Applied Univariate, Bivariate, and Multivariate Statistics. Daniel J. Denis
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:
RELIABILITY /VARIABLES=Item_1 Item_2 Item_3 Item_4 /SCALE('ALL VARIABLES') ALL /MODEL=ALPHA /STATISTICS=DESCRIPTIVE SCALE CORR /SUMMARY=TOTAL.