Thursday, March 15, 2018

(R) Cronbach’s Alpha / Reliability Analysis (SPSS)

Cronbach’s Alpha, AKA tau-equivalent reliability, AKA coefficient alpha, is an estimate of internal consistency reliability. Cronbach’s Alpha is primarily utilized to measure for the correlation of response data collected from sociological surveys. This methodology was originally derived by Lee Joseph Cronbach, an American psychologist.

What this statistical method is seeking to quantify, is the reliability of survey questions pertaining to a specific survey category. The alpha statistic, which is the eventual product of the analysis, is derived though a formula which is comprised of aspects which account for both the number of questions contained within a category, and their shared correlations.

So for example, if you were administering a survey to measure the satisfaction of employees within a particular department as it pertains to supervisor interaction. Typically, you would expect all of the responses of the survey participants, as it is relates to the questions of that category, to cluster in a particular manner. If the responses were not arranged in such a way, it would be more difficult to assess the accuracy of the overall categorical rating. If such were the case, it typically would be best to remove the questions containing outlier responses prior to administering the survey during a subsequent cycle.


Below is a data set which contains categorical responses to a factious survey.

From the “Analyze” menu, select “Scale”, then select “Reliability Analysis”.

This should populate the following menu:

Using the center middle arrow, designate all question response variables as “Items”.

Next, click on the “Statistics” button.

The menu sub-menu above should appear. Select the check boxes adjacent to the options “Scale if item deleted” and “Correlations”.

After clicking “Continue”, click “OK” to generate the system output.

Reliability Statistics – This table displays the Cornbach’s Alpha score. Typically, according to the various research papers produced by the researcher Nunnally*, the alpha score should typically fall somewhere between .70 - .79 if the research is exploratory, between .80 - .89 if the research is basic, and above .90 in applied research scenarios.

Inter-Item Correlation Matrix – This table is displaying the correlation of each variable as it pertains to the other variables within the analysis.

Item-Total Statistics – The most important aspect of this table is the section which reads “Cronbach’s Alpha if Item Deleted”. This column is presenting exactly what the column header suggests, the value which alpha would assume if the corresponding variable were removed.

One final note on Cornbach’s Alpha, variables are not required to utilize the same scale of measurement. However, it is uncommon to witness the utilization of this methodology given those circumstances.

Analysis within the R platform

I will now briefly illustrate how to obtain the same results in R.

# With package "psy" installed and enabled #

Q1 <- c(2, 3, 5, 1, 5)

Q2 <- c(5, 2, 2, 2, 2)

Q3 <- c(2, 1, 5, 5, 2)

Q4 <- c(1, 3, 5, 4, 4)

Q5 <- c(2, 5, 3, 4, 2)

x <- data.frame(Q1, Q2, Q3, Q4, Q5)


Which produces the output:

[1] 5

[1] 5

[1] -0.5255682

That’s all for now, Data Heads. Stay tuned for future articles!


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