In This Topic
Covariance
Formula
For two items x and y, the covariance is calculated as follows:
Notation
| Term | Description |
|---|---|
 | sample mean for the first item |
 | sample mean for the second item |
| n | column length |
Correlation
Formula
For two items x and y, the correlation is calculated as follows:
In the Omitted Item Statistics table, the item-adjusted correlation is the correlation between the scores of the omitted item and the total score of all other items.
Notation
| Term | Description |
|---|---|
 | sample mean for the first item |
| sx | standard deviation for the first item |
 | sample mean for the second item |
| sy | standard deviation for the second item |
| n | column length |
Squared multiple correlation
Formula
Notation
| Term | Description |
|---|---|
 | ith predicted score for the omitted item using the regression equation based on remaining items in your analysis |
 | average of observed scores of omitted item |
 | ith observed score on the omitted item |
Cronbach's alpha
Formula
Cronbach's alpha for all items is calculated as follows:
Cronbach's alpha after omitting an item is calculated as follows:
Notation
| Term | Description |
|---|---|
 | sample variance of the ith item |
 | sample variance of the total |
 | sample variance of the total calculated after omitting the jth item |
| T | total scores |
| k | number of items in your analysis |
Mean
The item mean is the sum of all the scores for one item divided by the number of scores for that item.
The total mean is the sum of all the item means.
The adjusted total mean is the sum of all the item means except the omitted item.
Standard deviation
Formula
The item standard deviation is the square root of the average squared deviation of the scores in one item from the item mean.
The standard deviation of the total mean is the square root of the average squared deviation of all total scores from the total mean score.
The adjusted total standard deviation is the standard deviation of the total score after omitting an item.
Notation
| Term | Description |
|---|---|
| xi | the ith observation |
 | mean of the observations |
| N | number of nonmissing observations |
Total
Total is the sum of all item scores for a single observation (row). For example, if the item scores for an individual survey respondent are 2, 5, and 3, the total for the observation is 10.
