula 20 (KR-20) first published in 1937 is a measure of internal consistency reliability
Reliability (statistics)
In statistics, reliability is the consistency of a set of measurements or of a measuring instrument, often used to describe a test. Reliability is inversely related to random error.-Types:There are several general classes of reliability estimates:...
for measures with dichotomous choices. It is analogous to Cronbach's α
Cronbach's alpha
Cronbach's \alpha is a coefficient of reliability. It is commonly used as a measure of the internal consistency or reliability of a psychometric test score for a sample of examinees. It was first named alpha by Lee Cronbach in 1951, as he had intended to continue with further coefficients...
, except Cronbach's α is also used for non-dichotomous (continuous) measures. A high KR-20 coefficient (e.g., >0.90) indicates a homogeneous test.
Values can range from 0.00 to 1.00 (sometimes expressed as 0 to 100), with high values indicating that the examination is likely to correlate with alternate forms (a desirable characteristic). The KR20 may be affected by difficulty of the test, the spread in scores and the length of the examination.
In the case when scores are not tau-equivalent (for example when there is not homogeneous but rather examination items of increasing difficulty) then the KR-20 is an indication of the lower bound of internal consistency (reliability).
where K is the length of the test and
where the variance for the denominator is
.If it is important to use unbiased operators then the Sum of Squares should be divided by degrees of freedom (N − 1) and the probabilities are multiplied by
Since Cronbach's α
Cronbach's alpha
Cronbach's \alpha is a coefficient of reliability. It is commonly used as a measure of the internal consistency or reliability of a psychometric test score for a sample of examinees. It was first named alpha by Lee Cronbach in 1951, as he had intended to continue with further coefficients...
was published in 1951, there has been no known advantage to KR-20 over Cronbach. KR-20 is seen as a derivative of the Cronbach formula, with the advantage to Cronbach that it can handle both dichotomous and continuous variables.