Chapter 14 Coefficient Alpha

14.1 Intro

Coefficient Alpha [also known as Cronbach’s Alpha, but Cronbach disliked that association; Cronbach and Shavelson (2004)] is considered a measure of internal consistency and can, if a set of severe assumptions is met, estimate the reliability of a set of items.

14.1.1 Example dataset

This example uses the Rosetta Stats example dataset “pp15” (see Chapter 1 for information about the datasets and Chapter 3 for an explanation of how to load datasets).

14.1.2 Variable(s)

From this dataset, this example uses variables highDose_AttGeneral_good, highDose_AttGeneral_prettig, highDose_AttGeneral_slim, highDose_AttGeneral_gezond & highDose_AttGeneral_spannend.

14.2 Input: jamovi

In the “Analyses” tab, click the “Factor” button and from the menu that appears, select “Reliability Analysis” as shown in Figure 14.1.

Figure 14.1: Opening the reliability analysis menu in jamovi

In the box at the left, select all variables you want to include in this analysis and move them to the box labelled “Items” using the button labelled with the rightward-pointing arrow as shown in Figure 14.2.

Figure 14.2: Adding the items to analyse in jamovi

Because Coefficient Alpha (called Cronbach’s Alpha in the jamovi interface) has already been checked (see the left-most column at the bottom labelled “Scale Statistics”), you will immediately see Coefficient Alpha for the selected items appear in the table in jamovi’s Results pane on the right-hand side. You can now also order additional statistics, such as the value Coefficient Alpha would have if you were to omit each item, as shown in Figure 14.3.

Figure 14.3: Ordering “Alpha if item dropped” in jamovi

14.3 Input: R

14.3.1 R: rosetta

rosetta::reliability(
  data = dat,
  items = c(
    "highDose_AttGeneral_good",
    "highDose_AttGeneral_prettig",
    "highDose_AttGeneral_slim",
    "highDose_AttGeneral_gezond",
    "highDose_AttGeneral_spannend"
  )
);

14.4 Input: SPSS

To compute Coefficient Alpha in SPSS, use the following command:

RELIABILITY
  /VARIABLES =
    highDose_AttGeneral_good
    highDose_AttGeneral_prettig
    highDose_AttGeneral_slim
    highDose_AttGeneral_gezond
    highDose_AttGeneral_spannend
  /MODEL =
    ALPHA.

To order additional information, such as descriptive statistics, inter-item correlations, and other scale statistics, you can specify additional options:

RELIABILITY
  /VARIABLES =
    highDose_AttGeneral_good
    highDose_AttGeneral_prettig
    highDose_AttGeneral_slim
    highDose_AttGeneral_gezond
    highDose_AttGeneral_spannend
  /MODEL = ALPHA
  /STATISTICS = DESCRIPTIVE SCALE CORR
  /SUMMARY = TOTAL.

14.5 Output: jamovi

Figure 14.4: The output of a reliability analysis where Coefficient Alpha is computed in jamovi

14.6 Output: R

14.6.1 R: rosetta

14.6.1.1 Reliability analysis

14.6.1.1.1 Scale structure

14.6.1.1.1.1 Scale structure

14.6.1.1.1.1.1 Information about this scale

Dataframe:	res$data
Items:	highDose_AttGeneral_good, highDose_AttGeneral_prettig, highDose_AttGeneral_slim, highDose_AttGeneral_gezond & highDose_AttGeneral_spannend
Observations:	303
Positive correlations:	10
Number of correlations:	10
Percentage positive correlations:	100

14.6.1.1.1.1.2 Estimates assuming interval level

Omega (total):	0.79
Omega (hierarchical):	0.80
Revelle’s Omega (total):	0.79
Greatest Lower Bound (GLB):	0.87
Coefficient H:	0.85
Coefficient Alpha:	0.78

Note: the normal point estimate and confidence interval for omega are based on the procedure suggested by Dunn, Baguley & Brunsden (2013) using the MBESS function ci.reliability, whereas the psych package point estimate was suggested in Revelle & Zinbarg (2008). See the help (‘?ufs::scaleStructure’) for more information.

14.7 Output: SPSS

The SPSS output still has to be added.

References

Cronbach, Lee J., and Richard J. Shavelson. 2004. “My Current Thoughts on Coefficient Alpha and Successor Procedures.” Educational and Psychological Measurement 64 (3): 391–418. https://doi.org/bwg2pm.