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--- knowledge_assessment:q-matrix [2012/07/05 14:41]
jpetrovic
+++ knowledge_assessment:q-matrix [2012/07/11 10:31]
jpetrovic [How does a q-matrix look like?]
@@ Line 1: / Line 1: @@
-Q-matrix is a
+==== What is a q-matrix? ====
+Q-matrix is a matrix describing relations of questions and concepts required for their understanding. It is a domain-independent model of knowledge represented by a binary matrix showing the relationship between test items and latent or underlying attributes, or concepts.
+==== How does a q-matrix look like? ====
+== 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.
+== Matrix example ==
+An example of a q-matrix is shown in the following image.
+{{  :knowledge_assessment:qm.jpg  }}
+== Understanding the matrix values and implications ==
+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.
+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? ====
+==== How do I create a q-matrx? ====
    * "//method, which examines the inputs of many students to automatically extract relationships between questions and underlying concepts, and then uses those relationships in diagnosing and correcting student misconceptions.//"
    * domain-independent knowledge model
@@ Line 5: / Line 31: @@
    * 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.

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