knowledge_assessment:q-matrix
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knowledge_assessment:q-matrix [2012/07/11 10:02] jpetrovic [What is a q-matrix?] |
knowledge_assessment:q-matrix [2012/07/11 10:15] jpetrovic [How does a q-matrix look like?] |
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| Q-matrix is a M//x//N matrix, where M equals the number of questions in an assessment, and N equals the total number of concepts required for understanding all questions. The matrix element A[i,j] equals 1 if the i-th concept is required for correctly answering j-th question and 0 if the i-th concept is NOT required for correctly answering j-th question. Alternatively, matrix values can be not just {0,1}, but real numbers from the interval [0,1], describing the probability that a student who knows i-th concept will correctly answer j-th question. | Q-matrix is a M//x//N matrix, where M equals the number of questions in an assessment, and N equals the total number of concepts required for understanding all questions. The matrix element A[i,j] equals 1 if the i-th concept is required for correctly answering j-th question and 0 if the i-th concept is NOT required for correctly answering j-th question. Alternatively, matrix values can be not just {0,1}, but real numbers from the interval [0,1], describing the probability that a student who knows i-th concept will correctly answer j-th question. | ||
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| + | An example of a q-matrix is shown in the following image. | ||
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| + | {{:knowledge_assessment:qm.jpg}} | ||
| ==== What can I do with a q-matrix? ==== | ==== What can I do with a q-matrix? ==== | ||
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| * To build the q-matrix, experts constructed a relationship between test questions and concepts (referred to as attributes) and students taking the test were assigned knowledge states based on their test answers and the constructed q-matrix ((see Ham85 for a discussion of item-response theory)) | * To build the q-matrix, experts constructed a relationship between test questions and concepts (referred to as attributes) and students taking the test were assigned knowledge states based on their test answers and the constructed q-matrix ((see Ham85 for a discussion of item-response theory)) | ||
| - | {{:knowledge_assessment:qm.jpg}} | + | |
| The goal of q-matrix construction is to extract underlying, or latent, variables, which account for studentsí differential performance on questions. | The goal of q-matrix construction is to extract underlying, or latent, variables, which account for studentsí differential performance on questions. | ||
knowledge_assessment/q-matrix.txt · Last modified: 2023/06/19 18:03 (external edit)
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