Abstract
BackgroundWe aimed to assess the impact of inconsistent responses on the internal reliability of a multi-item scale by developing a procedure to adjust Cronbach's alpha.MethodsA procedure for adjusting Cronbach's alpha when there are inconsistent responses was developed and used to assess the impact of inconsistent responses on internal reliability by evaluating the standard Chinese 12-item Short Form Health Survey in adolescents.ResultsContrary to common belief, random responses may inflate Cronbach's alpha when their mean differ from that of the true responses. Fixed responses inflate Cronbach's alpha except in scales with both positive and negative polarity items. In general, the bias in Cronbach's alpha due to inconsistent responses may change from negative to positive with an increasing number of items in a scale, but the effect of additional items beyond around 10 becomes small. The number of response categories does not have much influence on the impact of inconsistent responses.ConclusionsCronbach's alpha can be biased when there are inconsistent responses, and an adjustment is recommended for better assessment of the internal reliability of a multi-item scale.
Highlights
We aimed to assess the impact of inconsistent responses on the internal reliability of a multi-item scale by developing a procedure to adjust Cronbach’s alpha
Internal reliability is an attribute of a multi-item scale that refers to the extent to which items in the scale are related; it is very often evaluated to assess the reliability of patient-reported outcomes (PROs)
A real example to illustrate the adjustment of inconsistent responses As an example, we evaluate the internal reliability of the standard Chinese SF-12v2
Summary
We aimed to assess the impact of inconsistent responses on the internal reliability of a multi-item scale by developing a procedure to adjust Cronbach’s alpha. There are tested personality scales, namely, the Minnesota Multiphasic Personality Inventory-2 (MMPI-2) and the Minnesota Multiphasic Personality Inventory-Adolescent (MMPI-A), that assess the level of inconsistency for a response [4,5] Both of them have a variable response inconsistency (VRIN) scale for assessing random responding and a true response inconsistency (TRIN) scale for assessing fixed responding. Depending on the instrument used, the VRIN scale comprises at least 50 item pairs and the TRIN at least 23 item pairs As their length does not always allow for concurrent use with PRO instruments, we can only assess the sensitivity of internal reliability within an anticipated range of the proportion of inconsistent responses. To the best of our knowledge, no method is available for adjusting the internal reliability due to inconsistent responses
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