Cronbach’s alpha

What alpha actually measures

Take a job satisfaction scale with eight items. A satisfied person should mostly agree with all eight, and a dissatisfied person should mostly disagree with all eight. Alpha looks at how far this happens across your whole sample. If the items go up and down together, alpha will be high. If each item goes in its own direction, alpha comes low.

Cronbach gave the formula in his 1951 paper. It is written like this.

α = (k / (k − 1)) × (1 − Σ item variances / variance of the total score)

In this, k means the number of items. See one small worked example. A scale has four items, and their variances are 1.0, 1.2, 0.9 and 1.1. Added together that is 4.2. The variance of the total score is 11.0. So α = (4 / 3) × (1 − 4.2 / 11.0) = 1.333 × 0.618 = .82. Nobody does this by hand for a thesis, but the example shows two points. First, when the items agree with each other, the total score varies much more than the single items do, and alpha goes up. The second point is that alpha keeps rising as you add more items, so a long scale with loosely connected items can still show a high value.

If SPSS is not with you right now, you can paste the item scores in our Cronbach’s alpha calculator and it will give the same figure for a quick check.

Running it in SPSS

Before anything, recode the reverse-worded items. How to do that is given further down, and once it is done you can go through the steps below in SPSS.

1. Open Analyze → Scale → Reliability Analysis.
2. Put the items of one scale only into the Items box. Do one construct at a time.
3. Keep the Model as Alpha.
4. Click Statistics. Under “Descriptives for”, tick Item, Scale, and Scale if item deleted. Under Inter-Item, tick Correlations. Then click Continue and OK.

Do the same for each construct. With five constructs, you run it five times and report five alpha values. Putting all 45 items in one go gives a very big alpha with no meaning, because alpha goes up with the item count. Examiners know this well and they will ask about it.

For those who use syntax, the same run looks like this. RELIABILITY /VARIABLES=JS1 JS2 JS3 JS4 JS5 JS6 JS7 JS8 /SCALE('Job satisfaction') ALL /MODEL=ALPHA /STATISTICS=DESCRIPTIVE SCALE CORR /SUMMARY=TOTAL. We always tell scholars to save this syntax file along with the data, because when some data error comes up later the whole run can be repeated in few seconds.

Reading the two tables that matter

SPSS gives many tables in the output. For the decision, you need only two of them.

Reliability Statistics has three values, Cronbach’s Alpha, Cronbach’s Alpha Based on Standardized Items and N of Items. The first one is what you report. The standardised value is useful only when your items have different response formats.

Item-Total Statistics has one row for each item. Two columns are important here. Corrected Item-Total Correlation tells how much each item agrees with the remaining items of the scale. A value under about .30 for any item is a warning sign for us. If it is negative, almost always it is a reverse-coding problem. The column Cronbach’s Alpha if Item Deleted shows what alpha would be if that item is removed. Say one item’s row shows alpha going from .64 to .78. Then that item is the one creating the trouble.

The table below gives the common way alpha values are read. These bands are only a convention, and fields differ. In management, some examiners will accept .60 for a new scale in exploratory work. Some others want .70 and nothing less. Ask your guide where your department fixes the line.

Why alpha comes out low, and what to check

Many scholars get tension when alpha comes low and start deleting items the same day, which we don’t recommend. Check the causes in the order given here, as the first two are the most common by far.

Reverse-worded items not recoded. In a commitment scale, somebody who agrees with “I often think about leaving” is less committed, so that item runs opposite to the rest. If you did not recode it, its corrected item-total correlation will be negative and alpha will drop, sometimes even below zero.

Data entry errors. Someone types 55 in place of 5. Or 9 is used as a missing-value code, but it is not declared as missing in SPSS. Both spoil the variances. Run Analyze → Descriptive Statistics → Frequencies for each item and look for any value outside scale range.

Too few items. A scale of three decent items can stay at .62 just because k is small. This is a known property of alpha, and you can mention it in the text.

More than one construct inside the scale. Suppose your “service quality” items ask about staff behaviour and also about the building. Then the items fall into two groups and alpha comes down. When you run an exploratory factor analysis, the two groups mostly load on separate factors and you can see it.

The wrong items in the scale. Compare the items in your Reliability Analysis box with the questionnaire once. It happens more times than people expect.

Recoding reverse-worded items

In a five-point scale, reverse coding changes 1 to 5 and 2 to 4. The 3 stays as it is, 4 becomes 2 and 5 becomes 1. In SPSS the fastest method is Transform → Compute Variable. Make a new variable like JS4_R and give the expression 6 − JS4. For a seven-point scale, use 8 − the item. The general rule is (highest point + 1) minus the score.

Another way is Transform → Recode into Different Variables, where you enter the old and new values one by one. Both are fine. But please avoid Recode into Same Variables, since your original column gets replaced, and if you run it two times by mistake the item flips back to the old direction.

After recoding, use JS4_R in the reliability analysis and in the scale total also. Mention the reverse-coded item numbers in your method chapter because the examiner may ask. If the questionnaire is still being prepared, see our questionnaire design guide, where we have discussed about when reverse-worded items help and when they only confuse the respondents.

When you may drop an item

The “Alpha if Item Deleted” column can tempt you. Remove two or three items and .66 becomes .74. But every deletion changes the published scale you took from another author. Examiners do notice when the eight-item scale in your proposal has become five items by the time of the viva.

Our suggestion is to drop an item only when its corrected item-total correlation is clearly weak and alpha really improves. There should be a reason also which you can tell the examiner, for example the regional-language translation of that item did not work or respondents in the pilot misunderstood the wording. Remove one item at a time and rerun each time. In the thesis, give the original item count and the items you removed, with the reason. If you are deleting items one after another just to touch .70, stop there and talk to your guide.

What alpha doesn’t tell you

Alpha checks consistency. Whether the scale measures the correct thing is a different question, and that is validity. Think of eight items that all ask about salary. As a “job satisfaction” measure they would give a fine alpha, but most of job satisfaction is missing.

Behind alpha there is one assumption that every item carries the same weight for the construct. When this is not true, alpha usually underestimates the reliability. For this reason, studies that use structural equation modelling report composite reliability (usual floor .70) and average variance extracted, AVE (floor .50), along with alpha or instead of it. McDonald’s omega is one more option, and some journals now prefer it. Where these figures come from in the software output, we have covered in our note on AMOS vs SmartPLS.

A very high alpha is also not always good. Tavakol and Dennick (2011) suggest about .90 as the maximum. Above that, some items are probably the same question in different words, and the scale can be shorter.

How to report reliability in your thesis

As per APA 7 style, alpha is written without the leading zero, since it cannot go above 1. So write α = .84 and not α = 0.84. Two decimal places is enough.

If there is one scale, one sentence is sufficient. For example, “The eight-item job satisfaction scale showed good internal consistency in this sample (α = .84).” If there are several scales, make a small table with the construct, number of items, alpha value and source of the scale. Refer to it in one sentence. Any item you dropped should be mentioned in a small note below that table.

Report the alpha you got from your main sample. Quoting only the original author’s value is not enough, because reliability belongs to the scores of a particular sample and not to the scale permanently. Many times scholars copy the .91 from the original study without running their own, and examiners catch this gap quickly. After reliability there are more tables to write up, and our guide on reporting SPSS results takes those one by one.