ITEM DISCRIMINATION

• THE ITEM DISCRIMINATION INDEX IS A MEASURE OF HOW WELL AN ITEM IS ABLE TO DISTINGUISH BETWEEN EXAMINEES WHO ARE KNOWLEDGEABLE AND THOSE WHO ARE NOT, OR BETWEEN MASTERS AND NON-MASTERS

• THIS STATISTIC LOOKS AT THE RELATIONSHIP BETWEEN AN EXAMINEE'S PERFORMANCE ON THE GIVEN ITEM (CORRECT OR INCORRECT) AND THE EXAMINEE'S SCORE ON THE OVERALL TEST

• FOR AN ITEM THAT IS HIGHLY DISCRIMINATING, IN GENERAL THE EXAMINEES WHO RESPONDED TO THE ITEM CORRECTLY ALSO DID WELL ON THE TEST, WHILE IN GENERAL THE EXAMINEES WHO RESPONDED TO THE ITEM INCORRECTLY ALSO TENDED TO DO POORLY ON THE OVERALL TEST

http://www.proftesting.com/test_topics/steps_9.php

JOURNAL OF EDUCATIONAL MEASUREMENT, 25, 1, 15, 1988. "ITEM DISCRIMINATION: WHEN MORE IS WORSE" BY

GEOFFEREY N. MASTERS.

“HIGH ITEM DISCRIMINATION CAN BE A SYMPTOM OF A SPECIAL KIND OF MEASUREMENT DISTURBANCE INTRODUCED BY AN ITEM THAT GIVES PERSONS OF HIGH ABILITY A SPECIAL ADVANTAGE OVER AND ABOVE THEIR HIGHER ABILITIES. THIS TYPE OF DISTURBANCE, WHICH CAN BE INTERPRETED AS A FORM OF ITEM “BIAS,” CAN BE ENCOURAGED BY METHODS THAT ROUTINELY INTERPRET HIGHLY DISCRIMINATING ITEMS AS THE “BEST” ITEMS ON A TEST AND MAY BE COMPOUNDED BY PROCEDURES THAT WEIGHT ITEMS BY THEIR DISCRIMINATION”

• THE RASCH MODEL SPECIFIES THAT ITEM DISCRIMINATION, ALSO CALLED THE ITEM SLOPE, BE UNIFORM ACROSS ITEMS. THIS SUPPORTS ADDITIVITY AND CONSTRUCT STABILITY.

• WINSTEPS ESTIMATES WHAT THE ITEM DISCRIMINATION PARAMETER WOULD HAVE BEEN IF IT HAD BEEN PARAMETERIZED. THE RASCH SLOPE IS THE AVERAGE DISCRIMINATION OF ALL THE ITEMS. IT IS NOT THE MEAN OF THE INDIVIDUAL SLOPES BECAUSE DISCRIMINATION PARAMETERS ARE NON-LINEAR. MATHEMATICALLY, THE AVERAGE SLOPE IS SET AT 1.0 WHEN THE RASCH MODEL IS FORMULATED IN LOGITS, OR 1.70 WHEN IT IS FORMULATED IN PROBITS (AS 2-PL AND 3-PL USUALLY ARE). 0.59 IS THE CONVERSION FROM LOGITS TO PROBITS.

http://www.winsteps.com/winman/discriminationestimation.htm

• THE POSSIBLE RANGE OF AI IS -∞ TO +∞, WHERE +∞ CORRESPONDS TO A GUTTMAN DATA PATTERN (PERFECT DISCRIMINATION) AND -∞ TO A REVERSED GUTTMAN PATTERN

• RASCH ESTIMATION USUALLY FORCES THE AVERAGE ITEM DISCRIMINATION TO BE NEAR 1.0. CONSEQUENTLY AN ESTIMATED DISCRIMINATION OF 1.0 ACCORDS WITH RASCH MODEL EXPECTATIONS.

• VALUES GREATER THAN 1.0 INDICATE OVER-DISCRIMINATION, AND VALUES LESS THAN 1.0 INDICATE UNDER-DISCRIMINATION. OVER-DISCRIMINATION IS THOUGHT TO BE BENEFICIAL IN MANY RAW-SCORE AND IRT ITEM ANALYSES. HIGH DISCRIMINATION USUALLY CORRESPONDS TO LOW MEAN SQUARE VALUES, AND LOW DISCRIMINATION WITH HIGH MEAN SQUARE VALUES

http://www.winsteps.com/winman/discriminationestimation.htm

• THERE ARE A NUMBER OF TECHNIQUES WHICH MAY BE USED TO DETERMINE A LOWER LIMIT BELOW WHICH THE INDEX OF DISCRIMINATION IS NOT SIGNIFICANTLY DIFFERENT FROM ZERO

• THE FIRST, AND MOST TEDIOUS, WOULD BE TO DETERMINE THE STATISTICAL SIGNIFICANCE OF THE DIFFERENCE BETWEEN TWO PROPORTIONS, THAT IS, THE DIFFERENCE BETWEEN THE PROPORTION OF THE UPPER GROUP WHO ANSWERED THE ITEM CORRECTLY AND THE PROPORTION OF THE LOWER GROUP WHO ANSWERED THE ITEM CORRECTLY.

• A THIRD METHOD OF DETERMINING THE STATISTICAL SIGNIFICANCE OF THE INDEX OF DISCRIMINATION WOULD BE TO COMPUTE ITS STANDARD ERROR. THIS MIGHT BE ACCOMPLISHED BY DOING AN ITEM ANALYSIS ON TWO SAMPLES OF A LARGE GROUP. THE RELIABILITY OF THE INDEX OF DISCRIMINATION MAY BE DETERMINED BY CORRELATING THE PAIRS OF VALUES FROM THE TWO ITEM ANALYSES. THE RULE MAY THEN BE APPLIED THAT THE INDEX OF DISCRIMINATION MUST BE MORE THAN TWICE AS LARGE AS THE STANDARD ERROR IN ORDER FOR THE INDEX TO BE STATISTICALLY DIFFERENT FROM ZERO AT THE 2.5 PERCENT LEVEL OF SIGNIFICANCE.

http://scoring.msu.edu/indexdis.html

ITEM CHARACTERISTIC CURVE

THE BASICS OF ITEM RESPONSE THEORY

BY FRANK B. BAKER• THE ITEM CHARACTERISTIC CURVE IS THE BASIC BUILDING BLOCK OF ITEM RESPONSE

THEORY; ALL THE OTHER CONSTRUCTS OF THE THEORY DEPEND UPON THIS CURVE

• THERE ARE TWO TECHNICAL PROPERTIES OF AN ITEM CHARACTERISTIC CURVE THAT ARE USED TO DESCRIBE IT. THE FIRST IS THE DIFFICULTY OF THE ITEM. UNDER ITEM RESPONSE THEORY, THE DIFFICULTY OF AN ITEM DESCRIBES WHERE THE ITEM FUNCTIONS ALONG THE ABILITY SCALE.

• THE SECOND TECHNICAL PROPERTY IS DISCRIMINATION, WHICH DESCRIBES HOW WELL AN ITEM CAN DIFFERENTIATE BETWEEN EXAMINEES HAVING ABILITIES BELOW THE ITEM LOCATION AND THOSE HAVING ABILITIES ABOVE THE ITEM LOCATION. THIS PROPERTY ESSENTIALLY REFLECTS THE STEEPNESS OF THE ITEM CHARACTERISTIC CURVE IN ITS MIDDLE SECTION. THE STEEPER THE CURVE, THE BETTER THE ITEM CAN DISCRIMINATE. THE FLATTER THE CURVE, THE LESS THE ITEM IS ABLE TO DISCRIMINATE SINCE THE PROBABILITY OF CORRECT RESPONSE AT LOW ABILITY LEVELS IS NEARLY THE SAME AS IT IS AT HIGH ABILITY LEVELS. USING THESE TWO DESCRIPTORS, ONE CAN DESCRIBE THE GENERAL FORM OF THE ITEM CHARACTERISTIC CURVE

TO THE LEFT OF THE VERTICAL LINE AT Θ = 1.5, THE PROBABILITY OF CORRECT RESPONSE IS ZERO; TO THE RIGHT OF THE LINE, THE PROBABILITY OF CORRECT RESPONSE IS 1. THUS, THE ITEM DISCRIMINATES PERFECTLY BETWEEN EXAMINEES WHOSE ABILITIES ARE ABOVE AND BELOW AN ABILITY SCORE OF 1.5

THE BASICS OF ITEM RESPONSE THEORYBY FRANK B. BAKER

4-PL IRT Item Characteristic Curve

A 4PL ITEM CHARACTERISTIC CURVE

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