Medical researchers often use questionnaires to measure concepts that cannot be observed directly, such as quality of life, pain, or treatment adherence. Before a total score is used, the researcher should show that the items measure the concept consistently. Cronbach’s alpha is the most widely used objective measure of this reliability (Tavakol & Dennick, 2011). A common mistake is to calculate it before reverse-coding negatively worded items, which can give a very low value for a good scale. This guide explains the method in simple steps, using one hypothetical clinical example from the beginning to the end.
Table of Contents
What Is Cronbach’s Alpha?
Lee Cronbach introduced this coefficient in 1951 to measure the internal consistency of a test or scale. It is expressed as a number between 0 and 1 (Tavakol & Dennick, 2011). The items usually come from a structured questionnaire, which is one of the common data collection techniques in clinical research.
Reliability and Internal Consistency
Reliability is the ability of an instrument to measure consistently. Validity is a different property, and it describes whether the instrument measures what it is intended to measure. Internal consistency describes the extent to which all the items measure the same concept. Moreover, Cronbach’s alpha requires only one administration of the questionnaire.
Raw Alpha and Standardized Alpha
Raw alpha is based on item variances and the variance of the total score. Standardized alpha is based on the correlations between items. SPSS can display both values. When the standardized value is higher than the raw value, the assumptions of the method should be examined further (Tavakol & Dennick, 2011).
Cronbach Alpha Interpretation
Published reports give acceptable values ranging from 0.70 to 0.95. A low value can result from too few items, poor correlation between items, or items that measure different concepts. In contrast, a value above 0.90 may indicate redundant items (Tavakol & Dennick, 2011). Therefore, Cronbach alpha interpretation should consider the number of items and the purpose of the scale, not one cut-off only.
Importance of Cronbach’s Alpha in Medical Research
Confidence in the Total Score
A total score adds the answers to several items. If these items do not agree with each other, the sum has no clear meaning. Consequently, any later comparison that uses this score becomes difficult to interpret.
Evidence for Translated and Adapted Questionnaires
Cronbach’s alpha is a property of the scores from a specific sample, not a fixed property of the questionnaire. Therefore, investigators should measure it each time the questionnaire is administered and should not rely on published estimates (Tavakol & Dennick, 2011). This point is especially relevant when a questionnaire is translated or used in a new patient group.
Meeting the Expectations of Peer Reviewers
Reviewers often ask for reliability evidence when a study uses a multi-item scale. A clear report of the coefficient, its confidence interval, and any deleted item prevents this comment and improves the credibility of the manuscript.
Applications of Cronbach’s Alpha in Clinical Studies
Questionnaire Development and Pilot Studies
Internal consistency is commonly evaluated in the pilot phase of questionnaire development and validation (Bujang et al., 2018). The pilot results help the team to revise or remove weak items before the main study.
Clinical Rating Scales
The method also applies to scales scored by clinicians. For example, a balance instrument for elderly patients contained 14 movements, each scored from 0 to 4, and its internal consistency was evaluated with this approach (Bujang et al., 2018).
Patient Surveys
Surveys often contain several domains, such as symptoms, function, and satisfaction. In this situation, alpha should be calculated for each domain. After reliability is confirmed, the researcher can follow our guide on choosing the right statistical test to compare the scores.
Assumptions of Cronbach’s Alpha
Before calculating the coefficient, the following conditions should be checked:
- One concept per scale: the items should measure one construct. Factor analysis can identify the dimensions of a questionnaire.
- Tau-equivalence: each item should measure the same trait on the same scale. When this assumption is violated, alpha underestimates reliability.
- Same direction of scoring: a higher score should have the same meaning for every item.
- Numeric item scores: Likert responses are treated as numbers, usually with five or more categories.
- Independent observations: each patient should contribute one set of answers.
- Adequate sample size: a small sample gives an imprecise estimate.
How to Calculate Cronbach’s Alpha: A Clinical Example
Consider a hypothetical cross-sectional survey of 150 adults with type 2 diabetes. Each patient completed a six-item Medication Adherence Confidence Scale, scored from 1 (strongly disagree) to 5 (strongly agree). There were no missing data. The data were created for teaching purposes, and every value below was calculated from these data.
| Item | Statement |
|---|---|
| Q1 | I take my diabetes medicines at the same time every day. |
| Q2 | I can keep taking my medicines when my routine changes. |
| Q3 | I remember my evening dose without a reminder. |
| Q4 | I often stop my medicines when I feel well. (negatively worded) |
| Q5 | I refill my prescriptions before they run out. |
| Q6 | I am satisfied with the clinic waiting area. |
Step 1: Check the Direction of Each Item
Q4 is negatively worded, so a high score means low confidence. On a 1 to 5 scale, the new score equals 6 minus the old score. Without this correction, Cronbach’s alpha was only 0.395, and Q4 had a corrected item-total correlation of −0.616. A negative correlation of this kind is a clear warning sign. After reverse-coding, all calculations used the corrected Q4.
Step 2: Calculate the Item and Total Variances
Calculate the mean and standard deviation of each item. Then, calculate the variance of each item and of the total score.
| Item | Mean | SD | Variance |
|---|---|---|---|
| Q1 | 3.59 | 1.04 | 1.090 |
| Q2 | 3.39 | 1.04 | 1.072 |
| Q3 | 3.39 | 1.03 | 1.071 |
| Q4 (reverse-coded) | 3.25 | 0.91 | 0.835 |
| Q5 | 3.61 | 0.98 | 0.964 |
| Q6 | 3.30 | 0.98 | 0.963 |
| Sum of item variances | 5.995 | ||
| Total score | 20.53 | 4.09 | 16.734 |
Step 3: Apply the Cronbach’s Alpha Formula
The formula is α = [k ÷ (k − 1)] × [1 − (sum of item variances ÷ variance of the total score)], where k is the number of items. Therefore, α = (6 ÷ 5) × (1 − 5.995 ÷ 16.734) = 1.2 × 0.642 = 0.770.
Step 4: Inspect the Item-Total Statistics
The corrected item-total correlation is the Pearson correlation between one item and the sum of the other items. The last column shows the value of alpha if that item is deleted.
| Item | Corrected item-total correlation | Alpha if item deleted |
|---|---|---|
| Q1 | 0.689 | 0.687 |
| Q2 | 0.644 | 0.700 |
| Q3 | 0.592 | 0.715 |
| Q4 (reverse-coded) | 0.616 | 0.713 |
| Q5 | 0.609 | 0.712 |
| Q6 | 0.016 | 0.848 |
Step 5: Review the Weak Item and Recalculate
Q6 had a correlation close to zero, and items of this kind are candidates for revision or deletion (Tavakol & Dennick, 2011). The content supports this decision because satisfaction with a waiting area is not adherence confidence. After removing Q6, the sum of item variances was 5.031 and the total variance was 15.643. Therefore, α = (5 ÷ 4) × (1 − 5.031 ÷ 15.643) = 0.848.
Step 6: Calculate the 95% Confidence Interval
The Feldt method uses the F distribution with n − 1 = 149 and (n − 1)(k − 1) = 596 degrees of freedom. The lower limit is 1 − (1 − 0.848) × 1.277 = 0.806, and the upper limit is 1 − (1 − 0.848) × 0.768 = 0.883. Our article on confidence intervals explains how to read this range. With the same alpha and only 30 patients, the interval would be 0.74 to 0.92.
Step 7: Confirm One Dimension and Interpret the Result
A principal component analysis of the five retained items gave a first eigenvalue of 3.113, which explained 62.3% of the variance. The second eigenvalue was 0.561. In the six-item version, the second eigenvalue was 1.008, which is consistent with Q6 measuring something else.
| Final five-item scale | Value |
|---|---|
| Cronbach’s alpha | 0.848 |
| 95% CI | 0.806 to 0.883 |
| Mean inter-item correlation | 0.528 |
| Range of inter-item correlations | 0.465 to 0.598 |
| Range of corrected item-total correlations | 0.625 to 0.712 |
The value lies within the commonly reported range and is below 0.90, so there is no sign of redundant items.
How to Report Cronbach’s Alpha Results in a Manuscript
The Methods section should name the coefficient, the confidence interval method, and the rule used to review items. The Results section can then be written as follows:
Internal Consistency of the Medication Adherence Confidence Scale
Cronbach’s alpha for the initial six-item scale was 0.770 (95% CI, 0.708 to 0.823). Item 6 had a corrected item-total correlation of 0.016 and was removed. The final five-item scale had a Cronbach’s alpha of 0.848 (95% CI, 0.806 to 0.883) among 150 patients. Moreover, corrected item-total correlations ranged from 0.625 to 0.712, and the mean inter-item correlation was 0.528. (Table 2)
A p-value is not needed here because the aim is to estimate reliability, not to test a difference. Notably, the explanation of these findings and comparisons with previous studies belong to the Discussion section.
Common Mistakes When Using Cronbach’s Alpha
Forgetting to Reverse-Code Items
Step 1 showed that alpha was 0.395 before correction and 0.770 after correction, using the same answers. Therefore, the coding of every item should be checked first.
Reporting One Value for a Multi-Domain Questionnaire
When a questionnaire contains more than one concept, a value for the whole instrument may not make sense. Alpha should be calculated for each concept (Tavakol & Dennick, 2011).
Adding Items Only to Increase Alpha
The coefficient rises as the number of items increases, even when the correlation between items stays the same. The next table keeps the mean inter-item correlation fixed at 0.30:
| Number of items | Standardized alpha |
|---|---|
| 5 | 0.68 |
| 10 | 0.81 |
| 20 | 0.90 |
| 40 | 0.94 |
Deleting Items Based on Numbers Only
Alpha if item deleted is a guide, not a rule. An item that is clinically essential should not be removed only to gain a small increase. Similar pitfalls in statistical analysis arise whenever a result drives the analysis plan.
Treating a High Alpha as Proof of Validity
A high coefficient shows that the items are related. However, it does not show that the scale measures the intended concept. Separate evidence of validity is still required.
Running Cronbach’s Alpha in SPSS and R
For alpha Cronbach SPSS analysis, first reverse-code negative items with Transform → Recode into Different Variables. Then choose Analyze → Scale → Reliability Analysis, move the items to the right, and keep the model as Alpha. Click Statistics and select Scale if item deleted and inter-item Correlations. For the 95% CI, select Intraclass correlation coefficient, choose Two-Way Mixed and Consistency, and read the Average Measures row. In R, one line gives the full output: psych::alpha(d[, c("Q1", "Q2", "Q3", "Q4r", "Q5")]).
Conclusion
Cronbach’s alpha is a simple and useful measure of internal consistency when the items are coded in one direction and measure one concept. A correct analysis includes item-total statistics, a confidence interval, and a clear justification for any deleted item. If you need support in validating a questionnaire, analyzing your data, or writing your Results section, the StatisMed team of biostatisticians provides statistical analysis services for medical studies. You can request a free quote today.
Frequently Asked Questions
1. What is a good Cronbach’s alpha value?
Published reports give acceptable values from 0.70 to 0.95, and a maximum of 0.90 has been recommended to avoid redundant items (Tavakol & Dennick, 2011).
2. How many patients do I need?
The answer depends on the number of items and the hypothesized values. For a five-item scale with 80% power, 16 patients are required to test 0.70 against 0.00, and 26 patients are required to test 0.80 against 0.50 (Bujang et al., 2018). A larger sample gives a narrower confidence interval.
3. Does Cronbach’s alpha replace test-retest reliability?
No. Alpha describes agreement between items at one time point. Test-retest reliability requires a second administration and describes stability over time.
References
Bujang, M. A., Omar, E. D., & Baharum, N. A. (2018). A review on sample size determination for Cronbach’s alpha test: A simple guide for researchers. The Malaysian Journal of Medical Sciences, 25(6), 85–99. https://doi.org/10.21315/mjms2018.25.6.9
Tavakol, M., & Dennick, R. (2011). Making sense of Cronbach’s alpha. International Journal of Medical Education, 2, 53–55. https://doi.org/10.5116/ijme.4dfb.8dfd
