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knowledge_assessment:q-matrix [2012/07/11 10:16] jpetrovic [How does a q-matrix look like?] |
knowledge_assessment:q-matrix [2012/07/11 10:31] jpetrovic [How does a q-matrix look like?] |
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==== How does a q-matrix look like? ==== | ==== How does a q-matrix look like? ==== | ||
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+ | == Matrix elements == | ||
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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+ | == Matrix example == | ||
An example of a q-matrix is shown in the following image. | An example of a q-matrix is shown in the following image. | ||
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{{ :knowledge_assessment:qm.jpg }} | {{ :knowledge_assessment:qm.jpg }} | ||
+ | == Understanding matrix values and implications == | ||
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+ | From the matrix, one can read that knowledge of concept 1 is required in order to answer correctly questions 3, 4 and 5. One can also read that questions 1 and 2 test only the knowledge of concept 2. | ||
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+ | Furthermore, one could also say that the //ideal response// of a student taking the test formed of those 5 questions who knows only concept 1 should be "00001". This is so since he does not know concept 2 which is required for questions 1 and 2 (therefore the leading "00"). Yet this concept is also required for correct ansqering of questions 3 and 4 so he can not answer those questions neither (therefore the following "00"). Finally, 5th question requires only knowledge about the concept 1 so the student can answer this question correctly (therefore the ending "1", forming all together "00001"). | ||
==== What can I do with a q-matrix? ==== | ==== What can I do with a q-matrix? ==== | ||