Reliability (statistics)
In statistics and psychometrics, reliability is the overall consistency of a measure.[1] A measure is said to have a high reliability if it produces similar results under consistent conditions:
For other uses, see Reliability.There are several general classes of reliability estimates:
In practice, testing measures are never perfectly consistent. Theories of test reliability have been developed to estimate the effects of inconsistency on the accuracy of measurement. The basic starting point for almost all theories of test reliability is the idea that test scores reflect the influence of two sorts of factors:[7]
1. Consistency factors: stable characteristics of the individual or the attribute that one is trying to measure.
2. Inconsistency factors: features of the individual or the situation that can affect test scores but have nothing to do with the attribute being measured.
These factors include:[7]
The goal of estimating reliability is to determine how much of the variability in test scores is due to measurement errors and how much is due to variability in true scores (true value).[7]
A true score is the replicable feature of the concept being measured. It is the part of the observed score that would recur across different measurement occasions in the absence of error.
Errors of measurement are composed of both random error and systematic error. It represents the discrepancies between scores obtained on tests and the corresponding true scores.
This conceptual breakdown is typically represented by the simple equation:
Item response theory[edit]
It was well known to classical test theorists that measurement precision is not uniform across the scale of measurement. Tests tend to distinguish better for test-takers with moderate trait levels and worse among high- and low-scoring test-takers. Item response theory extends the concept of reliability from a single index to a function called the information function. The IRT information function is the inverse of the conditional observed score standard error at any given test score.
The goal of estimating reliability is to determine how much of the variability in test scores is due to errors in measurement and how much is due to variability in true scores.
Four practical strategies have been developed that provide workable methods of estimating test reliability.[7]
1. Test-retest reliability method: directly assesses the degree to which test scores are consistent from one test administration to the next.
It involves:
The correlation between scores on the first test and the scores on the retest is used to estimate the reliability of the test using the Pearson product-moment correlation coefficient: see also item-total correlation.
2. Parallel-forms method:
The key to this method is the development of alternate test forms that are equivalent in terms of content, response processes and statistical characteristics. For example, alternate forms exist for several tests of general intelligence, and these tests are generally seen equivalent.[7]
With the parallel test model it is possible to develop two forms of a test that are equivalent in the sense that a person's true score on form A would be identical to their true score on form B. If both forms of the test were administered to a number of people, differences between scores on form A and form B may be due to errors in measurement only.[7]
It involves:
The correlation between scores on the two alternate forms is used to estimate the reliability of the test.
This method provides a partial solution to many of the problems inherent in the test-retest reliability method. For example, since the two forms of the test are different, carryover effect is less of a problem. Reactivity effects are also partially controlled; although taking the first test may change responses to the second test. However, it is reasonable to assume that the effect will not be as strong with alternate forms of the test as with two administrations of the same test.[7]
However, this technique has its disadvantages:
3. Split-half method:
This method treats the two halves of a measure as alternate forms. It provides a simple solution to the problem that the parallel-forms method faces: the difficulty in developing alternate forms.[7]
It involves:
The correlation between these two split halves is used in estimating the reliability of the test. This halves reliability estimate is then stepped up to the full test length using the Spearman–Brown prediction formula.
There are several ways of splitting a test to estimate reliability. For example, a 40-item vocabulary test could be split into two subtests, the first one made up of items 1 through 20 and the second made up of items 21 through 40. However, the responses from the first half may be systematically different from responses in the second half due to an increase in item difficulty and fatigue.[7]
In splitting a test, the two halves would need to be as similar as possible, both in terms of their content and in terms of the probable state of the respondent. The simplest method is to adopt an odd-even split, in which the odd-numbered items form one half of the test and the even-numbered items form the other. This arrangement guarantees that each half will contain an equal number of items from the beginning, middle, and end of the original test.[7]
4. Internal consistency: assesses the consistency of results across items within a test. The most common internal consistency measure is Cronbach's alpha, which is usually interpreted as the mean of all possible split-half coefficients.[9] Cronbach's alpha is a generalization of an earlier form of estimating internal consistency, Kuder–Richardson Formula 20.[9] Although the most commonly used, there are some misconceptions regarding Cronbach's alpha.[10][11]
These measures of reliability differ in their sensitivity to different sources of error and so need not be equal. Also, reliability is a property of the scores of a measure rather than the measure itself and are thus said to be sample dependent. Reliability estimates from one sample might differ from those of a second sample (beyond what might be expected due to sampling variations) if the second sample is drawn from a different population because the true variability is different in this second population. (This is true of measures of all types—yardsticks might measure houses well yet have poor reliability when used to measure the lengths of insects.)
Reliability may be improved by clarity of expression (for written assessments), lengthening the measure,[9] and other informal means. However, formal psychometric analysis, called item analysis, is considered the most effective way to increase reliability. This analysis consists of computation of item difficulties and item discrimination indices, the latter index involving computation of correlations between the items and sum of the item scores of the entire test. If items that are too difficult, too easy, and/or have near-zero or negative discrimination are replaced with better items, the reliability of the measure will increase.