Applied Univariate, Bivariate, and Multivariate Statistics - Daniel J. Denis

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      To compute a Cronbach's alpha, and obtain a handful of statistics useful for conducting an item analysis, we code in SPSS:

      RELIABILITY /VARIABLES=Item_1 Item_2 Item_3 Item_4 Item_5 /SCALE('ALL VARIABLES') ALL /MODEL=ALPHA /STATISTICS=DESCRIPTIVE SCALE CORR /SUMMARY=TOTAL.

      The MODEL = ALPHA statement requests SPSS to compute a Cronbach's alpha. Select output now follows:

Reliability Statistics
Cronbach's Alpha Cronbach's Alpha Based on Standardized Items No of Items
0.633 0.691 5
Item Statistics
Mean Std. Deviation N
Item_1 7.3000 2.71006 10
Item_2 8.8000 5.05085 10
Item_3 9.1000 4.74810 10
Item_4 9.4000 2.71621 10
Item_5 7.0000 3.80058 10
Inter‐Item Correlation Matrix
Item_1 Item_2 Item_3 Item_4 Item_5
Item_1 1.000 0.679 0.351 0.827 0.022
Item_2 0.679 1.000 0.612 0.743 −0.463
Item_3 0.351 0.612 1.000 0.462 −0.129
Item_4 0.827 0.743 0.462 1.000 −0.011
Item_5 0.022 −0.463 −0.129 −0.011 1.000

      We can see that SPSS reports a raw reliability coefficient of 0.633 and 0.691 based on standardized items. SPSS also reports item statistics, which include the mean and standard deviation of each item, as well as the inter‐item correlation matrix, which, not surprisingly, has values of 1.0 down the main diagonal (i.e., the correlation of an item with itself is equal to 1.0).

      Next, SPSS features Item‐Total Statistics, which contains useful information for potentially dropping items and seeking to ameliorate reliability:

Item‐Total Statistics
Scale Mean if Item Deleted Scale Variance if Item Deleted Corrected Item‐Total Correlation Squared Multiple Correlation Cronbach's Alpha if Item Deleted
Item_1 34.3000 108.900 0.712 0.726 0.478
Item_2 32.8000 80.400 0.558 0.841 0.476
Item_3 32.5000 88.278 0.512 0.448 0.507
Item_4 32.2000 104.844 0.796 0.776 0.445
Item_5 34.6000 164.267 −0.228 0.541 0.824

      The most relevant column of the above is the last one on the far right, “Cronbach's Alpha if Item Deleted.” What this reports is how much alpha would change if the given item were excluded. We can see that for all items, alpha would decrease if the given item were excluded, but for item 5, alpha would increase. If we drop item 5 then, we should expect alpha to increase. We recompute alpha after removing item 5:

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