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Correction for Guessing1

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Correction for Guessing1

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    1. Correction for Guessing1 Dr. Scott McDaniel Middle Tennessee State University

    2. What if… Suppose you gave a Quantum Mechanics multiple choice test a 20 question test that has 4 options to a 6 year old. There is about a 40% chance that they score at least a 30 on the test just by guessing.

    3. Adjustments There is a way to compensate for students’ guessing on tests. That is, there is a mathematical way to adjust or correct for guessing.

    4. The Concept The more questions an person missed, the more like they were to guess on ones that they got right.

    5. The Model Some Assumptions: The person tested either has the knowledge to answer it correctly doesn't. With the knowledge the person will answer correctly; without the knowledge the person will guess. Each incorrect response was the result of a random guess (among all options given).

    6. Standard Correction Formula

    7. Standard Correction Formula

    8. Standard Correction Formula

    9. Example Suppose that k = 4.

    10. Standard Correction Formula The number guessed at is larger than the number wrong because some of the guesses will turn out correct.

    11. Standard Correction Formula

    12. The logarithmic correction

    13. The logarithmic correction

    14. Example w/ Average Correction Suppose we administer a 25 item test with 17 right answers and 8 wrong answers. Each answer has 4 choices (k = 4).The corrected score using the average formula is

    15. Example w/ Log Correction

    16. Compare Let’s compare the 3: No Correction: 68 Standard Correction: 57 Log Correction: 48

    17. Why? The reasons on why we do the corrections: The standard correction takes into account that if students miss more problems, they probably got some correct that they guessed on The log correction takes into account that students may be able to eliminate poor distractors. We integrate to find the average function.

    18. Item Analysis Determining the difficulty level of an item

    19. Example Suppose 25 students took a test. You look at item 12 and notice that 15 students answered it correctly.

    20. Rule of Thumb for Difficulty Level

    21. Item Difficulty: Correction Factor

    22. Example Suppose 20 students took a multiple choice test with 4 choices. Suppose one of the questions had 12 wrong answers and 8 right ones. We obtain the following:

    23. Discrimination Index (DI) Degree to which item discriminates between students with high and low achievement. This is calculated for each question. We may use the following formula when doing this by hand:

    24. Discrimination Index (DI)

    25. Example:

    26. Discriminatory Index

    27. Example from Computer (WebCT)

    28. Note Item and discrimination analysis is best used on Norm Reference test, not Criterion Reference tests. They can be used but not nearly as important.

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