The item–total correlation is 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 ...

between a scored item and the total

test score A test score is a piece of information, usually a number, that conveys the performance of an examinee on a test. One formal definition is that it is "a summary of the evidence contained in an examinee's responses to the items of a test that are ...

. It is an item

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 ...

used in

psychometric Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally covers specialized fields within psychology and education devoted to testing, measurement, assessment, and rela ...

analysis to diagnose assessment items that fail to indicate the underlying psychological trait so that they can be removed or revised.

The item-total correlation in item analysis

item analysis Within psychometrics, Item analysis refers to statistical methods used for selecting test items for inclusion in a psychological test. The concept goes back at least to . The process of item analysis varies depending on the psychometric model. Fo ...

, an item–total correlation is usually calculated for each item of a scale or test to diagnose the degree to which assessment items indicate the underlying trait. Assuming that most of the items of an assessment do indicate the underlying trait, each item should have a reasonably strong positive correlation with the total score on that assessment. An important goal of item analysis is to identify and remove or revise items that are not good indicators of the underlying trait. A small or negative item-correlation provides

empirical evidence Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law. There is no general agreement on how the ...

that the item is not measuring the same construct measured by the assessment. Exact values depend on the type of measure, but as a heuristic, a correlation value less than 0.2 indicates that the corresponding item does not correlate very well with the scale overall and, thus, it may be dropped. A negative value indicates that the item may be damaging the overall psychometric reliability of the measure. Identifying and removing (or revising) poorly-performing items is a critical way that psychometric analysis can improve the quality of a measure. When items are scored dichotomously, as in exams with correct and incorrect answers, the item-total correlation may be calculated as either a point-biserial correlation or a

biserial correlation The point biserial correlation coefficient (''rpb'') is a correlation coefficient used when one variable (e.g. ''Y'') is dichotomous; ''Y'' can either be "naturally" dichotomous, like whether a coin lands heads or tails, or an artificially dichoto ...

. This is considered important because items vary in difficulty and the point-biserial correlation cannot attain its theoretical maxima 1,-1unless the proportion correct is 0.50 (50% answering the item correctly). The biserial correlation has a correction that, in theory, avoids this issue. In practice, analysts should choose either the point-biserial or biserial and not try to compare, because the correction of the biserial will always produce a slightly larger magnitude as compared to the point-biserial. The item-reliability index (IRI) is defined as the product of the point-biserial item-total correlation and the item standard deviation. In

classical test theory Classical test theory (CTT) is a body of related psychometric theory that predicts outcomes of psychological Test (assessment), testing such as the difficulty of items or the ability of test-takers. It is a theory of testing based on the idea that ...

, the IRI indexes the degree to which an item contributes true score variance to the exam observed score variance. In practice, a negative IRI indicates the relative degree which an item damages the reliability estimate and a positive value indicates the relative degree which it contributes towards a high reliability estimate.

References

Comparison of assessments Covariance and correlation Statistical hypothesis testing Statistical reliability {{statistics-stub

The item-total correlation in item analysis

See also

References