Cronbach's alpha

Command:

Statistics Agreement & responsiveness Cronbach's alpha

Description

Cronbach's alpha is a widely used measure of internal consistency reliability (Cronbach, 1951; Bland & Altman, 1997). It calculates the average correlation among all items in a scale or questionnaire. It ranges from 0 to 1, with higher values indicating greater internal consistency. Cronbach’s alpha is based on the assumption that the items are measuring the same underlying construct.

How to enter data

Each question of the questionnaire results in one variable and the answers (numerically coded) are entered in the respective columns of the spreadsheet. The answers of one subject are entered on one row of the spreadsheet.

Required input

• Variables: the variables that contain the answers to the different questions of the questionnaire.
• Select: an optional filter to include only a selected subgroup of subjects (rows).
• Options
  • Correct for scale reversal: Some variables may be inversely related to other variables. When you select the option "Correct for scale reversal", MedCalc will detect these variables automatically (based on the correlation matrix) and reverse the values of those variables before analysis.

Results

Cronbach's alpha

Cases in spreadsheet	5
Cases with missing values	0
Cases included in the analysis	5

The following variable was reversed prior to analysis:

Q3

1. Cronbach's alpha with raw variables

Cronbach's alpha	0.8966
95% lower confidence limit	0.6628

Inter-Item correlation

	Q2	Q3	Q4
Q1	0.8663	0.7456	0.9363
Q2		0.9435	0.7715
Q3			0.6508

Average Inter-Item correlation	0.8190

Item-Total correlation

Variable	Correlation coefficient
Q1	0.9492
Q2	0.7346
Q3	0.5885
Q4	0.9279

Effect of dropping variables

Variable dropped	Alpha	Change
Q1	0.7914	-0.1051
Q2	0.8608	-0.03579
Q3	0.9121	0.01554
Q4	0.8759	-0.02064

2. Cronbach's alpha with standardized variables

Cronbach's alpha	0.9476
95% lower confidence limit	0.8294

Item-Total correlation

Variable	Correlation coefficient
Q1	0.9165
Q2	0.9323
Q3	0.8197
Q4	0.8282

Effect of dropping variables

Variable dropped	Alpha	Change
Q1	0.9180	-0.02968
Q2	0.9130	-0.03468
Q3	0.9477	0.00008852
Q4	0.9452	-0.002456

In the example, the results of Question 3 were found to be inversely related to the results of the other questions. Therefore the results of Question 3 were reversed prior to analysis.

MedCalc performs the calculations on (1) the raw data and (2) on the standardized variables (a transformation so that their mean is 0 and variance is 1).

Using the "raw" data, questions that have more variability contribute more to the variability of the resulting scale; in the "standardized" form, each question gets equal weight.

For both the raw data, and the standardized data, MedCalc reports the following.

Cronbach's Alpha

Cronbach's alpha is given with its lower confidence limit (Feldt, 1965).

For research purposes alpha should be more than 0.7 to 0.8, but for clinical purposes alpha should at least be 0.90 (Bland & Altman, 1997).

Inter-Item correlation

The Inter-Item correlation table reports the correlation between each variable and every other variable. The average of these is the Inter-Item correlation.

This provides an estimate of the overall internal consistency of the items. The higher the average Inter-Item correlation, the greater the internal consistency.

Note: the Inter-Item correlation table is only reported for the raw data. These correlations are the same for the standardized data.

Item-Total correlation

Item-Total correlation examines the correlation between each variable i and the totals obtained by summing all other variables.

Item-Total correlation measures how well an individual item relates to the overall scale. Variables with low Item-Total correlations may indicate poor internal consistency and may need to be revised or removed.

Note: use of the Item-Total correlation table on the standardized variables may be preferred over that on the raw data.

Effect of dropping variables

Finaly, MedCalc calculates the alpha obtained with each question in turn dropped. If the deletion of a question causes a considerable increase in alpha then you should consider dropping that question from the questionnaire.

Literature

• Cronbach LJ (1951) Coefficient alpha and the internal structure of tests. Psychometrika 16:297-334.
• Bland JM, Altman DG (1997) Statistics notes: Cronbach's alpha. British Medical Journal 314:572.
• Feldt LS (1965) The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty. Psychometrika 30:357-371.

See also

• Intraclass correlation coefficient
• Concordance correlation coefficient
• Inter-rater agreement (kappa)

External links

• Cronbach's alpha on Wikipedia.