# Comparing the Normal Ogive and Logistic Item Characteristic Curves

Comparing the Normal Ogive and Logistic Item Characteristic Curves

In item response theory, the relationship between a latent ability () and the probability of a correct response () on a test item is modelled by an item characteristic curve. This Demonstration plots the item characteristic curve of a single dichotomous item under two different models: the normal ogive model and the logistic model. The parameters , , and represent item properties related to discrimination, difficulty, and guessing. The constant is used to scale the logistic curve. Notice that the two curves are nearly identical when .

θ

P

a

b

c

D

D≈1.7