1	Fundamentals of IRT, How it can change your program Casey Marks, PhD National Council of State Boards of Nursing Sandra Neustel, PhD American Registry of Radiological Technicians Reed Castle, PhD Schroeder Measurement Technologies
2	Introduction to IRT Reed Castle, PhD Schroeder Measurement Technologies
3	Shortcomings of Classical Test Theory (CTT) Item difficulty and discrimination indexes are group dependent Item difficulty varies with proficiency of sample Item discrimination and reliability vary with heterogeneity of sample SAMPLE DEPENDENT
4	Shortcomings of CTT continued Examinee scores are test dependent Observed scores vary with test form difficulty Requires test equating after administration Assumes equal error variance and a high degree of “parallel” test forms
5	What do we want? Item statistics with limited dependency to group ability Examinee scores not dependent on test form difficulty Model that places examination item characteristics, test characteristics and proficiency estimates on a same scale.
6	IRT History Concept developed in the 1930’s Became more a reasonable model in 1950’s and 1960’s with Birnbaum’s contribution Math became simple with Birnbaum’s logistic modeling Computers have helped Cat Excel Item banking software
7	IRT Candidate Proficiency Candidate proficiency is expressed as a statistical function (monotonically increasing) relating to item attributes Probability associated with a correct response given candidate proficiency and IRT item parameters
8	Items
9	Item parameter estimates (statistics) Item Difficulty “b parameter” (1-parameter) Low and negative values reflect easy items -3 to +3 (centering varies on model type) Interpretation is opposite of p-value Item Discrimination “a parameter” (2-parameter) High values indicate item discriminates better 0 to 2.0 (typically .3 to 1) Lower Asymptote “c parameter” (3-parameter) 0 to 1 (typically .10 to .30)
10	How parameters affect ogive b parameter – affects the placement of the point of inflection on the x-axis a parameter – affects the pitch or steepness of the ogive (flat or steep) a parameter – affects the intersection of the y-axis
11	Sample Items
12	IRT Unidminsional Models 1 parameter Requires fewer candidates (150) Discrimination is constant and no c parameter 2 parameter Requires more candidates (800 plus depending on linkage) Discrimination varies No c parameter 3 parameter Requires more candidates (1,000) All parameters vary
13	Item Information Function a = .8, b = -1.5, c = .20
14	Test Information Test Characteristic Curve Test Information Function Conditional Standard Error
15	Test Characteristic Curve
16	Test Information and CSE