Cronbach’s Alpha: Definition, Calculations & Example

What is Cronbach’s Alpha?

Cronbach’s alpha coefficient measures the internal consistency, or reliability, of a set of survey items. Use this statistic to help determine whether a collection of items consistently measures the same characteristic. Cronbach’s alpha quantifies the level of agreement on a standardized 0 to 1 scale. Higher values indicate higher agreement between items.

High Cronbach’s alpha values indicate that response values for each participant across a set of questions are consistent. For example, when participants give a high response for one of the items, they are also likely to provide high responses for the other items. This consistency indicates the measurements are reliable and the items might measure the same characteristic.

Conversely, low values indicate the set of items do not reliably measure the same construct. High responses for one question do not suggest that participants rated the other items highly. Consequently, the questions are unlikely to measure the same property because the measurements are unreliable.

For this statistic, data usually originate from survey responses, assessment instruments, and test scores. Data can be continuous but will often be Likert and binary values. The calculations assume that all items measure the same trait using the same scale. Statisticians call this a tau equivalent model.

Read on to learn more about using, interpreting, and calculating Cronbach’s alpha. I close with an example analysis.

What is Cronbach’s Alpha Used For?

Analysts frequently use Cronbach’s alpha when designing and testing a new survey or assessment instrument. This statistic helps them evaluate the quality of the tool during the design phase before deploying it fully. It is a measure of reliability.

Surveys and assessment instruments frequently ask multiple questions about the same concept, characteristic, or construct. By including several items on the same aspect, the test can develop a more nuanced assessment of the phenomenon.

Analysts can combine multiple related items to form a scale for the construct. However, before including various questions in a scale, they must be sure that all items reliably measure the same construct. Cronbach’s alpha helps with that process.

Imagine researchers are developing a self-esteem scale and are developing multiple items to measure that construct. If all items actually assess self-esteem, then scores across items should generally agree, producing a high Cronbach’s alpha. For instance, individuals with high self-esteem will tend to score highly on all items. Conversely, individuals with low self-esteem will tend to score low on all items.

However, if not all items assess self-esteem, individuals can measure high on some questions and low on others. The scores across items disagree, producing a lower Cronbach’s alpha.

Typically, researchers use Cronbach’s alpha to ensure that items agree, but they need to use it with other analyses that evaluate whether the items measure the correct characteristic. More on that in the limitations section!

Cronbach’s Alpha Interpretation

Interpreting Cronbach’s alpha is a little more complex than higher is better. Let’s cover the highlights as well as some caveats and warnings.

Cronbach’s alpha ranges from 0 to 1.

• Zero indicates that there is no correlation between the items at all. They are entirely independent. Knowing the value of a response to one question provides no information about the responses to the other questions.
• One indicates that they are perfectly correlated. Knowing the value of one response provides complete information about the other items.

Of course, your value will usually be somewhere in between. What is an acceptable range for Cronbach’s alpha?

Analysts frequently use 0.7 as a benchmark value for Cronbach’s alpha. At this level and higher, the items are sufficiently consistent to indicate the measure is reliable. Typically, values near 0.7 are minimally acceptable but not ideal. However, some fields and industries have different minimum values. Be sure to check for your study area.

It might surprise you, but Cronbach’s alpha can be too high. Extremely high values can indicate that the questions are redundant. For example, if respondents always give the same response to two items, you might be able to remove one of them. Again, different analysts/fields of study differ on what constitutes “too high.” Frequently, it’ll be either Cronbach’s alpha > 0.95 or 0.99.

Warnings and Limitations

Finally, here are several cautions about what Cronbach’s alpha does not tell you.

Cronbach’s alpha is a measure of reliability but not validity. It can indicate whether responses are consistent between items (reliability), but it cannot determine whether the items measure the correct concept (validity). For example, the responses to the questions can be very consistent, but they might measure positive outlook rather than self-esteem as you intended. Learn more about Reliability vs. Validity.

Furthermore, while high Cronbach’s values indicate consistency, they do not necessarily prove that your items are unidimensional, measuring a single characteristic. Items can measure multiple related concepts and, thereby, produce high alpha values.

In this light, you should see obtaining a high Cronbach’s alpha as a necessary step for establishing reliability, but it’s not sufficient by itself for determining validity. To help ensure that a set of items measures the correct characteristic, and only that characteristic, analysts frequently use factor analysis and principal components analysis.

Learn about more ways to Evaluate Validity.

How to Calculate Cronbach’s Alpha

Usually, you’ll have your statistical software calculate Cronbach’s alpha for you. However, knowing how to calculate it yourself can help you understand it.

Below is the formula for Cronbach’s alpha.

Where:

• N = number of items
• c̅ = mean covariance between items.
• v̅ = mean item variance.

The calculations for Cronbach’s alpha involve taking the average covariance and dividing it by the average total variance. Therefore, a high alpha value requires the covariance to be high relative to the item variance. In other words, the relationships between the questions account for most of the overall variability.

Additionally, the number of items is a factor. Cronbach’s alpha tends to increase as you add more items.

Analysis Example

Imagine a bank wants to survey customers to evaluate how satisfied they are with the timeliness of its service. You develop the following four survey questions:

• Item 1 – My telephone, email, or letter inquiry was answered in a reasonable amount of time.
• Item 2 – I am satisfied with the timeliness of the service provided.
• Item 3 – The time I waited for services was reasonable.
• Item 4 – I am satisfied with the services I received.

These questions all use a 5-point Likert scale ranging from 1 Very Dissatisfied to 5 Very Satisfied. You ask 60 customers to take the survey during the pilot study phase before distributing the survey more widely. Download the CSV dataset: Cronbachs_alpha.

For this analysis, the statistical software calculates the overall Cronbach’s alpha. Then it recalculates the statistic after omitting each item because that process can provide valuable information about specific items. The statistical output is below.

The overall Cronbach’s alpha is 0.7853. It’s minimally acceptable by most standards.

Let’s see if we can improve it some.

Under Omitted Item Statistics, the software recalculates Cronbach’s alpha after removing an item. If omitting an item substantially increases Cronbach’s alpha, consider removing that question from the instrument because it is suspect.

Removing Item 4 causes Cronbach’s alpha to increase from 0.7853 to 0.921674. This result suggests that only items 1, 2, and 3 measure customer service timeliness. We should either remove item 4 or reword and retest it.