But it is not appropriate to do so if the instrument is a survey such as an attitude scale. It is a common mistake that people look at each item individually and throw out the item that appears to be too difficult or too easy. Actually you should take the entire test into consideration. This will be discussed later. The stronger the items are inter-related, the more likely the test is consistent.
Covariance is a measure of the distributions of two variables.
The higher the correlation coefficient is, the higher the covariance is. Some people mistakenly believe that the standardized Alpha is superior to the raw Alpha because they thought that standardization normalizes skewed data. Actually standardization is a linear transformation, and thus it never normalizes data. Standardized Alpha is not superior to its raw counterpart. It is used when scales are comparable, because as mentioned before, variance and covariance are taken into account for computation.