Cronbach’s Alpha

Suppose we run a service satisfaction survey of hotel guests. The researcher wrote several items to assess staff courtesy, responses to requests, accuracy of service, and so on. But are all the items in the survey consistently measuring service satisfaction?

For example, if guests who rated staff courtesy highly also tend to rate service responsiveness and accuracy highly, the items are probably related to one another. On the other hand, if some items show a completely different response pattern from the rest, we need to consider whether it is appropriate to add all the items into a single score.

The standard reliability measure used in this situation is Cronbach’s alpha (α).

Cronbach’s alpha is a coefficient that assesses the internal consistency of a scale made up of several items. Based on how strongly the items are related to one another, it lets us look at how consistent the scale score is.

However, a high alpha does not let us conclude that a survey is necessarily measuring the right concept, or that all the items measure a single factor.

In this lesson we cover the basic principle of Cronbach’s alpha and how to calculate it, a real survey example, item-level diagnostics, deciding whether to drop items, the difference between reliability and validity, how it compares with McDonald’s omega, and how to report the results.

For example, suppose we use five items to measure customers’ service satisfaction. Each item is answered on a scale from 1 to 5.

The researcher can sum or average the five item scores to create a service satisfaction score for each customer. Before doing that, though, it is a good idea to check whether the items are measuring related content. Cronbach’s alpha is calculated for this purpose from the covariances between items and the variance of the total scale score.

In general, the closer alpha is to 1, the higher the internal consistency among the items. But a high coefficient on its own does not guarantee unidimensionality or validity, and under certain conditions alpha can even be negative. So Cronbach’s alpha should be used as one of several pieces of evidence for judging the quality of a scale.

For example, if the items written to measure hotel service satisfaction show similar response patterns, internal consistency may come out high. But if the items are in fact just repeatedly asking how much guests like the staff rather than about service satisfaction, they may not fully capture the concept you want to measure.

Cronbach’s alpha is the measure among these that relates to internal consistency. It is different from test-retest reliability, which directly assesses how stable the results are when the same people take the survey several times.

So to evaluate the quality of survey items, you need to look not only at reliability but also at the content of the items, the factor structure, relationships with external variables, and so on.

The researcher wrote six items to measure the experience of staff interactions and service delivery. All items were answered on a Likert scale from 1, ‘strongly disagree’, to 5, ‘strongly agree’.

Service satisfaction survey items

The first five items are about the experience of staff interactions and service delivery. S6, however, is a rating of the room decor, so it may be measuring a different concept from the other items. The researcher wants to check whether the six items can be combined into a single service satisfaction scale.

The standard formula is:

Here k is the number of items, σ_i² is the variance of each item, and σ_T² is the variance of the scale score obtained by summing all the items. For example, suppose we have a scale with three items. If each item has a variance of 1 and the total summed score has a variance of 7, the calculation is as follows.

So Cronbach’s alpha is about 0.857. What matters in this calculation is how much the items covary with one another. Larger covariances between items affect the variance of the total summed score, and so change alpha.

However, alpha is also affected by the number of items. Adding many similar items can raise alpha even if they don’t add much new information.

Here are rough guidelines often used in practice and research.

These categories are not an absolute pass/fail standard. In exploratory research, relatively low values can still be informative, but a measurement instrument used for important decisions about individuals may need stronger evidence of reliability.

Conversely, if alpha is very high, such as 0.95 or above, you should also check whether the items are just repeating similar content. So alpha should be interpreted together with the purpose of the scale, the number of items, the characteristics of the respondents, the concept being measured, and so on.

Overall scale reliability

Cronbach’s alpha for all items was 0.78. By common rules of thumb, this can be read as acceptable internal consistency.

But it may not be appropriate to stop the analysis here. Even if one of the six items is only weakly related to the others, the overall alpha alone makes this hard to detect. So it is good to look at the item-level diagnostics as well.

In particular, the corrected item-total correlation and Cronbach’s alpha if item deleted are useful for finding items that need a closer look.

This measure shows how consistently each item moves with the rest of the scale. For example, S1’s corrected item-total correlation is the correlation between the S1 score and the summed score of S2–S6.

Item diagnostics

S1–S5 showed relatively high correlations with the other items. S6’s corrected item-total correlation, on the other hand, was relatively low at 0.12. This suggests that S6 may be measuring something different from the other items, or may have a different response pattern.

In practice, values such as 0.30 are sometimes used as a reference point, but this is not an absolute cut-off for dropping items either. You need to look at the item content, the theoretical structure of the scale, the response distributions, and so on.

It shows how the internal consistency of the scale changes when a particular item is excluded.

Alpha if item deleted

The overall alpha was 0.78, but excluding S6 raises it to 0.86.

This result suggests that S6 may not be consistent enough with the other items. In particular, S6 measures satisfaction with the room decor, so it may differ conceptually from the other items, which focus on the experience of staff interactions and service delivery.

So you could consider splitting S6 into a separate measurement area or dropping it from the scale.

A higher alpha does not by itself mean the scale has become more valid.

The alpha of the scale without S6 was 0.86. This means the internal consistency among the remaining five items is higher than it was for the original six items. But the important judgment here is not just that alpha rose from 0.78 to 0.86.

If the concept the researcher wants to measure is the hotel’s overall guest experience, room decor may be an important component. If, on the other hand, the goal is to measure satisfaction with staff interactions and the service delivery process, dropping the room decor item may make more sense conceptually.

In other words, whether to remove an item should be decided by considering both the statistics and the concept you want to measure.

For example, suppose a hotel guest satisfaction survey has three items on staff interactions and three items on room cleanliness. If the two areas are related, the overall alpha can come out high. In reality, though, there may be two distinct factors: satisfaction with staff interactions and satisfaction with room cleanliness.

To examine this kind of structure, you can consider exploratory factor analysis (EFA) or confirmatory factor analysis (CFA).

So in scale development or validation studies, it is generally more appropriate to examine the factor structure first and then calculate reliability separately for the items belonging to each factor. Also, because alpha is tied to reliability only under certain assumptions, confirming the factor structure does not by itself mean all of alpha’s assumptions are met.

Both assess the reliability of scale scores, but they rely on different assumptions and information. Cronbach’s alpha uses the covariances between items and the variance of the total scale score. Omega, by contrast, is usually calculated from the factor loadings and error variances estimated in a factor model.

For example, even when items measure the same factor, each item may be related to that factor to a different degree; that is, their factor loadings may differ. In such cases omega can give more appropriate reliability information than alpha. But omega also assumes a correct factor model, so it cannot be considered automatically better in every situation.

So in research, you can examine the measurement model and, where needed, report alpha and omega together.

It is common to say that 0.70 or above is adequate, but the level needed can vary with the research purpose, the intended use of the instrument, and the number of items. You should not automatically discard a scale just because alpha is below some threshold, or consider it fully validated just because alpha is high.

Check for reverse-worded items.

If reverse-worded items, written in the opposite direction to the others, are not properly reverse-coded, correlations between items can drop or even turn negative. So before calculating reliability, make sure all items are scored in the same direction.

Consider the effect of the number of items.

Alpha can rise as the number of items increases. So adding many items that repeat similar content to push up the coefficient is not necessarily the way to build a good scale.

Check how missing values were handled.

If some respondents skipped certain items, the results can differ depending on whether only complete cases were used or another missing-data method was applied. It is good to report clearly the number of respondents actually used in the analysis.

Consider the items’ response scale.

For data made up of ordered categories, such as Likert items, you can consider ordinal alpha based on polychoric correlations, in addition to the usual alpha based on Pearson covariances. Ordinal alpha, however, also depends on the latent response model and distributional assumptions used.

Don’t use alpha alone as evidence of validity.

Even if the items are highly correlated with one another, there is no guarantee they properly measure the intended concept. Scale validation requires examining the content, the factor structure, and relationships with related variables together.

If you removed or revised items, it is good to explain the reasoning behind that decision and the final composition of the scale.

Summary of reliability analysis results

In real research you should state clearly how the scale was constructed and why items were removed. Where needed, it is also good to report McDonald’s omega or factor analysis results to give an overall assessment of the instrument’s reliability and structural validity.

It is useful in surveys when concepts that are hard to observe directly, such as satisfaction, attitudes or perceptions, are measured with several items.

But a high alpha alone does not let you conclude that all the items measure a single factor or accurately capture the concept you want to measure. And because it is affected by the number of items and the correlations between them, the quality of a scale should not be decided by the number alone.

So in reliability analysis, it is good to look not only at the overall alpha but also at the corrected item-total correlations, alpha if item deleted, the item content and the factor structure. If needed, you can also look at other reliability measures, such as McDonald’s omega.