Cronbach's alpha calculator online

Cronbach's alpha is the most widely used reliability index for questionnaires; more precisely, it measures internal consistency. Say you have written five items to measure job satisfaction. If the items really measure one thing, someone who scores high on one usually scores high on the others too. Alpha sums up that agreement in a single number, usually between zero and one. Lee Cronbach introduced the coefficient in 1951.

Alpha is a property of your data, not a fixed property of the questionnaire. The same standard questionnaire may give a different alpha in another population or in another translation. So even when you use a validated, published instrument, recalculate alpha on your own sample and report it.

• k: number of items.
• σᵢ²: variance of each item; Σσᵢ² is the sum of all item variances.
• σₜ²: variance of the total score, i.e. the variance of each respondent's sum across all items.
• r̄: mean pairwise correlation between items.

The logic is simple. When items move together, the variance of the total score is much larger than the sum of the individual item variances, because the positive covariances between items are added to it. The fraction in the brackets then shrinks and alpha rises. When items are unrelated, the two quantities are almost equal and alpha is close to zero.

Standardized alpha is alpha computed as if every item had been put on the same scale before summing. When all items use the same scale, e.g. all are five-point items, the two values are close and raw alpha is reported. When items use different scales, standardized alpha is more meaningful.

Alpha is sensitive to the number of items. With more items, alpha rises even when the correlations between them are only moderate: with a mean inter-item correlation of 0.3, three items give an alpha of 0.56, ten items 0.81 and twenty items 0.9. So an alpha of 0.65 on a three-item scale may reflect better consistency than 0.8 on a twenty-item scale. For short scales, also look at the mean inter-item correlation, which the tool above shows; Clark and Watson (1995) consider 0.15 to 0.5 desirable.

If your questionnaire has several dimensions, e.g. satisfaction with pay, with the supervisor and with co-workers, calculate and report alpha separately for the items of each dimension. Alpha for a whole multidimensional questionnaire usually comes out high simply because there are many items, and says little about each dimension. In the tool above, untick items to see the alpha of each dimension on its own.

1. 1

   Prepare the data

   Each respondent should be one row and each item one variable. Reverse negatively worded items before anything else: Transform, then Recode into Different Variables; on a 1–5 scale define 1 → 5, 2 → 4, 4 → 2 and 5 → 1, and leave 3 as 3.

2. 2

   Open the reliability dialog

   From the Analyze menu choose Scale, then Reliability Analysis.

3. 3

   Select the items

   Move the items of one dimension into the Items box and make sure Model is set to Alpha.

4. 4

   Turn on the statistics

   In the Statistics dialog tick Item, Scale and Scale if item deleted. To see the mean inter-item correlation, also tick Correlations under Summaries. Then Continue and OK.

5. 5

   Read the output

   The Reliability Statistics table shows raw alpha and standardized alpha (Based on Standardized Items). In the Item-Total Statistics table, the Corrected Item-Total Correlation column is each item's correlation with the rest, and the Cronbach's Alpha if Item Deleted column shows what alpha would be without that item.

6. 6

   Cross-check with this tool

   Paste the same data here; the numbers should match. Like this tool, SPSS drops incomplete rows and reports how many in the Case Processing Summary table.

• A reversed item was not recoded. A statement such as "I am tired of my job" in a job-satisfaction questionnaire must be reversed before calculating. The tell-tale sign is a negative correlation with the other items. In the tool's sample data, item Q4 has a negative correlation of 0.58, and alpha is 0.44 before reversing it and 0.81 after.
• Blank cells were filled with numbers. If non-responses were coded as 0 or 99, those numbers are treated as real answers and distort alpha. Delete them before pasting so the cells stay empty.
• One or two items do not move with the rest. Look at the alpha if item deleted column: an item whose removal clearly raises alpha and whose corrected item-total correlation is below 0.3 is a candidate for revision. In the sample data, removing Q6 raises alpha from 0.81 to 0.85.
• The questionnaire is multidimensional. Don't confuse overall alpha with the alpha of each dimension; calculate each dimension's items separately.
• The sample is small or homogeneous. With fifteen respondents, or when almost everyone gives the same answer, variance is low and alpha becomes unstable. Thesis pilot studies usually use about 30 people.
• Items are vague or double-barrelled. A question that asks about two things at once, such as "pay and benefits are adequate", gets scattered answers. For tips on writing good items and choosing a scale, see the guide to designing a standard questionnaire and Likert scale: 5 or 7 points.

The methods chapter usually has a paragraph on the instrument's reliability. Always state three things: how many people alpha was calculated on (pilot or full sample), alpha for each dimension and for the whole questionnaire, and whether any items were reversed or removed. Example:

If you run your questionnaire online, the responses are a clean table from the start that goes straight into this tool or SPSS. Porsino has Likert scales and matrix questions, and gives you an Excel export or an SPSS file (.sav) with codes and option labels. Just copy the item columns and paste them here. For the questionnaire itself, see Build an online questionnaire and to decide on the sample size see the Cochran's formula calculator for details.