How to use the cronbach's alpha calculator
- Paste your scores with one respondent per line and one column per item, separated by commas, spaces or tabs. Every line needs the same number of scores.
- If some items are worded in the opposite direction, type their numbers under Reverse-scored items and open More options to set the lowest and highest possible score, so those items can be flipped first.
- Read Cronbach's alpha first, then the item table. An item whose "Alpha if removed" is higher than the overall alpha is pulling the scale down.
- Use Copy or CSV to keep the item table with your notes.
Formula
alpha = k / (k - 1) x (1 - sum of item variances / variance of total scores)
the same value from covariances: alpha = k x c / (v + (k - 1) x c)
standardized alpha = k x r / (1 + (k - 1) x r)
k is the number of items, v the average item variance, c the average covariance between two different items and r the average correlation between items. Every variance uses n - 1. The two raw formulas always give the same number, which makes a good check.
Eight respondents, four items
The default data has 8 respondents who answered 4 items scored 1 to 5. The item variances add up to 5.0536 and the total scores have a variance of 16.8393, so alpha = 4 / 3 x (1 - 5.0536 / 16.8393) = 0.933. From covariances, the average item variance is 1.2634 and the average covariance between items is 0.9821, so 4 x 0.9821 / (1.2634 + 3 x 0.9821) = 0.933 again.
The average correlation between items is 0.775, which gives a standardized alpha of 0.932. Removing item 1 lowers alpha to 0.875, because it is the item most closely tied to the rest of the scale (item-total correlation 0.952). Flipping items 2 and 4 when they were not reverse worded pushes alpha down to -3.004, a sign that the direction of some items is wrong.
What alpha tells you
Alpha is a measure of internal consistency: if the items of a scale all measure the same thing, people who score high on one item tend to score high on the others, and alpha is close to 1. If the items hardly relate to each other, alpha is close to 0, and if they pull in opposite directions it can go below 0.
Alpha grows when you add items, even if the new items add little, so compare scales of similar length. It also depends on the group you tested. The same questionnaire can give a different alpha in a different sample. A very high alpha can mean that items repeat each other.
What alpha does not tell you
A high alpha does not show that a scale measures one idea. A scale made of two strongly related ideas can still give a high value. It also says nothing about whether the scale measures the right thing. For test questions scored right or wrong, the same formula is known as KR-20, which the Test Item Analysis Calculator reports along with item difficulty.
More statistics tools
To fit a curve to data, compare two groups or estimate a spread, try the Curve Fit Calculator, Odds Ratio and Relative Risk Calculator and Grouped Data Statistics Calculator.
Assumptions and limits
- Each item is scored on a numeric scale, and a higher score means more of the same thing for every item (after reverse scoring).
- The respondents are separate people who answered independently.
- There are no blanks: every respondent answered every item.
- Alpha is a point estimate for this sample. No confidence interval is shown.
- The example scores are only an illustration. Replace them with your own before using the result.
Frequently asked questions
What is a good value for Cronbach's alpha?
There is no universal cutoff. Some guides quote 0.7 as a minimum for research scales and a higher value for decisions about individuals, but the right target depends on your field and on how the scale will be used.
Why is my alpha negative?
A negative alpha means the items are, on average, negatively related. The usual cause is an item worded in the opposite direction that has not been reverse scored. Check the item-total correlations for a negative value.
Why does alpha go up when I add more items?
The formula includes the number of items, and more items usually add more shared variance than error. A long scale can therefore score high even when each item relates only weakly to the others.
How many respondents do I need?
The estimate is rough with few respondents. This page gives only the point estimate, so treat a result from a small group as a first look and collect more responses before drawing conclusions.