Cronbach’s alpha in R (reliability analysis)

How to compute and interpret Cronbach’s alpha in R with the psych package — measuring the internal consistency reliability of a questionnaire scale, and what the item statistics tell you.

If your questionnaire has several items meant to measure one thing (say, six items for “job satisfaction”), Cronbach’s alpha tells you how consistently they hang together. It’s the standard reliability statistic in psychology, education and health research. Here’s how to compute and read it in R.

The data

We’ll simulate 200 respondents answering six items that share a common underlying trait:

set.seed(12)
n <- 200
trait <- rnorm(n)
items <- as.data.frame(sapply(1:6, function(i) round(3 + 1.1 * trait + rnorm(n))))
names(items) <- paste0("Q", 1:6)
head(items, 3)

  Q1 Q2 Q3 Q4 Q5 Q6
1 -2  1  0  1 -1  1
2  5  3  6  5  5  4
3  3  1  2  2  4  2

Compute alpha with psych

library(psych)
a <- alpha(items)
a$total$raw_alpha

[1] 0.8630898

Rough guidelines for internal consistency:

• α ≥ 0.9 excellent · 0.8–0.9 good · 0.7–0.8 acceptable · < 0.7 questionable.

(Very high alpha, above ~0.95, can actually signal redundant items — it’s not “the higher the better” without limit.)

The most useful output: item diagnostics

alpha() also reports what happens to reliability if each item is dropped — the quickest way to spot a bad item:

round(a$alpha.drop[, "raw_alpha", drop = FALSE], 3)

   raw_alpha
Q1     0.835
Q2     0.840
Q3     0.837
Q4     0.842
Q5     0.840
Q6     0.846

If raw_alpha rises when an item is removed, that item is dragging the scale down — often because it’s reverse-worded and wasn’t recoded, or it simply measures something else.

Cautions

• Reverse-scored items must be recoded before running alpha, or reliability looks artificially low. psych will warn you and can key them automatically.
• Alpha assumes the items are unidimensional (measure one construct). If your scale has sub-scales, compute alpha per sub-scale, and consider McDonald’s omega (psych::omega) or a factor analysis first.

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Building or validating a scale? Reliability is just the start — we handle the full psychometric analysis.