Example of Item Analysis
main topic     interpreting results     session command     see also 

A bank is interested in surveying customers to determine how satisfied they are with the timeliness of its service. You develop the following four survey questions:

Item 1 - My telephone, email, or letter inquiry was answered in a reasonable amount of time.

Item 2 - I am satisfied with the timeliness of the service provided.

Item 3 - The time I waited for services was reasonable.

Item 4 - I am satisfied with the services I received.

Each of the questions are answered on a 5-point Likert scale: 1 = Very dissatisfied, 2 = Dissatisfied, 3 = Neutral, 4 = Satisfied, and 5 = Very satisfied. Before you distribute the survey, you want to test the questions to ensure they consistently measure customer service timeliness. 60 customers are requested to answer these four questions.

1    Open the worksheet CRONBACH.MTW.

2    Choose Stat > Multivariate > Item Analysis.

3    In Variables, enter Item 1 - Item 4.

4    Click Graphs and check Matrix plot of data with smoother.

6    Click OK in each dialog box.

Session window output

Item Analysis of Item 1, Item 2, Item 3, Item 4

 

 

Correlation Matrix

 

        Item 1  Item 2  Item 3

Item 2   0.814

Item 3   0.795   0.789

Item 4   0.038   0.017  -0.003

 

Cell Contents: Pearson correlation

 

 

Item and Total Statistics

 

          Total

Variable  Count    Mean  StDev

Item 1       60   3.450  1.333

Item 2       60   3.383  1.415

Item 3       60   3.317  1.255

Item 4       60   2.167  0.827

Total        60  12.317  3.833

 

 

Cronbach’s alpha = 0.7853

 

 

Omitted Item Statistics

 

                       Adj.               Squared

Omitted   Adj. Total  Total   Item-Adj.  Multiple  Cronbach’s

Variable        Mean  StDev  Total Corr      Corr       Alpha

Item 1         8.867  2.665    0.818768  0.725307    0.599499

Item 2         8.933  2.603    0.802999  0.717877    0.606279

Item 3         9.000  2.768    0.785333  0.691912    0.625996

Item 4        10.150  3.727    0.019250  0.004488    0.921674

Graph window output  

Interpreting the results

The overall Cronbach's alpha is 0.7853, which is higher than a commonly used benchmark value of 0.7. This suggests that at least some of the items measure the same construct of customer service timeliness.

Caution

Benchmarks usually depend on the standards in your subject area and the number of items.

To assess whether all items measure the same construct, evaluate the inter-item correlations and omitted item statistics.

Correlation Matrix

Use the correlation matrix to evaluate whether two items are correlated. Because you want all items to measure the same construct, customer service timeliness, you need them to be highly correlated. The closer the values are to 1 the more highly correlated the items are.  Negative correlations are theoretically possible but, in practice, they generally are not seen in item analysis.

In this example, items 1, 2, and 3 are highly correlated with values ranging around 0.8. Item 4 is not correlated with the other items because the correlation values range around 0.

Further, the Matrix Plot graphically shows that items 1, 2 and 3 have a positive relationship while item 4 has no relationship with other items in the construct.

Omitted Item Statistics

·    Item-Adj. Total Corr - Correlation between the scores of one omitted item and the total score of all other items. If an item has a low Item-Adj. Total Corr, then it may not measure the same construct as the other items.

·    Squared Multiple Corr - Coefficient of determination (R2) when the omitted item is regressed on the remaining items. If an item has a low Squared Multiple Correlation, then it may not measure the same construct as the other items.

·    Cronbach's Alpha - Calculated after an item is omitted from the analysis. If omitting an item substantially increases Cronbach's alpha value, then you might consider removing it from the construct.

In this example, item 4 has a low Item-Adj. Total Corr (0.019250), a low Squared Multiple Correlation (0.004488), and removing it from the construct increases Cronbach's alpha from 0.7853 to 0.921674.

Collectively, the results suggest that only items 1, 2, and 3 measure customer service timeliness. The manager should either remove item 4 or reword and retest to make sure the items are measuring the same construct.