8.7. Reliability Analysis
Reliability Analysis is used to create a measurement scale for a number of variables none of which is representative of the complete group on their own. A number of reliability coefficients are computed to construct the sum scales.
Reliability Analysis is an attempt to find the true score using a set of items. These items are believed to reflect the true score and would involve some random error. The sum of these items (called the sum scale) will give an indication of the true score. The mean value of the error terms across the items will be zero. The true score component remains the same when summing across items. Therefore, the more items that are added, the more true score (relative to the error score) will be reflected in the sum scale.
The assessment of scale reliability is based on the correlation between the individual items or measurements that make up the scale, relative to the variances of the items.
The columns containing the items are selected by clicking on [Variable]. Any rows containing one or more missing values are removed from the analysis.
Reliability Results: The output will display summary information about the sum scale and the items. It will also display the Cronbach’s alpha statistic.
The variance of the sum scale will be smaller than the sum of item variances if the items measure the same variability. We can estimate the proportion of true score variance in the sum scale by comparing the sum of item variance with the variance of the sum scale. If the items have no error and measure the true score then alpha will equal 1. If the items are unrelated then alpha will equal 0. Standardised alpha is the value of alpha if the items had been standardised before the Reliability Analysis.
Means and Standard Deviations: The mean and standard deviation of each item is displayed.
Covariance Matrix: The covariance between the items is displayed.
Correlation Matrix: The correlation between the items is displayed.
Item Total Statistics: Sum statistics relating to each item are displayed. The first two columns contain the mean and variance that the sum scale would take if the item was removed from the scale. The third column shows the correlation between the item and the sum scale with the item removed. The final column shows the value of Cronbach’s alpha if the item was removed from the scale.
ANOVA: A one way repeated measures ANOVA table is displayed where the items (columns) are the levels of the factor and the rows are the repeated measures (subjects).
Split Analysis: The items are split into two groups. Select the items for group one by clicking on [Group 1]. The remaining items are placed in group two. If the sum scale is reliable, the two groups should be highly correlated. Split analysis calculates sum scale statistics for both groups and the correlation between the two groups.
Example
Open DEMODATA, select Statistics 2 → Reliability Analysis and select Wages to Fixed Capital (C2 to C5), Output 1 and Output 2 (C8 and C9) as [Variable]s. Select all the output options to obtain the following results.
Reliability Analysis
Variables Selected
Wages, Energy, Interest, Fixed Capital, Output1, Output2
Reliability Results
Statistics for 
Mean 
Variance 
Standard Deviation 
Variables 
Scale 
582.5786 
3733.7172 
61.1042 
6 
Statistics for 
Mean 
Minimum 
Maximum 
Variance 
Item Mean 
97.0964 
84.1014 
107.3121 
105.2151 
Item Variance 
128.4060 
44.8069 
214.6677 
4778.0683 
Covariance 
98.7760 
23.3530 
186.6305 
2706.6123 
Correlation 
0.7996 
0.5141 
0.9653 
0.0176 
Number of Cases = 
56 
Cronbach’s Alpha = 
0.9524 
Standardised Alpha = 
0.9599 
Means and Standard Deviations
Item 
Mean 
Standard Deviation 
Wages 
101.9893 
13.1962 
Energy 
100.9995 
14.6515 
Interest 
84.1995 
12.1420 
Fixed Capital 
84.1014 
11.9729 
Output1 
103.9768 
6.6938 
Output2 
107.3121 
6.7855 
Covariance Matrix

Wages 
Energy 
Interest 
Fixed Capital 
Output1 
Output2 
Wages 
174.1406 
186.6305 
149.4251 
145.7093 
60.4203 
67.2986 
Energy 
186.6305 
214.6677 
162.2643 
165.7807 
76.1006 
65.4243 
Interest 
149.4251 
162.2643 
147.4287 
135.4810 
61.1438 
59.3716 
Fixed Capital 
145.7093 
165.7807 
135.4810 
143.3492 
65.5625 
57.6750 
Output1 
60.4203 
76.1006 
61.1438 
65.5625 
44.8069 
23.3530 
Output2 
67.2986 
65.4243 
59.3716 
57.6750 
23.3530 
46.0431 
Correlation Matrix

Wages 
Energy 
Interest 
Fixed Capital 
Output1 
Output2 
Wages 
1.0000 
0.9653 
0.9326 
0.9222 
0.6840 
0.7516 
Energy 
0.9653 
1.0000 
0.9121 
0.9450 
0.7759 
0.6581 
Interest 
0.9326 
0.9121 
1.0000 
0.9319 
0.7523 
0.7206 
Fixed Capital 
0.9222 
0.9450 
0.9319 
1.0000 
0.8181 
0.7099 
Output1 
0.6840 
0.7759 
0.7523 
0.8181 
1.0000 
0.5141 
Output2 
0.7516 
0.6581 
0.7206 
0.7099 
0.5141 
1.0000 
Item Total Statistics

MeanDel 
VarDel 
CorrDel 
AlphaDel 
Wages 
480.5893 
2340.6090 
0.9547 
0.9315 
Energy 
481.5791 
2206.6489 
0.9534 
0.9352 
Interest 
498.3791 
2450.9170 
0.9444 
0.9323 
Fixed Capital 
498.4771 
2449.9511 
0.9622 
0.9301 
Output1 
478.6018 
3115.7501 
0.7670 
0.9589 
Output2 
475.2664 
3141.4291 
0.7181 
0.9618 
Scale mean, scale variance and Cronbach’s alpha denote the
values if the item is deleted from the scale.
Correlation denotes the corrected itemtotal correlation
ANOVA
Due To 
Sum of Squares 
DoF 
Mean Square 
Fstat 
Prob 
Between Subjects 
34225.741 
55 
622.286 


Within Subjects 
37608.484 
280 
134.316 


Between Measures 
29460.233 
5 
5892.047 
198.854 
0.0000 
Error 
8148.251 
275 
29.630 


Total 
71834.225 
335 
214.431 


Split Analysis
Group 1
Wages, Energy, Interest
Group 2
Fixed Capital, Output1, Output2

Number of Items 
Mean 
Sum 
Standard Deviation 
Variance 
Cronbach’s Alpha 
Group 1 
3 
287.1882 
16082.5400 
39.1520 
1532.8768 
0.9753 
Group 2 
3 
295.3904 
16541.8600 
22.9648 
527.3802 
0.8339 
Correlation Between Part 1 and Part 2 = 
0.9306 
Spearman Brown Split Half Reliability = 
0.9641 
Guttman Split Half Reliability = 
0.8964 