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Item reliability is the consistency of a set of items (variables); that is to what extent they measure the same thing. When a set of items are consistent, they can make a measurement scale such as a sum scale.
Cronbach’s alpha is the most popular measure of item reliability; it is the average correlation of items in a measurement scale. If the items have variances that significantly differ, standardized alpha is preferred.
When all items are consistent and measure the same thing, then the coefficient alpha is equal to 1. A high value for alpha does not imply that the measure is unidimensional. To prove that a scale is unidimensional, you can use factor analysis to check the dimensionality.
It is possible to see the effect of an individual item on the overall alpha value by recomputing Cronbach's alpha excluding that item. If alpha increases when you exclude an item, that item does not highly correlate with the other items in the scale. If the alpha decreases, that item does correlate with the other items in the scale.