Hi,
I read an article from Kathleen F. Janz, Elena M. Lutuchy, Phyllis Wenthe and Steven M. Levy called Measuring Activity in Children and Adolescents Using Self-Report: PAQ-C and PAQ-A.
They rescaled question 1 regarding this formula: Q1rescaled = 4(q1 - 1)/(1.7(max raw score) - 1) + 1. Does somebody any idea why? And could me somebody help to understand this formula?
It's unclear for me... Thanks. Marcela
When I look at the formula, I see two things:
1) Obviously the item q1 of a questionnaire consisting of x items has a range from 1 to 1.7
2) All other items of the questionnaire must have had a range from 1 to 5.
Am I right? Because item q1 is rescaled by the formula to a value between 1 and 5.
The easiest way to understand is an example. A scale from 1 to 5 has an average scale value of 3. A scale from 1 to 1.7 has a mean scale value of 1.35. If you now insert 1.35 for q1 in the formula, you will get a result of 3. This checks out.
So I commit myself: the questionnaire item q1 has a range from 1 to 1.7 and the formula transforms it into the range of all other items, namely from 1 to 5. Do you have the original article and can you please check the item ranges?
The researchers were taking steps to make the question comparable to the rest of the questionnaire. As Albert Ziegler stated above, they are converting it to the same 1 -- 5 scale as the other questions.
From the article, Page 769: "The revised scoring strategy also included a rescaling of question 1 to reflect a range consistent with the other questions."
Page 769: "PAQ-A questionnaire responses ranged from 1 to 5 for all items except Q1, which ranged from 1 to 1.7."
Page 770: "Question 1 was rescaled so that it contributed to the summary score similarly to the other PAQ-A questions."
Page 770: "When these questions were eliminated and question 1 was rescaled so that it contributed to the summary score similarly to the other PAQ-A questions, associations between the PAQ-A (revised) summary score and the activity monitor variables were rho = 0.56 for total PA and rho = 0.63 for MVPA."
Page 771: "We also improved the validity of the PAQ-A by rescaling an item (Q1) that was strongly associated with the activity monitor (rho = 0.63)."
So, the rescaling seems to have worked in terms of providing stronger associations, and thereby more evidence of validity for the self-report instruments. Another way to say this is that their rescaling technique has apparently reduced bias toward the null hypothesis.
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