Statistics notes: Cronbach's alpha

BMJ 1997;314:572 (22 February)

General practice

Statistics notes: Cronbach's alpha

J Martin Bland, professor of medical statistics,^a Douglas G Altman, head ^b

^a Department of Public Health Sciences St George's Hospital Medical School London SW17 0RE, ^b ICRF Medical Statistics Group Centre for Statistics in Medicine Institute of Health Sciences PO Box 777 Oxford OX3 7LF

Correspondence to: Professor Bland

Article

Top
Article
References

Many quantities of interest in medicine, such as anxiety ordegree of handicap, are impossible to measure explicitly. Instead,we ask a series of questions and combine the answers into asingle numerical value. Often this is done by simply addinga score from each answer. For example, the mini-HAQ is a measureof impairment developed for patients with cervical myelopathy.¹This has 10 items (table 1)) recording the degree of difficultyexperienced in carrying out daily activities. Each item is scoredfrom 1 (no difficulty) to 4 (can't do). The scores on the 10items are summed to give the mini-HAQ score.

View this table:
[in this window]
[in a new window]

Table 1 Mini-HAQ scale in 249 severely impaired subjects

When items are used to form a scale they need to have internalconsistency. The items should all measure the same thing, sothey should be correlated with one another. A useful coefficientfor assessing internal consistency is Cronbach's alpha.² Theformula is:

[This figure is not available.]

where k is the number of items, si² is the variance of the ithitem and sT² is the variance of the total score formed by summingall the items. If the items are not simply added to make thescore, but first multiplied by weighting coefficients, we multiplythe item by its coefficient before calculating the variancesi². Clearly, we must have at least two items–that is k>1, or {alpha} will be undefined.

The coefficient works because the variance of the sum of a groupof independent variables is the sum of their variances. If thevariables are positively correlated, the variance of the sum willbe increased. If the items making up the score are all identicaland so perfectly correlated, all the si² will be equal and sT²= k² si², so that {Sigma} si²/sT² = 1/k and {alpha} = 1. On the other hand,if the items are all independent, then sT² = {Sigma} si² and {alpha} = 0. Thus {alpha} will be 1 if the items are all the same and 0 if none is relatedto another.

For the mini-HAQ example, the standard deviations of each itemand the total score are shown in the table. We have {Sigma} si² = 11.16,sT² = 77.44, and k = 10. Putting these into the equation, we have

[This figure is not available.]

which indicates a high degree of consistency.

For scales which are used as research tools to compare groups, {alpha} may be less than in the clinical situation, when the valueof the scale for an individual is of interest. For comparing groups, {alpha} values of 0.7 to 0.8 are regarded as satisfactory. For theclinical application, much higher values of {alpha} are needed. Theminimum is 0.90, and {alpha} =0.95, as here, is desirable.

In a recent example, McKinley et al devised a questionnaireto measure patient satisfaction with calls made by general practitionersout of hours.³ This included eight separate scores, which they interpretedas measuring constructs such as satisfaction with communicationand management, satisfaction with doctor's attitude, etc. Theyquoted {alpha} for each score, ranging from 0.61 to 0.88. They concludethat the questionnaire has satisfactory internal validity, asfive of the eight scores had {alpha} >0.7. In this issue Bosma etal report similar values, from 0.67 to 0.84, for assessmentsof three characteristics of the work environment.⁴

Cronbach's alpha has a direct interpretation. The items in ourtest are only some of the many possible items which could beused to make the total score. If we were to choose two randomsamples of k of these possible items, we would have two differentscores each made up of k items. The expected correlation betweenthese scores is {alpha} .

References

Top
Article
References

Casey ATH, Crockard HA, Bland JM, Stevens J, Moskovich R, Ransford AO. Development of a functional scoring system for rheumatoid arthritis patients with cervical myelopathy Ann Rheum Dis (in press).
Cronbach LJ. Coefficient alpha and the internal structure of tests. Psychometrika 1951;16:297-333.
McKinley RK, Manku-Scott T, Hastings AM, French DP, Baker R. Reliability and validity of a new measure of patient satisfaction with out of hours primary medical care in the United Kingdom: development of a patient questionnaire. BMJ 1997;314:193-8. [Abstract/Free Full Text]
Bosma H, Marmot MG, Hemingway H, Nicholson AC, Brunner E, Stansfield SA. Low job control and risk of coronary heart disease in Whitehall II (prospective cohort) study. BMJ 1997;314:558-65.

CiteULike

Complore

Connotea

Del.icio.us Add to Digg

Digg

StumbleUpon Add to Technorati

Technorati What's this?

This article has been cited by other articles:

Matheson, C, Matheson, D (2009). How well prepared are medical students for their first year as doctors? The views of consultants and specialist registrars in two teaching hospitals. Postgrad. Med. J. 85: 582-589 [Abstract] [Full text]
Patwardhan, K., Gehlot, S., Singh, G., Rathore, H. C. S. (2009). The Ayurveda Education in India: How Well are the Graduates Exposed to Basic Clinical Skills?. Evid Based Complement Alternat Med 0: nep113v1-nep113 [Abstract] [Full text]
Roddy, E., Muller, S., Thomas, E. (2009). Defining disabling foot pain in older adults: further examination of the Manchester Foot Pain and Disability Index. Rheumatology (Oxford) 48: 992-996 [Abstract] [Full text]
Mukoma, W., Flisher, A. J., Helleve, A., Aaro, L. E., Mathews, C., Kaaya, S., Klepp, K.-I. (2009). Development and test--retest reliability of a research instrument designed to evaluate school-based HIV/AIDS interventions in South Africa and Tanzania. Scand J Public Health 37: 7-15 [Abstract]
Kuntsche, E, Kuendig, H, Gmel, G (2008). Alcohol outlet density, perceived availability and adolescent alcohol use: a multilevel structural equation model. J. Epidemiol. Community Health 62: 811-816 [Abstract] [Full text]
Goncalves, F, Bento, M., Alvarenga, M, Costa, I, Costa, L (2008). Validation of a Consciousness Level Scale for Palliative Care. Palliat Med 22: 724-729 [Abstract]
Immer, F. F., Moser, B., Krahenbuhl, E. S., Englberger, L., Stalder, M., Eckstein, F. S., Carrel, T. (2008). Arterial Access Through the Right Subclavian Artery in Surgery of the Aortic Arch Improves Neurologic Outcome and Mid-Term Quality of Life. Ann. Thorac. Surg. 85: 1614-1618 [Abstract] [Full text]
Wedderburn, C, Wear, H, Brown, J, Mason, S J, Barker, R A, Hodges, J, Williams-Gray, C (2008). The utility of the Cambridge Behavioural Inventory in neurodegenerative disease. J. Neurol. Neurosurg. Psychiatry 79: 500-503 [Abstract] [Full text]
Harland, J., Bath, P. (2007). Assessing the quality of websites providing information on multiple sclerosis: evaluating tools and comparing sites. Health Informatics Journal 13: 207-221 [Abstract]
Dirks, M., Niessen, L. W, Koudstaal, P. J, Franke, C. L, van Oostenbrugge, R. J, Dippel, D. W J, the members of the Delphi panel on indications and, (2007). Intravenous thrombolysis in acute ischaemic stroke: from trial exclusion criteria to clinical contraindications. An international Delphi study. J. Neurol. Neurosurg. Psychiatry 78: 685-689 [Abstract] [Full text]
Benito-Leon, J., Martinez-Martin, P., Frades, B., Martinez-Gines, M.L., de Andres, C., Meca-Lallana, J.E., Antiguedad, A.R., Huete-Anton, B., Rodriguez-Garcia, E., Ruiz-Martinez, J. (2007). Impact of fatigue in multiple sclerosis: the Fatigue Impact Scale for Daily Use (D-FIS). Mult Scler 13: 645-651 [Abstract]
Hill, S., Dziedzic, K., Thomas, E., Baker, S. R., Croft, P. (2007). The illness perceptions associated with health and behavioural outcomes in people with musculoskeletal hand problems: findings from the North Staffordshire Osteoarthritis Project (NorStOP). Rheumatology (Oxford) 46: 944-951 [Abstract] [Full text]
van Roosmalen, M S, Braspenning, J C C, De Smet, P A G M, Grol, R P T M (2007). Antibiotic prescribing in primary care: first choice and restrictive prescribing are two different traits. Qual Saf Health Care 16: 105-109 [Abstract] [Full text]
Wolf, C. A., Wijdicks, E. F. M., Bamlet, W. R., McClelland, R. L. (2007). Further Validation of the FOUR Score Coma Scale by Intensive Care Nurses. Mayo Clin Proc. 82: 435-438 [Abstract] [Full text]
Scarpa, M., Ruffolo, C., Polese, L., Martin, A., D'Inca, R., Sturniolo, G. C., D'Amico, D. F., Angriman, I. (2007). Quality of Life After Restorative Proctocolectomy for Ulcerative Colitis: Different Questionnaires Lead to Different Interpretations. Arch Surg 142: 158-165 [Abstract] [Full text]
KUNTSCHE, E., KNIBBE, R., GMEL, G., ENGELS, R. (2006). 'I DRINK SPIRITS TO GET DRUNK AND BLOCK OUT MY PROBLEMS...' BEVERAGE PREFERENCE, DRINKING MOTIVES AND ALCOHOL USE IN ADOLESCENCE. Alcohol Alcohol 41: 566-573 [Abstract] [Full text]
White, R, Walker, P, Roberts, S, Kalisky, S, White, P (2006). Bristol COPD Knowledge Questionnaire (BCKQ): testing what we teach patients about COPD. Chronic Respiratory Disease 3: 123-131 [Abstract]
Flapper, B C.T., Koopman, H M, ten Napel, C, van der Schans, C P (2006). Psychometric properties of the TACQOL-asthma, a disease-specific measure of health related quality-of-life for children with asthma and their parents. Chronic Respiratory Disease 3: 65-72 [Abstract]
Immer, F. F., Grobety, V., Lauten, A., Carrel, T. P. (2006). Does malperfusion syndrome affect early and mid-term outcome in patients suffering from acute type A aortic dissection?. ICVTS 5: 187-190 [Abstract] [Full text]
Sawadogo, P. S., Martin-Prevel, Y., Savy, M., Kameli, Y., Traissac, P., Traore, A. S., Delpeuch, F. (2006). An Infant and Child Feeding Index Is Associated with the Nutritional Status of 6- to 23-Month-Old Children in Rural Burkina Faso. J. Nutr. 136: 656-663 [Abstract] [Full text]
Engels, Y., Dautzenberg, M., Campbell, S., Broge, B., Boffin, N., Marshall, M., Elwyn, G., Vodopivec-Jamsek, V., Gerlach, F. M, Samuelson, M., Grol, R. (2006). Testing a European set of indicators for the evaluation of the management of primary care practices. Fam Pract 23: 137-147 [Abstract] [Full text]
Smith, B J, Dalziel, K, McElroy, H J, Ruffin, R E, Frith, P A, McCaul, K A, Cheok, F (2005). Barriers to success for an evidence-based guideline for chronic obstructive pulmonary disease. Chronic Respiratory Disease 2: 121-131 [Abstract]
Boyer, F, Novella, J L, Bertaud, S, Delmer, F, Vesselle, B, Etienne, J C (2005). Hereditary neuromuscular disease and multicomposite subjective health status: feasibility, internal consistency and test-retest reliability in the French version of the Nottingham Health Profile, the ISPN. Clin Rehabil 19: 644-653 [Abstract]
Bunge, E M, Essink-Bot, M-L, Kobussen, M P H M, van Suijlekom-Smit, L W A, Moll, H A, Raat, H (2005). Reliability and validity of health status measurement by the TAPQOL. Arch. Dis. Child. 90: 351-358 [Abstract] [Full text]
Raat, H., Botterweck, A. M, Landgraf, J. M, Hoogeveen, W C., Essink-Bot, M.-L. (2005). Reliability and validity of the short form of the child health questionnaire for parents (CHQ-PF28) in large random school based and general population samples. J. Epidemiol. Community Health 59: 75-82 [Abstract] [Full text]
Chaudhuri, K. R., Martinez-Martin, P. (2004). Clinical assessment of nocturnal disability in Parkinson's disease: The Parkinson's Disease Sleep Scale. Neurology 63: S17-S20 [Full text]
Immer, F. F., Lippeck, C., Barmettler, H., Berdat, P. A., Eckstein, F. S., Kipfer, B., Saner, H., Schmidli, J., Carrel, T. P. (2004). Improvement of Quality of Life After Surgery on the Thoracic Aorta: Effect of Antegrade Cerebral Perfusion and Short Duration of Deep Hypothermic Circulatory Arrest. Circulation 110: II-250-II-255 [Abstract] [Full text]
Stiggelbout, A M, Molewijk, A C, Otten, W, Timmermans, D R M, van Bockel, J H, Kievit, J (2004). Ideals of patient autonomy in clinical decision making: a study on the development of a scale to assess patients' and physicians' views. J. Med. Ethics 30: 268-274 [Abstract] [Full text]
Marinus, J, Visser, M, Stiggelbout, A M, Rabey, J M., Martinez-Martin, P, Bonuccelli, U, Kraus, P H, van Hilten, J J (2004). A short scale for the assessment of motor impairments and disabilities in Parkinson's disease: the SPES/SCOPA. J. Neurol. Neurosurg. Psychiatry 75: 388-395 [Abstract] [Full text]
Pediatric Eye Disease Investigator Group, (2003). Impact of Patching and Atropine Treatment on the Child and Family in the Amblyopia Treatment Study. Arch Ophthalmol 121: 1625-1632 [Abstract] [Full text]
Nichols, J. J., Mitchell, G. L., Saracino, M., Zadnik, K. (2003). Reliability and Validity of Refractive Error-Specific Quality-of-Life Instruments. Arch Ophthalmol 121: 1289-1296 [Abstract] [Full text]
Schulze, M. B., Hoffmann, K., Kroke, A., Boeing, H. (2003). Risk of Hypertension among Women in the EPIC-Potsdam Study: Comparison of Relative Risk Estimates for Exploratory and Hypothesis-oriented Dietary Patterns. Am J Epidemiol 158: 365-373 [Abstract] [Full text]
(2003). Development and validation of an international appraisal instrument for assessing the quality of clinical practice guidelines: the AGREE project. Qual Saf Health Care 12: 18-23 [Abstract] [Full text]
Qureshi, N, Hapgood, R, Armstrong, S (2002). Continuous medical education approaches for clinical genetics: a postal survey of general practitioners. J. Med. Genet. 39: e69-69 [Full text]
Meakin, R., Weinman, J. (2002). The 'Medical Interview Satisfaction Scale' (MISS-21) adapted for British general practice. Fam Pract 19: 257-263 [Abstract] [Full text]
Bland, J M., Altman, D. G (2002). Statistics Notes: Validating scales and indexes. BMJ 324: 606-607 [Full text]
Marinus, J, Ramaker, C, van Hilten, J J, Stiggelbout, A M (2002). Health related quality of life in Parkinson's disease: a systematic review of disease specific instruments. J. Neurol. Neurosurg. Psychiatry 72: 241-248 [Abstract] [Full text]
Thumboo, J, Feng, P-H, Chan, S-P, Boey, M-L, Thio, S-t, Fong, K-Y (2002). A Chinese version of the Rheumatology Attitudes Index is a valid and reliable measure of learned helplessness in patients with SLE. Lupus 11: 88-94 [Abstract]
Immer, F. F., Krahenbuhl, E., Immer-Bansi, A. S., Berdat, P. A., Kipfer, B., Eckstein, F. S., Saner, H., Carrel, T. P. (2002). Quality of life after interventions on the thoracic aorta with deep hypothermic circulatory arrest. Eur. J. Cardiothorac. Surg. 21: 10-14 [Abstract] [Full text]
Iglesias, C.P., Birks, Y.F., Torgerson, D.J. (2001). Improving the measurement of quality of life in older people: the York SF-12. QJM 94: 695-698 [Abstract] [Full text]
Lookk, J., Nilsson, M., Norberg, B., Hultdin, J., Sandstrom, H., Westman, G. (2001). Shifts in B12 opinions in primary health care of Sweden. Scand J Public Health 29: 122-128 [Abstract]
Jansen, R., Niemeyer, M. G., Cleophas, T. J., Zwinderman, A. H. (2000). Factors Influencing Efficacy of Nitrate Therapy for Stable Angina Pectoris: A Multiple Linear Regression Analysis. ANGIOLOGY 51: 1007-1012 [Abstract]
Thumboo, J, Feng, P-H, Soh, C-H, Boey, M-L, Thio, S-t, Fong, K-Y (2000). Validation of a Chinese version of the Medical Outcomes Study Family and Marital Functioning Measures in patients with SLE. Lupus 9: 702-707 [Abstract]
Thumboo, J, Feng, P-H, Boey, M-L, Soh, C-H, Thio, S-t, Fong, K-Y (2000). Validation of the Chinese SF-36 for quality of life assessment in patients with systemic lupus erythematosus. Lupus 9: 708-712 [Abstract]
Hautvast, J. L., Tolboom, J. J., Kafwembe, E. M, Musonda, R. M, Mwanakasale, V., van Staveren, W. A, van �t Hof, M. A, Sauerwein, R. W, Willems, J. L, Monnens, L. A. (2000). Severe linear growth retardation in rural Zambian children: the influence of biological variables1. Am. J. Clin. Nutr. 71: 550-559 [Abstract] [Full text]
Grunfeld, E. A., Morland, A. B., Bronstein, A. M., Gresty, M. A. (2000). Adaptation to oscillopsia: A psychophysical and questionnaire investigation. Brain 123: 277-290 [Abstract] [Full text]
MAZEIKA, P K (2000). Quality of life four years after myocardial infarction: short form 36 scores compared with a normal population. Heart 83: 103b-103 [Full text]
Zwinderman, A. H., Cleophas, T. J., van der Sluijs, H., Niemeyer, M. G., Buunk, B. P., van der Wall, E. E., Cleophas, T. J., Dutch Mononitrate Quality of Life Study Group, (1999). Comparison of 50-mg and 100-mg Sustained-Release Isosorbide Mononitrate in the Treatment of Stable Angina Pectoris: Effects on Quality-of-Life Indices. ANGIOLOGY 50: 963-969 [Abstract]
Thumboo, J, Fong, K-Y, Chan, S-P, Leong, K-H, Feng, P-H, Thio, S-T, Boey, M-L (1999). Validation of the medical outcomes study family and marital functioning measures in SLE patients in Singapore. Lupus 8: 514-520 [Abstract]
Cardol, M., de Haan, R. J, van den Bos, G. A M, de Jong, B. A, de Groot, I. J M (1999). The development of a handicap assessment questionnaire: the Impact on Participation and Autonomy (IPA). Clin Rehabil 13: 411-419 [Abstract]
Olsson, C., Thelin, S. (1999). Quality of life in survivors of thoracic aortic surgery. Ann. Thorac. Surg. 67: 1262-1267 [Abstract] [Full text]
Marshall, M. N (1999). How well do GPs and hospital consultants work together? A survey of the professional relationship. Fam Pract 16: 33-38 [Abstract] [Full text]
Terwee, C. B, Gerding, M. N, Dekker, F. W, Prummel, M. F, Wiersinga, W. M (1998). Development of a disease specific quality of life questionnaire for patients with Graves' ophthalmopathy: the GO-QOL. Br J Ophthalmol 82: 773-779 [Abstract] [Full text]