Saturday, November 27, 2010

Guttman Scalogram

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The information in Ministep Table 22.1 Guttman Scalogram of Responses has been re-plotted, to the right, into a perfect Guttman pattern. A string of right marks is followed by a string of wrong marks. In this perfect pattern, when a student misses a question on the test, all questions that are more difficult are also missed. The easiest question the student misses sets the student's ability. 

[Winsteps Table 22.2 Guttman Scalogram of Zoned Responses adds more information to PUP Table 3. 
Observations more than 0.5 rating points away from their expected category are marked with a letter equivalent: @ = 0, in expected category, and A = 1, just outside of expected category. 

The observations that are outside of their expected category are plotted in blue in this not so perfect world. Each blue mark shows a right answer assumed to be too difficult for that student. Green is both an unexpected and a too difficult right response. Only Item 20 shows a perfect performance pattern.

Otherwise there is a mix of right and wrong marks at the boundary of a student knowing and not knowing, and of a question being marked right or wrong, on PUP Table 3. Table 22.3 Guttman Scalogram of Original Responses is identical, in content, to PUP Table 3. PUP Table 3 is a Guttman Scalogram. 

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