## 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.

Jule says

Hey, can Cronbach’s Alpha also be used for nominal scales, or do they need to be ordinal or interval scaled?

Thank you for the support! 🙂

Jim Frost says

Hi Jule,

Unfortunately, you really can’t use Cronbach’s alpha for nominal scale data. Nominal data consists of categories that have no inherent order (e.g., gender, eye color), and Cronbach’s alpha is based on the idea of measuring the correlations between items or variables. Correlation implies a relationship where higher values correspond with higher or lower values, which isn’t meaningful for nominal data where categories are just labels without any ranked order.

For nominal data, other measures such as Cohen’s kappa is better suited for assessing reliability, particularly when evaluating agreement between raters or classification consistency.

Alex says

Thanks, that’s great.

How do you calculate it for two different groups (treatment and control): the items are the same, but the question is slightly different.

Jim Frost says

Hi Alex,

You can just calculate Cronbach’s alpha for each group separately using the normal method.

Drew Saunders says

Hey, thanks. FYI, somewhere in there you put in a link to your article on “factors”, but I think you intended to link to the one on “factor analysis” (https://statisticsbyjim.com/?s=factor+analysis ).

Cheers.

Jim Frost says

Hi Drew, thanks for catching that! The glossary plugin I use automatically highlights some terms like that and it chose “factor.” I went ahead and manually added a link to “factor analysis,” which is more appropriate.

Morgyn says

Very helpful explanation and example – thanks!

Mariel says

Hi thanks for the help Mr. Jim 🙂 It helps in my masteral degree program. I will cite you in my paper.

Abiodun Oluwafemi Oluwadare says

Your explanation is very useful and explicit. Thank you for the usefulness of this topic.

Tara M says

Hi Jim,

Thank you for your very prompt and helpful response. I wish I had asked you days ago!

I think it makes much more sense to input the scores for each item rather than each score point, so that’s great. I’m using SPSS version 29 so I should be able to convert to standard scores quite easily.

Thanks again for your advice, Jim.

Jim Frost says

You’re very welcome, Tara! So glad I could help!

Best of luck with your analysis!

Tara M says

Hi Jim,

Thanks for this helpful explanation, it’s very clear and user-friendly.

I wonder if you may be able to help me with my problem. I want to use Cronbach’s alpha to evaluate the internal consistency of a brief cognitive screening test, but I can’t seem to find any guidance on doing this with continuous data (it’s always ordinal!). Responses to the test questions are not measured using a Likert scale, but are awarded points (e.g., some test items are awarded a maximum of 2 points, whereas others are awarded a maximum of 5 points). Could you advise (a) the best way of setting up the data (so far, my best guess has been to separate out each item for which a respondent can achieve a single point) and (b) if there are any differences to running the analysis, compared with how you’ve described it above for ordinal data?

Any help would be very much appreciated.

Jim Frost says

Hi Tara,

Cronbach’s alpha can definitely be applied to continuous data where test items have different point scales!

Here are some tips for setting up your data and running the analysis:

Data Setup: For continuous data like yours, you can directly input the scores for each item as they are. There’s no need to break down each item into single points. For instance, if a test item is scored out of 5, you can enter the actual score the respondent achieved (say, 3 out of 5). The key is to have each item’s score as a separate variable in your dataset.Handling Different Point Scales: When your test items have different maximum points, it’s important to consider how this might affect the alpha calculation. One approach is to standardize the scores (convert them to z-scores) before computing Cronbach’s alpha. This can help account for the different scales and provide a more accurate measure of internal consistency. I generally recommend this practice when the responses have different scales. Some statistical software have an option for doing this without requiring extra calculations on your part.Running the Analysis: The process of calculating Cronbach’s alpha with continuous data is similar to ordinal data. Most statistical software packages have functions or procedures for computing itin the same way as for ordinal data.I hope that helps!

Johanna Hume says

Thank you! I need to teach this topic in a class presentation; really appreciate the straightforward and detailed explanation.

Jim Frost says

You’re very welcome, Johanna. So glad to hear it was helpful!

Chelsea Torres says

hello, jim! i would like to ask if you know a reference or a study where a 0.97 or 0.98 cronbach’s alpha is deemed acceptable? our research instrument is adopted from a certain university’s online teachers evaluation and has been used by a lot of student for a long time already. however, for our pilot testing the value we have gotten are around 0.97 or 0.98. our mentor suggested that we can use lock and fornier as our reference but i can’t seem to find their statistics book or any study that uses it. thank you!

Jim Frost says

Hi Chelsea,

Unfortunately, I’m also unable to find a Lock and Fornier reference. Any chance those names are misspelled?

That is a very high Cronbach’s alpha. Generally speaking, you don’t want to go over 0.95 because you might be asking redundant questions or measuring an overly narrow aspect of the construct. There might also be some sort of response bias generating the very high value, such as social desirability bias.

In short, an overly high Cronbach’s alpha might indicate that the instrument might not have enough variability to distinguish between different levels or types of the trait being measured.

I don’t know if any of those issues apply to your instrument but excessively high values warrant a closer examination of the test items and their relationship to the overall construct.

nada says

hello ,, Is there any explanation as to who stated the Cronbach Alpha value was 0.7?

Jim Frost says

Hi, I don’t know for sure where this value started. 0.7 is really a minimum acceptable value. But it goes back at least as far as this source.

Nunnally J, Bernstein L.

Psychometric theory. New York: McGraw-Hill Higher, INC; 1994.This source applies to psychological constructs. Acceptable values can vary according to context.

inigo says

Could you please provide me a research paper where I could get the Cronbach alpha values and its interpretation ?

Why blogs are not accepted as reference ?

Monica says

Hello. Its a nice article and gives good idea of the topic. I wanted to know how this test can be applied to index scores consisting of number of components using SPSS.

Thank you

Youssef says

Hi, thank you for this great post. My question is how to use chronbach for a syrvey that has several sections each section deals with a different concept[construct? thank you

Jim Frost says

Hi Youssef,

When a survey measures multiple concepts/constructs, you’ll need to perform a separate analysis for each one because Cronbach’s Alpha assess consistency within a single construct. If you look at Cronbach’s alpha across different constructs, you’ll see low consistency. That’s expected in that scenario because you’re looking at multiple construct simultaneously, but it doesn’t help you evaluate how reliably a set of questions measure one construct.

So, divide your items up by the construct they measure. Then evaluate Cronbach’s alpha for each set of items. That way if all those items do measure the same thing, you’ll see high internal reliability.

I hope that helps!

Narciso Barreda says

SPSS is a very friendly package. IBM provides a trial version.

Shannon Swan says

I have had SPSS for many years. However I bought it back when the price was reasonable and academic rates were good. Once IBM bought it, prices skyrocketed and I don’t believe perpetual licenses are still in existence. Academic subscriptions are ok but you have to renew every year. There are other more affordable applications that can calculate alpha and many other psychometrics. R is of course free, but there is a learning curve. Medcalc is wonderful and a perpetual license (pay only once) is $550, which will pay for itself in a few years and is probably the best price. Medcalc doesn’t do factor analysis. They have a reasonable subscription too. Stata is also nice and the coding is not difficult. They still have perpetual licenses but you have to ask for the pricing. There are of course others out there, but it is hard to find perpetual licenses anymore.

Rich says

What statistical software would you recommend to calculate Cronback’s alpha as well as give suggested omitted variables?

John says

I understand Cronbach’s alpha is used to assess the reliability or internal consistency of a set of scale or test items. I am new to this concept and must I test it before I collect my data if so could you advise the ‘ABC’s how to do this test. Thks

Jim Frost says

Hi John,

Cronbach’s alpha is not something you can test before collecting data. Instead, you administer a survey and then use statistical software to calculate it. Researchers will frequently administer a smaller pilot survey before the full survey to test various aspects of the survey, including things like internal consistency. You might want to try that approach before launching the full-scale survey.

In this post, I show an example analysis that includes an interpretation and a possible method for improving surveys.

kafia says

thanks, Please tell me what is different between Cronbach’s alpha and a pilot study?

Harini S says

Got it.. much clear now. many thanks.

Harini S says

Hello Jim,,

That’s a nice section on cronbrach’s Alpha.

I’m just starting to understand statistics in research..your posts help me a lot. Thanks.

I wanted to know – is cronbach’s Alpha something like ‘cohen’s effect size ‘ calculations?

Are they related and say the same thing?

Jim Frost says

Hi Harini,

I’m thrilled to hear that my posts have been helpful!

Cronbach’s alpha and Cohen’s d are very different. The only similarity they share is that they are both unitless measures. But what they measure is entirely different.

Cronbach’s alpha measures the internal consistency of multiple survey items.

Cohen’s d is a standardized effect size that relates the mean difference between two groups to their pooled standard deviation. Click the link to learn more about it!

No reply says

Great post. I think it might have nicer to start with the example and then get into the explanation. It would be the “columbo” method of writing a blog post.

Odunayo Oluwajuwonlo Matthew says

Thanks for the insight, please can you share how to calculate the mean covariance between items and the mean item variance.

dhanya says

is this test is for multiple questions of single domain or for full scale ?

Jim Frost says

Hi, Cronbach’s alpha assesses the internal reliability for a single domain (i.e., a single underlying concept). If an entire test contains multiple domains, you’ll need to assess Cronbach’s alpha for each domain separately.

A.wasay says

In above example how did you find total mean value? Could you please share the step by step calculation for alpha value. Thank you.

Prof Y says

Thank you. I haven’t used Chronbach’s alpha in years. My understanding was quite rusty. This quickly brought me back up to speed

RATNAVELL says

This article is very helpful for my quantitative assignment. Can I know when this article is written for my citation? Tq author.

Jim Frost says

Hi!

When citing online resources, you typically use an “Accessed” date rather than a publication date because online content can change over time. For more information, read Purdue University’s Citing Electronic Resources.