# 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

### 9.1.3 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.

### 9.1.4 SAS

PROC CORR DATA=work.Reliability ALPHA;
VAR Q1 Q4 Q5 Q6 Q7 Q8 Q10;
RUN;

### 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.