Study Smart Tutors SAT Curriculum Overview and Samples

STUDY SMART TUTORS

IRT (Item Response Theory) aims to remove blind guessing from benefiting students on multiple-choice tests. What is IRT? It’s what the SAT uses. IRT on the SAT? But IDK IRT! OMG! Don’t panic; it’s really not that big of a deal. Here’s what you need to know.

IRT assesses the likelihood that a student is guessing by incorporating a “guessing parameter” (often denoted as c ) in its model. The c -parameter represents the probability that a student will correctly answer a question by guessing. IRT also assesses the likelihood that a student is guessing by examining the student’s response patterns.

c -parameter

1−𝑐 1+𝑒 −𝑎(𝜃−𝑏)

𝑃(correct) = 𝑐 +

To make sense of all of this, let’s look at a very simple example. Let’s imagine the SAT was just twelve questions 127 and compare how two different students performed.

Student 1

Student 2

Question’s Number

Question’s Difficulty

Student’s Answer

Question’s Number

Question’s Difficulty

Student’s Answer

Outcome

1 2 3 4 5 6 7 8 9

Easy Easy Easy

B A A D B C A B C A D B

Correct Correct Incorrect Correct Incorrect Correct Correct Incorrect Incorrect Correct Incorrect Incorrect

1 2 3 4 5 6 7 8 9

Easy Easy Easy

B D A D B C C B A A A A

Correct Incorrect Incorrect Correct Incorrect Correct Incorrect Incorrect Correct Correct Incorrect Correct

Medium Medium Medium Medium Medium

Hard Hard Hard

10 11 12

Really Hard

Both students missed six questions, but Student 1 would likely receive a slightly higher score. Why? Well, Student 2 got lucky: take a look at those last four questions where Student 2 just answered A every time. It just so happens that A was the correct answer for three of them! Even more suspiciously, Student 2 only answered 33% of the “easy” questions correctly yet somehow managed to get 75% of the “hard” questions right? No way. That’s like saying …

1−𝑐 1+𝑒 −𝑎(𝜃−𝑏)

“ 𝑃(𝑐𝑜𝑟𝑟𝑒𝑐𝑡) = 𝑐 +

: I got this.”

“ " 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒” = 1 2

𝑏ℎ : No can do.”

So, what’s the upshot of all of this? Don’t blindly guess. Use the process of elimination. Out of the four answer choices, you should be able to eliminate at least one of them—hopefully two. Just try your best on every question.

STRIKETHROUGH

When eliminating an answer, use the strikethrough button!

127 You wish!

131

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