MedCalc

# 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. Cronbachâ€™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 0 5
 The following variable was reversed prior to analysis: Q3

## 1. Cronbach's alpha with raw variables

 Cronbach's alpha 0.8966 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 0.819

## Item-Total correlation

Variable

Correlation coefficient

Q1

0.9492

Q2

0.7346

Q3

0.5885

Q4

0.9279

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 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.

Including variable i in the total would result in an inflated correlation between variable i and that total, see SPSS note.

Because the variable i is excluded from the total, this Item-Total correlation is sometimes called the "Item-Rest" or "Item-Remainder" correlation.

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.