How this calculation works
A multi-item score combines responses that may share variation. Cronbach’s alpha compares individual item variances with the variance of their total. This page calculates raw-score alpha and shows what happens when each item is removed. It is a consistency summary, not a direct test of one underlying trait. A high value can arise from redundant items, and it does not automatically establish validity or stability over time.
Raw alpha = k/(k−1) × [1−sum(item sample variances)/sample variance(total score)]A worked example
Three respondents with item rows (1,1,1), (2,2,2) and (3,3,3) have three identical items. Each item’s sample variance is one, and total-score sample variance is nine. The formula gives 3/2 times (1−3/9), or one. Deleting any one item still leaves two identical items with alpha one; this constructed check does not claim that real surveys should be redundant.
Good to know
Only complete respondent-by-item data and unweighted totals are supported. Clustered observations, missing-data models and ordinal latent-variable alternatives are outside this calculation. No universal acceptable cutoff, factor analysis or measurement-validity conclusion is supplied. The item-deletion table is a diagnostic aid, not an automatic instruction to remove questions to maximize a number.
Reference: R psy — Cronbach coefficient alpha (opens in a new tab) ↗
What this calculation answers
A multi-item score combines responses that may share variation. Cronbach’s alpha compares individual item variances with the variance of their total. This page calculates raw-score alpha and shows what happens when each item is removed.
It is a consistency summary, not a direct test of one underlying trait. A high value can arise from redundant items, and it does not automatically establish validity or stability over time.
The Mean median mode variance and standard deviation calculator shows the sample variance used in raw alpha. The total-score covariance structure, rather than a mere average of item variances, determines consistency.
Use the right input conventions
Each row is one respondent and each column the same item across respondents. All rows must have the same number of complete numeric cells. Missing values are rejected rather than silently imputed or dropped pairwise.
Raw item scales are retained. If reverse coding is appropriate, perform it according to the item definition before entry; the page does not infer which items should be reversed from their observed correlations.
Interpret the result
Raw alpha uses the covariance structure implied by unstandardized scores. Items with different numeric scales can therefore affect the total differently. This is not standardized alpha computed from a correlation matrix.
Negative alpha is allowed when the data produce it. That outcome is information about the score structure, not a reason to clip the coefficient to zero or hide a possible coding problem.
Work through the example
Three respondents with item rows (1,1,1), (2,2,2) and (3,3,3) have three identical items. Each item’s sample variance is one, and total-score sample variance is nine.
The formula gives 3/2 times (1−3/9), or one. Deleting any one item still leaves two identical items with alpha one; this constructed check does not claim that real surveys should be redundant.
Where the model stops
Only complete respondent-by-item data and unweighted totals are supported. Clustered observations, missing-data models and ordinal latent-variable alternatives are outside this calculation.
No universal acceptable cutoff, factor analysis or measurement-validity conclusion is supplied. The item-deletion table is a diagnostic aid, not an automatic instruction to remove questions to maximize a number.
A few questions, answered
Does high alpha prove the scale measures one construct?
No. Internal consistency alone does not establish unidimensionality or substantive validity.
What changes in the comparison?
Reverse one item numerically and inspect the effect of inconsistent coding on the total score.