Methods and formulas for Item Analysis

Select the method or formula of your choice.

Covariance

Formula

For two items x and y, the covariance is calculated as follows:

Notation

TermDescription
sample mean for the first item
sample mean for the second item
ncolumn 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

TermDescription
sample mean for the first item
sxstandard deviation for the first item
sample mean for the second item
systandard deviation for the second item
ncolumn length

Squared multiple correlation

Formula

Notation

TermDescription
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

TermDescription
sample variance of the ith item
sample variance of the total
sample variance of the total calculated after omitting the jth item
Ttotal 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

TermDescription
xithe ith observation
mean of the observations
Nnumber 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.

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