Chapter 9 Reliability Module

9.1 Classical Single-Test Reliability Analysis

An example from Field (2018 pp. 795-796):

“I have noticed that a lot of students become very stressed about SPSS Statistics. Imagine that I wanted to design a questionnaire to measure a trait that I termed ‘SPSS anxiety’. I devised a questionnaire to measure various aspects of students’ anxiety towards learning SPSS, the SAQ. I generated questions based on interviews with anxious and non-anxious students and came up with 23 possible questions to include. Each question was a statement followed by a five-point Likert scale: ‘strongly disagree’, ‘disagree’, ‘neither agree nor disagree’, ‘agree’ and ‘strongly agree’ (SD, D, N, A and SA, respectively). What’s more, I wanted to know whether anxiety about SPSS could be broken down into specific forms of anxiety. In other words, what latent variables contribute to anxiety about SPSS? With a little help from a few lecturer friends I collected 2571 completed questionnaires.”

Note: Only questions 1, 4, 5, 6, 7, 8, and 10 have been used to simplify the analysis.

9.1.1 Results Overview

Table 9.1: Result Overview Reliability Analysis
JASP SPSS SAS Minitab R
Cronbachs \(\alpha\) 0.7574 0.758 0.7574 0.7574 0.7574

9.1.2 JASP

\label{fig:reliJASP}JASP Output for Reliability Analysis

Figure 9.1: JASP Output for Reliability Analysis

9.1.3 SPSS

DATASET ACTIVATE DataSet1.
RELIABILITY
  /VARIABLES=Question_01 Question_04 Question_05 Question_06 Question_07 Question_08 Question_10
  /SCALE('ALL VARIABLES') ALL
  /MODEL=ALPHA
  /STATISTICS=DESCRIPTIVE SCALE
  /SUMMARY=TOTAL MEANS.
\label{fig:reliSPSS}SPSS Output for Reliability Analysis

Figure 9.2: SPSS Output for Reliability Analysis

\label{fig:reliSPSS2}SPSS Output for Reliability Analysis

Figure 9.3: SPSS Output for Reliability Analysis

9.1.4 SAS

PROC CORR DATA=work.Reliability ALPHA;
    VAR Q1 Q4 Q5 Q6 Q7 Q8 Q10;
RUN;
\label{fig:reliSAS}SAS Output for Reliability Analysis

Figure 9.4: SAS Output for Reliability Analysis

9.1.5 Minitab

\label{fig:reliMinitab}Minitab Output for Reliability Analysis

Figure 9.5: Minitab Output for Reliability Analysis

\label{fig:reliMinitab2}Minitab Output for Reliability Analysis

Figure 9.6: Minitab Output for Reliability Analysis

9.1.6 R

# library(psych)
QuestionSelection <- reli.data[c(1,4,5,6,7,8,10)]
analysis <- psych::alpha(QuestionSelection, cumulative = T)
analysis$total
##  raw_alpha std.alpha   G6(smc) average_r      S/N         ase     mean       sd
##  0.7573813  0.757503 0.7440687 0.3085574 3.123762 0.007201353 17.55115 4.311329
##  median_r
##  0.297497
analysis$item.stats
##                   n     raw.r     std.r     r.cor    r.drop     mean        sd
## ï..Question_01 2571 0.6228945 0.6501973 0.5677797 0.4824078 2.374173 0.8280221
## Question_04    2571 0.6848824 0.6913312 0.6268423 0.5378476 2.786075 0.9485482
## Question_05    2571 0.6498827 0.6551175 0.5691098 0.4890456 2.722287 0.9646904
## Question_06    2571 0.6626598 0.6292060 0.5488700 0.4733243 2.227149 1.1220023
## Question_07    2571 0.7317687 0.7046681 0.6536507 0.5726486 2.923765 1.1023600
## Question_08    2571 0.5692230 0.5881757 0.4711300 0.4074534 2.236873 0.8725704
## Question_10    2571 0.5382484 0.5488999 0.4163395 0.3691902 2.280825 0.8771293
analysis$alpha.drop
##                raw_alpha std.alpha   G6(smc) average_r      S/N    alpha se
## ï..Question_01 0.7277017 0.7247454 0.7028417 0.3049925 2.633000 0.008153868
## Question_04    0.7142260 0.7129289 0.6916327 0.2927412 2.483457 0.008553717
## Question_05    0.7246553 0.7233622 0.7046391 0.3035270 2.614836 0.008232559
## Question_06    0.7300262 0.7305573 0.7020402 0.3112445 2.711364 0.008128863
## Question_07    0.7044218 0.7089704 0.6818863 0.2887689 2.436077 0.008995173
## Question_08    0.7412689 0.7415166 0.7232435 0.3234650 2.868721 0.007791848
## Question_10    0.7484933 0.7515384 0.7318020 0.3351629 3.024767 0.007620190
##                      var.r     med.r
## ï..Question_01 0.007856087 0.2837230
## Question_04    0.007391559 0.2837230
## Question_05    0.009125797 0.2974970
## Question_06    0.006534879 0.3053651
## Question_07    0.006679362 0.2686270
## Question_08    0.008291751 0.3053651
## Question_10    0.007077595 0.3307376
analysis$total$raw_alpha
## [1] 0.7573813

9.1.7 Remarks

All differences in results between the software are due to rounding. For this analysis JASP 0.15 was used.

9.1.8 References

Field, A. (2018). Discovering statistics using IBM SPSS statistics. Los Angeles, CA: SAGE.