Cronbach alpha

This page will show you how to use SPSS to calculate Cronbach's alpha reliability coefficient. For information on what Cronbach's alpha is used for, see the Internal Consistency section on the

measurement pages.

The data for this example are taken from Markland, Emberton & Tallon's (1997) validation study of the Subjective Exercise Experiences Scale (SEES) for use with children. This is a three factor questionnaire originally designed by McAuley and Courneya (1994) to measure exercise-induced feeling states, the three factors being psychological well-being, psychological distress and fatigue. Each subscale in the SEES has four items and respondents are asked to indicate on a 7-point scale the extent to which they are experiencing each feeling at that point in time. For more information on the SEES, see the Factorial Validity section on the measurement pages. The data can be accessed from the N: drive. Open SPSS then click on File then Open. Now browse through the Look in: box to find and click on the file called sees.sav under N:/resmeth. The dialogue box should now look like this:

Click on Open to open the file. Part of the file is shown below. The data comprise 115 childrens' scores on the twelve items of the SEES. For our example we will calculate Cronbach's alpha for the positive well-being subscale. This subscale is comprised of scores on the items pwb1, pwb2, pwb3, and pwb4. It should be fairly obvious that the psychological distress items are named pd1 to pd4 and the fatigue items fat1 to fat4, should you want to play with them as well.

To calculate alpha, click on Analyze and then Scale from the drop-down menu, and then Reliability analysis. The following dialogue box will appear:

Now select the variables for analysis from the left-hand box and transfer them using the little arrowhead to the right-hand box. In this case we want pwb1, pwb2,pwb3 and pwb4:

Now click on Statistics in order to choose options for the analysis. Click on the three check boxes under Descriptives for. As you can see, there are lots of other options, but we'll keep it simple for this example.

Now click on Continue to close this box and then click on OK to run the analysis.

The SPSS output follows in blue, with an explanation of each bit in red.

RELIABILITY ANALYSIS - SCALE (ALPHA)

RELIABILITY ANALYSIS simply lists the selected variables and gives descriptive statistics, followed by descriptives for the whole scale:

Mean Std Dev Cases

1. PWB1 4.8522 1.4464 115.02. PWB2 4.7913 1.5700 115.03. PWB3 4.6957 1.5285 115.04. PWB4 4.7913 1.5922 115.0

Statistics for Mean Variance Std DevN of

VariablesSCALE 19.1304 24.2372 4.9231 4

Item-total Statistics

Scale mean if

Item Deleted

Scale Variance

if Item Deleted

Corrected Item-Total Correlatio

n

Alpha if Item

Deleted

PWB1 14.2783 15.0272 .6348 .7677PWB2 14.3391 14.5068 .6075 .7800PWB3 14.4348 14.7742 .6065 .7800PWB4 14.3391 13.5945 .6906 .7394

Item-total Statistics gives statistics for relationships between individual items and the whole scale. The important bits for our purposes are the last two columns.Corrected item-total correlations are the correlations between scores on each item and the total scale scores. If the scale is internally consistent you would expect these correlations to be reasonably strong. In this case the correlations are all .6 or more, indicating good consistency. The final column tells us what Cronbach's alpha would be if we deleted an item and re-calculated it on the basis of the remaining three items. We'll come back to this below.

Reliability Coefficients

Reliability Coefficients gives us the Cronbach's alpha reliability coefficient for the set of four items. At .8147 it indicates good internal consistency. Now, thealpha-if-item-deleted statistics above (in the Item-total Statistics table) show that if we removed any one item, alpha for the remaining three would be worsethan alpha for all four items. Therefore it is worth retaining all four. If the alpha-if-item-deleted statistics showed that removing an item would lead to an increasein alpha, then we would consider doing that in order to improve the internal consistency of the scale. Try re-running the analysis but including the variable "fat1"and you will see what I mean.

N of Cases = 115.0 N of Items = 4

Alpha = .8147

http://www.real-statistics.com/reliability/cronbachs-alpha/

Real Statistics Using ExcelEverything you need to do real statistical analysis using Excel

Skip to content

Home Free Download Basics Distributions ANOVA Correlation Regression Appendix Blogs

Home » Reliability » Cronbach’s Alpha

Cronbach’s AlphaOne problem with the split-half method is that the

reliability estimate obtained using any random split of

the items is likely to differ from that obtained using

another.  One solution to this problem is to compute the

Spearman-Brown corrected split-half reliability

coefficient for every one of the possible split-halves and

then find the mean of those coefficients.  This mean is

known as Cronbach’s alpha.

Definition 1: Given variable x1,…,xk and x0 =   and

Cronbach’s alpha is defined to be

Property 1: Let xj = tj + ej where each ej is independent

of tj and all the ej are independent of each other. Also

let x0 =   and t0 =  . Then the reliability

of x0 ≥ α where αis Cronbach’s alpha.

Here we view the xj as the measured values, the tj as the

true values and the ej as the measurement error

values. Click here for a proof of Property 1.

Observation: Cronbach’s alpha provides a useful lower

bound on reliability (as seen in Property 1). Cronbach’s

alpha will generally increase when the correlations

between the items increase. For this reason the

coefficient measures the internal consistency of the test.

Its maximum value is 1, and usually its minimum is 0,

although it can be negative. This can happen when some

questions are reversed phrased.

E.g. suppose you are measuring citizens’ happiness with

their government and you ask a series of questions using

the Likert scale from 0 to 5 with 5 being strongly agree

and 0 being strongly disagree. Most of your questions

are of the form Q1: “My government is doing a good job

with the economy” and Q2: “I trust my government to do

the right thing”, but in order to reduce response bias (to

make sure that the responder reads the questions

carefully) you also ask some reversed phrased questions

like Q3: “My government tends to interfere in my life”. It

is important in calculating Cronbach’s alpha that you

first reverse the scale of these reversed phrased

questions; i.e. if a response was 5 (strongly agree) you

should use 0 instead, if it was 4 you should use 1

instead, etc.

A commonly-accepted rule of thumb is that an alpha of

0.6-0.7 indicates acceptable reliability, and 0.8 or higher

indicates good reliability. Very high reliability (0.95 or

higher) is not necessarily desirable, as this indicates that

the items may be entirely redundant. These are only

guidelines and the actual value of Cronbach’s alpha will

depend on many things. E.g. as the number of items

increases, alpha tends to increase too even without any

increase in internal consistency.

The goal in designing a reliable instrument is for scores

on similar items to be related (internally consistent), but

for each to contribute some unique information as well.

If your questionnaire measures multiple things (i.e. has

multiple factors) such as “happiness with government”

and “happiness with life”, then you should segregate the

questions by factor and perform Cronbach’s alpha

separately on each group of questions. We will return to

this issue when we study factor analysis (see [Za]).

Cronbach’s alpha is superior to Kuder and Richardson

Formula 20 since it can be used with continuous and

non-dichotomous data.

Example 1: Calculate Cronbach’s alpha for the data in

Example 1 of Kuder and Richardson Formula

20 (repeated in Figure 1 below).

Figure 1 – Cronbach’s Alpha for Example 1

Figure 1 – Cronbach’s Alpha for Example 1

The worksheet in Figure 1 is very similar to the

worksheet in Figure 1 of Kuder and Richardson Formula

20. Row 17 contains the variance for each of the

questions. E.g. the variance for question 1 (cell B17) is

calculated by the formula =VARP(B4:B15). Other key

formulas used to calculate Cronbach’s alpha in Figure 1

are described in Figure 2.

Figure 2 – Key formulas for worksheet in Figure 1

Since the questions only have two answers, Cronbach’s

alpha .73082 is the same as the KR20 reliability

calculated in Example 1 of Kuder and Richardson

Formula 20.

Observation: If the variances of the xj vary widely,

the xj can be standardized to obtain a standard deviation

of 1 prior to calculating Cronbach’s alpha.

To determine how each question on a test impacts the

reliability, Cronbach’s alpha can be calculated after

deleting the ith variable, for each i ≤ k. Thus for a test

with k questions, each with score xj, Cronbach’s alpha is

calculated for   for all i where   =  .

If the reliability coefficient increases after an item is

deleted, you can assume that the item is not correlated

highly with other items. Conversely, if the reliability

coefficient decreases, you can assume that the item is

highly correlated with other items.

Example 2: Calculate Cronbach’s alpha for survey in

Example 1, where any one question is removed.

The necessary calculations are displayed in Figure 3.

Figure 3 – Cronbach’s Alpha for Example 2

Figure 3 – Cronbach’s Alpha for Example 2

Each of the columns B through L represents the test

with one question removed. Column B corresponds to

question #1, column C corresponds to question #2, etc. 

Figure 4 displays the formulas corresponding to

question #1 (i.e. column B); the formulas for the other

questions are similar. Some of the references are to cells

shown in Figure 2.

Figure 4 – Key formulas for worksheet in Figure 3

As can be seen from Figure 3, the omission of any single

question doesn’t change the Cronbach’s alpha very

much. Removal of Q8 affects the result the most.

Observation: Another way to calculate Cronbach’s

alpha is to use the Two Factor ANOVA without

replication data analysis tool on the raw data and note

that:

Example 3: Calculate the Cronbach’s alpha for Example

1 using ANOVA.

Figure 5 – Calculation of Cronbach’s alpha using ANOVA

Figure 5 – Calculation of Cronbach’s alpha using

ANOVA

As you can see from Figure 5, Cronbach’s alpha

is .73802, the same value calculated in Figure 1.

https://statistics.laerd.com/spss-tutorials/cronbachs-alpha-using-spss-statistics.php

Cronbach's Alpha (α) using SPSS

Introduction

Cronbach's alpha is the most common measure of internal

consistency ("reliability"). It is most commonly used when you

have multiple Likert questions in a survey/questionnaire that form

a scale, and you wish to determine if the scale is reliable.

SPSStop ^

Example

A researcher has devised a nine-question questionnaire to

measure how safe people feel at work at an industrial complex.

Each question was a 5-point Likert item from "strongly disagree"

to "strongly agree". In order to understand whether the questions

in this questionnaire all reliably measure the same latent variable

(feeling of safety) (so a Likert scale could be constructed), a

Cronbach's alpha was run on a sample size of 15 workers.

SPSStop ^

Setup in SPSS

In SPSS, the nine questions have been labelled  Qu1  through

to  Qu9 . To know how to correctly enter your data into SPSS in

order to run a Cronbach's alpha test, see our Entering Data into

SPSS tutorial. Alternately, you can learn about our enhanced

data setup content here.

Join the 1,000s of students, academics and professionals who rely on Laerd Statistics.TAKE THE TOUR PLANS & PRICING

SPSStop ^

Test Procedure in SPSS

The eight steps below show you how to check for internal

consistency using Cronbach's alpha in SPSS. At the end of these

eight steps, we show you how to interpret the results from your

Cronbach's alpha.

Click Analyze > Scale > Reliability Analysis... on the top menu

as shown below:

Published with written permission from SPSS Inc., an IBM Company.

You will be presented with the Reliability Analysis dialogue box:

Published with written permission from SPSS Inc., an IBM Company.

Transfer the variables  Qu1  to  Qu9  into the Items: box. You can

do this by drag-and-dropping the variables into their respective

boxes or by using the   button. You will be presented with the

following screen:

Published with written permission from SPSS Inc., an IBM Company.

Leave the Model: set as "Alpha", which represents Cronbach's

alpha in SPSS. If you want to provide a name for the scale, enter

it in the Scale label: box. Since this only prints the name you enter

at the top of the SPSS output, it is certainly not essential that you

do; and in this case, we will leave it blank.

Click on the   button, which will present the Reliability

Analysis: Statistics dialogue box, as shown below:

Published with written permission from SPSS Inc., an IBM Company.

Select the Item, Scale and Scale if item deleted options in the -

Descriptives for- area, and the Correlations option in the -Inter-

Item- area, as shown below:

Published with written permission from SPSS Inc., an IBM Company.

Click the   button. This will return you to the Reliability

Analysis dialogue box.

Click the   button to generate the output.

TAKE THE TOUR

PLANS & PRICING

SPSStop ^

SPSS Output for Cronbach's Alpha

SPSS produces many different tables. The first important table is

the Reliability Statistics table that provides the actual value

for Cronbach's alpha, as shown below:

Published with written permission from SPSS Inc., an IBM Company.

From our example, we can see that Cronbach's alpha is 0.805,

which indicates a high level of internal consistency for our scale

with this specific sample.

SPSStop ^

Item-Total Statistics

The Item-Total Statistics table presents the Cronbach's Alpha

if Item Deleted in the final column , as shown below:

Published with written permission from SPSS Inc., an IBM Company.

This column presents the value that Cronbach's alpha would be if

that particular item was deleted from the scale. We can see that

removal of any question, except question 8, would result in a

lower Cronbach's alpha. Therefore, we would not want to remove

these questions. Removal of question 8 would lead to a small

improvement in Cronbach's alpha, and we can also see that

the Corrected Item-Total Correlation value was low (0.128) for

this item. This might lead us to consider whether we should

remove this item.

Cronbach's alpha simply provides you with an overall reliability

coefficient for a set of variables (e.g., questions). If your

questions reflect different underlying personal qualities (or other

dimensions), for example, employee motivation and employee

commitment, Cronbach's alpha will not be able to distinguish

between these. In order to do this and then check their reliability