Classical Test Theory (CTT) Statistics

CTT statistics
1) item difficulty
2) item-test correlation
3) reliability coefficient
4) standard error of measurement (SEM)

Item Diffuculty (ID)
A test that is too difficult or too easy reduces the reliability (ex: fewer test-takers get the answers correctly or vice-versa). A moderate level of difficulty increase test reliability.

1) For dichotomously scored items (1 for correct answer and 0 for incorrect answer)
2) Adjusted p-value for polytomously scored (Likert Scaled) items (this is computed so that the result will be on the similar scale as that of the dichotomous items).

Item-Test Correlation (Item Discrimination Power)
Point-biserial correlation correlation indicates the relation between individual's performance on an 0/1 scored item and their performance on the total test (measure)

Item-Test Correlation (Item Discrimination Power)
polytomously scored items (likert scaled). Perason Product Moment Correlation Coefficient.

Item Discrimination Power
1) Higher item-test correlation is desired, which indicates that high ability examines tend to get the item correct (have higher scores) and low ability examinees tend to get the item incorrect (lower scores).
2) item-test correlation tends to be senstive to item difficulty.
3) item discrimination indices (such as point-biseral correlation) plays an more important role in item selection than item difficulty.

Advantages:
1) easy to apply: hand calculations possible; widely available in statistical package
2) widely used  and easy to undetsand

Limitations:
1) sample dependence & test dependent of all item statistic item statistic apply only to that group of individuals on that collection of items (point: change samples and/or alter any items and th epsychometric properties of the measure changes).
2) restrictive assumptions about: is normally distributed; uncorrelated with true score; has a mean of zero