A study of item response theory equating with an anchor test design.
George A. Johanson · Scholarworks (University of Massachusetts Amherst) · 2023
1 1.1 Introduction . .;. IX 3.2.7 Stages Required for LOGIST Convergence with Combined Groups (Concurrent) .34 4.2.1 Mean Scores and Error for Equating Method Versus Anchor Length in Populations with a 10% Ability Overlap.54 4.2.2LOGIST Estimates of Anchor Item Difficulties in the 10% Ability Overlap Population.55 4.2.3Estimated Equating Constants in the 10% Ability Overlap with a 25 Item Anchor Test.57 4.2.4Estimated Equating Constants in the 10% Ability Overlap with a 13 Item Anchor Test.58 4.2.5Estimated Equating Constants in the 10% Ability Overlap with a 7 Item Anchor Test.59 4.2.6Estimated Equating Constants in the 10% Ability Overlap with a 4 I tern Anchor Test.60 4.2.7 Mean Squared Error for Equating Method Versus Anchor Length in Population with a 30% Ability Overlap .xi 64 4.2.8LOGIST Estimates of Anchor Item Difficulties in the 30% Ability Overlap Population 4.2.9Estimated Equating Constants in the 30% Ability Overlap with a 25 Item Anchor Test 4.2.10Estimated Equating Constants in the 30% Ability Overlap with a 13 Item Anchor Test .4.2.11Estimated Equating Constants in the 30% Ability Overlap with a 7 Item Anchor Test 4.2.12Estimated Equating Constants in the 30% Ability Overlap with a 4 Item Anchor Test .4.2.13Mean Squared Error for Equating Method Verses Anchor Length in Populations with a 50% Abi 1 ity Overlap . .4.2.14 LOGIST Estimates of Anchor Item Difficulties in the 50% Ability Overlap Population . . .4.2.15Estimated Equating Constants in the 50% Ability Overlap with a 25 Item Anchor Test .4.2.16Estimated Equating Constants in the 50% Ability Overlap with a 13 Item Anchor Test .4.2.17Estimated Equating Constants in the 50% Ability Overlap with a 7 Item Anchor Test . .4.2.18Estimated Equating Constants in the 50% Ability Overlap with a 4 Item Anchor Test . .66 73 74 75 77 78 80 81 82 83 4.3.1 Mean Squared Error for Anchor Length Verses Ability Overlap with a Concurrent Equating .85 4.3.2Mean Squared Error for Anchor Length Verses Ability Overlap with a CharacteriStic Curve Equating.89 4.3.3Mean Squared Error for Anchor Length Verses Ability Overlap with a Mean and Sigma Equating .... 91 4.3.4Mean Squared Error for Anchor Length Verses Ability Overlap with an Orthogonal Least Squares Equating .xii 93 4.3.5 4.4.1 4.4.24.4.34.4.44.4.5 Mean Squared Error for Anchor Length Verses Ability Overlap with an Ordinary Least Squared Equating .Mean Squared Error for Equating Method Verses Ability Overlap with an Anchor Length of 25 .Mean Squared Error for Equating Method Verses Ability Overlap with an Anchor Length of 13 ..• .. Mean Squared Error for Equating Method Verses Ability Overlap with an Anchor Length of 7 .Mean Squared Error for Equating Method Verses Ability Overlap with an Anchor Length of 4 .Parameter Estimation Error (PEE) for Anchor Length Verses Population Ability Overlap .95 96 98 99