How To Calculate Cronbach’s Alpha in SPSS

Cronbach’s Alpha is a reliability test developed by Cronbach (1951) and used to measure the internal consistency of a set of dichotomous or scale questions in a survey. In other words, Cronbach’s Alpha coefficient tells us how well the scale items vary as a group.

Cronbach’s Alpha is most likely the first analysis you will conduct to test if the scale items in your questionnaire are intercorrelated. The Cronbach’s Alpha coefficient takes values between 0 to 1 where values above 0.70 are accepted. There are, however, some exceptions, which we will discuss later in this article.

There are quite a few ways to conduct a Cronbach Alpha reliability test. However, in this statistics lesson, we will focus on how to calculate Cronbach’s Alpha coefficient in SPSS as well as how to interpret the reliability Alpha results.

You will also be able to download a sample SPSS data file and practice along.

Ready? Let’s learn something cool today!

What is Cronbach’s Alpha used for?

Cronbach Alpha is probably one of the most used reliability tests used for measuring the internal consistency between scaled or dichotomous questions (e.g., questions with two possible answers) in a questionnaire and is widely used in organizational and social sciences. 

The Cronbach’s Alpha formula is the following: 

a=\frac{N \cdot \bar{c}}{\bar{v}+(N-1) \cdot \bar{c}}

Where:

α  = Cronbach’s Alpha

N = the number of items in a group

c̅ = the average covariance between paired items:

v̅ = the average variance

If you want to dig deeper into the computations behind the Cronbach’s Alpha formula, I recommend you read a great study on Cronbach’s alpha reliability: Interval estimation, hypothesis testing, and sample size planning by Bonett and Wright (2015).

You may have noticed that we mentioned the term “item” a few times before. When we say “item” we are actually referring to a question that we intend to measure in a questionnaire. Here is an example of a multi-question Likert scale item:

In the above example, the answer is measured using a five-degree (1 to 5) Likert scale where 1 = strongly disagree; 2 = disagree; 3 = neutral; 4 = agree, and 5 = strongly agree.

In a survey questionnaire, you may have multiple items like this that describe a scale variable. In statistical research is important to prove that all the items within a scale question are intercorrelated with each other respectively the items are related and their values vary together.

So what is a good reliability test Alpha value in our analysis? Cronbach’s Alpha coefficient takes values between 0 and 1. In general, an Alpha coefficient above 0.70 will pass the reliability test with values closer to 1 being preferable. Here is a summary of Cronbach’s Alpha coefficient value ranges and how to interpret them in reliability analysis.

It is very important to remember that when we calculate Cronbach’s Alpha in SPSS we don’t include all the scale questions in analysis in one go. We have to calculate the reliability coefficient for each scale.

If this sounds confusing, don’t worry. Practice the example below with me and you will understand the whole concept once finished.

Example for Reliability Test in SPSS

Now that we learned what is Cronbach’s Alpha used for, let’s look at an example to understand how Cronbach’s analysis is conducted in SPSS.

Let’s assume we design a questionnaire that measures the online purchase intention and consists of two-scale variables consumer behavior and purchase intention. Each variable consists of four items measured with a five-degree Likert scale. 

Our goal is to find Cronbach’s Alpha coefficient for consumer behavior and purchase intention. 

If you want to follow along, download the SPSS dataset used in this example below.

Please note that this SPSS data file contains dummy values and should be used for educational purposes only. 

Unzip the file you download above and double-click on the .sav file to import it in SPSS on your computer and let’s jump into the analysis. 

How To Calculate Cronbach’s Alpha Coefficient in SPSS

The imported SPSS sample file downloaded above contains data set for 30 samples and looks like this:

You can see that we have two scales, respectively consumer behavior (CB) containing four items (CB1 to CB4) and purchase intention (PI) with four items as well (PI1 to PI4).

We can also observe that all items in our data set are measured with a five-degree Likert scale where 1 = strongly disagree, 2 = disagree, 3 = neutral, 4 = agree, and 5 = strongly agree).

Your data set may be larger and contain more than two scale variables. However, the process of conducting a reliability analysis in SPSS is the same.

1. On SPSS top menu, navigate to Analyze → Scale → Reliability Analysis. 

2. In the SPSS Reliability Analysis window, select all the items that measure a variable (e.g., consumer behavior) from the left block and use the arrow button to move them to the right.

3. Make sure the Model selected is Alpha.

4. Type a name in the Scale label block. This step is not mandatory but can help with the interpretation of the reliability analysis results in SPSS.

5. Click the Statistics button. We need need to select some options for the reliability analysis first.

4. From the Statistics tabs, select the Items, Scale, and Scale of item deleted options under the Descriptive for section. On the Summarize section select Means and Correlations. Finally, under Inter-item select Correlations. Click Continue then OK to proceed with the analysis.

Cronbach’s Alpha Results Interpretation

Alright. You should see the Alpha reliability output in a new SPSS window by now. Next, let’s have a look at Cronbach’s Alpha results interpretation.

1. The Case Processing Summary is the first table in the reliability output that shows a summary of the cases processed in this analysis. We can observe that 30 cases were processed (N = 30 samples). We can also see that no cases were excluded (100% of the sample size was included in the analysis).

If your summary estimates are lower than 100% samples (N Valid ≠ N Total) you should check your data set for mistakes, white spaces, or (most likely) missing values. 

The Reliability Statistics table shows us the reliability Alpha coefficient for all items included in the analysis. In our example, the Alpha value is 0.904 (> 0.7) which is interpreted as excellent. 

It is important to keep in mind that if you have fewer than 10 items on the scale it is quite difficult to get a high Alpha value. In such cases, an Alpha value > 0.5 is considered acceptable (Pallant, 2010). Values lower than < 0.5 should be a cause for concern in such cases.

2. The Item Statistics table provides information about the Mean, Standard Deviation, and the number of samples (N) for each of the items on the scale. The mean represents an average of the values in the data set and can be useful when analyzing descriptive statistics or frequencies in our study.

The Inter-Item Correlation Matrix shows us how items in the scale correlate with each other. The maxim value here is 1.000 when an item is correlated with itself in a matrix. A high correlation value shows a strong correlation between two items on a scale. 

In our example, we can see that CB2 and CB3 items are highly correlated (0.937) indicating a strong relationship. In contrast, the correlation between CB4 and CB2 (0.543) is not that strong indicating a weaker relationship between these items.

3. The Summary Item Statistics table shows us the mean for all items in the scale and how these items are intercorrelated. It also outputs the range of the means calculated as the difference between a maxim and minimum values. 

If you have a low inter-item correlation coefficient for the mean (< 0.5) due to low numbers of items on the scale is important to report it in your analysis (Pallant, 2010). In our case, the inter-item correlation mean is 0.771 (> 0.7) therefore acceptable. 

4. The Item Total Statistics table presents the scale mean and variance if specific items are deleted, the total correlation for corrected items, the square multiple correlations, and the value of Cronbach’s Alpha if an item is deleted. 

Let’s look first at the Corrected item – Total Correlation column. The values here represent the correlation for each item with the rest of the items combined. For instance, item CB1 (0.802) correlation with items CB2, CB3, CB4; item CB2 correlation with item CB1, CB3, and CB4; and so on. You should aim at values > 0.40 here.

Next, let’s analyze the Cronbach’s Alpha if Item Deleted column. This is important when dealing with poor Alpha scores and we want to identify which item is the cause for it. This collum tells us if an item is deleted what would be the resulting Alpha value. 

5. Finally, the Scale Statistics table shows the mean, variance, and standard deviation calculated for the whole scale.

Now go ahead and exercise what you’ve learned by running a reliability test in SPSS for the second scale variable in our example: purchase intention. Did it pass the reliability Alpha test?

Wrapping Up

Reliability analysis is extremely important in statistical research and is an assumption for most statistics analyses such as linear regression analysis. As long as your Alpha value is above 0.70, you are good to go. If not, check the Item-Total Statistics in the above section to identify the culprit. 

I hope by now, you are already familiar with what is Cronbachs’ Alpha used for, how to calculate Cronbach’s Alpha in SPSS as well as how to interpret Cronbach’s Alpha results in your research paper. Next, let’s have a look at how to calculate Cronbach’s Alpha in Excel.

If you found this lesson useful, please share it with your colleagues and friends. I am sure they will appreciate it. 

References

Bonett, D. G., & Wright, T. A. (2015). Cronbach’s Alpha Reliability Interval Estimation, Hypothesis Testing, and Sample Size Planning.

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334 (28,307 citations in Google Scholar as of 4/1/2016).

Pallant, Julie. SPSS Survival Manual: A Step by Step Guide to Data Analysis Using SPSS. Maidenhead: Open University Press/McGraw-Hill, 2010.