Math Released Item Algebra 2. Percent False Positives VF866689

Transcription

1 Math Released Item 2016 Algebra 2 Percent False Positives VF866689

2 Prompt

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4 Rubric Task is worth a total of 6 points, 4 points are scored using the rubric. VF Rubric Part A Score Description 2 Student response includes the following 2 elements. Computation component = 2 points o This part is machine-scored. Sample Student Response: 1 Student response includes 1 of the 2 correct tables. 0 Student response is incorrect or irrelevant.

5 VF Rubric Part B Score Description 2 Student response includes the following 2 elements. Modeling component = 2 points o Correct percent of false positives and negatives for Test R o Correct percent of false positives and negatives for Test S Sample Student Response: For Test R, the false positives are and the false negatives are For Test S, the false positives are and the false negatives are 1 Student response includes 1 of the 2 elements. 0 Student response is incorrect or irrelevant. VF Rubric Part C Score Description 2 Student response includes the following 2 elements. A valid decision that considers the relative frequency A valid decision that considers how the error impacts the patient Sample Student Response: A Decision for Test R: R has a greater chance of detecting the allergy in someone who has the allergy than S (9 out of 10 vs. 8 out of 10). The chance of a false negative is less than the chance of a false positive with test R. (1 out of 10 vs. 57 out of 190) You get more false positives with R than with S, however, a false negative is a worse error to make because if you have the allergy, you want to know so that you can be treated. False positives aren t so bad because you can always be retested to be sure about the allergy. I would choose Test R. Or a Decision for Test S: More people get a correct result with S than with R (160 vs. 142). The chance of a false positive is the same as the chance for a false negative with test S. (2 out of 8 vs. 38 out of 190). It is always better to get a correct result than an incorrect result. I would choose Test S. 1 Student response includes 1 of the 2 elements. 0 Student response is incorrect or irrelevant.

6 Anchor Set A1 A10 With Annotations

7 A1 Part B: Score Point 2 Part C: Score Point 2

8 Annotation Anchor Paper 1 Part B: Score Point 2 This response receives full credit. The student includes each of the two The correct false positives and false negatives for Test R are included (test R: false negative 10%, false positive 30%). The correct false positives and false negatives for Test S are included (test S, false negative 20%, false positive 20%). Part C: Score Point 2 This response receives full credit. The student includes each of the two A correct statement of relative frequency is included (test R because the probability of false negative is 10% less than test S). A correct consideration for error in context is provided (there is a less probability that an allergy will go undetected, and an undetected allergy has worse consequences than a falsely detected allergy).

9 A2 Part B: Score Point 2 Part C: Score Point 2

10 Annotation Anchor Paper 2 Part B: Score Point 2 This response receives full credit. The student includes each of the two The correct false positives and false negatives for Test R are included for the error in Part A (33.7% false positive in test R, 10% false negative in test R). Note that the response gives 64 positive results out of 190 people without the allergy, which is incorrect for Part A. However, based on this error the percentage of false positives for Test R is correct. A scoring decision was made stating that if an error is made in an earlier part (Part A) but is used correctly in a later part (Part B) credit can still be given to the later part (Part B) since the point was already deducted from the earlier part (Part A) wherein the error occurred. The correct false positives and false negatives for Test S are included (20% false positive in test S, 20% false negative in test S). Part C: Score Point 2 This response receives full credit. The student includes each of the two A correct statement of relative frequency is included (test R... it only has a 10% chance of being false negative. While test S has a 20% chance of being... false negative). A correct consideration for error in context is provided (it is beter to think you have an allergy and treat it then to think you do not have a allergy and not treat it).

11 A3 Part B: Score Point 2 Part C: Score Point 1

12 Annotation Anchor Paper 3 Part B: Score Point 2 This response receives full credit. The student includes each of the two The correct false positives and false negatives for Test R are included (r false positives are 30% and negativs are 10%). The correct false positives and false negatives for Test S are included (s false postives are 20% adn there false negatives are 20%). Part C: Score Point 1 This response receives partial credit. The student includes one of the two A correct statement of relative frequency is included (r for it had a fewer false negative precent). A consideration for error in context is missing.

13 A4 Part B: Score Point 1 Part C: Score Point 2

14 Annotation Anchor Paper 4 Part B: Score Point 1 This response receives partial credit. The student includes one of the two The correct false positives and false negatives for Test S are included (Test S:False Postive: 20%, False Negative: 20%). The false positives and false negatives given for Test R are incorrect (Test R: False Postive: 1%, False Negative: 70%). The correct numbers would be 30% for false positive and 10% for false negative. Part C: Score Point 2 This response receives full credit. The student includes each of the two A correct statement of relative frequency is included (the S Test because it has a 20% false positive and false negative. Test R has a... large false negative). A correct consideration for error in context is provided (Test R has a... large false negative that could mistake someone for not having an allergy).

15 A5 Part B: Score Point 1 Part C: Score Point 1

16 Annotation Anchor Paper 5 Part B: Score Point 1 This response receives partial credit. The student includes one of the two required elements with a mathematical imprecision. The correct false positives and false negatives for Test S are included (test S false positives is.2, test S false negatives is.2). The false positives and false negatives given for Test R are incorrect (test R false positives is.1, test R false negatives is.3). The numbers are reversed. Note that answers given as probability when percentages are asked for is considered mathematically imprecise. Had this been a top score response (2/2), one score point would have been deducted from Part B. As this is not a top score response, no points are deducted from the score here. Part C: Score Point 1 This response receives partial credit. The student includes one of the two A correct statement of relative frequency is included (test R because the probability of it being positive while true is higher at.9 and the probability of it being negative while not true is lower at.7). A consideration for error in context is missing.

17 A6 Part B: Score Point 0 Part C: Score Point 2

18 Annotation Anchor Paper 6 Part B: Score Point 0 This response receives no credit. The student includes neither of the two The false positives and false negatives for Test R are incorrect (90% for R). Only one percentage is given and it is not identified as a false positive or a false negative. The false positives and false negatives for Test S are incorrect (80% for S). Only one percentage is given and it is not identified as a false positive or a false negative. Part C: Score Point 2 This response receives full credit. The student includes each of the two A correct statement of relative frequency is included (test R because there are less false negatives). This is an acceptable answer based on the information given in Part A since the information given in Part B does not identify the percentages given as false negatives. A correct consideration for error in context is provided (if people have a severe alergie asnd are tested negative for it then they could end up geetting harmed or dieing from not knowing they had an alergy. it s better to think you have an alergy that you dont have than to not know you have one at all).

19 A7 Part B: Score Point 1 Part C: Score Point 0

20 Annotation Anchor Paper 7 Part B: Score Point 1 This response receives partial credit. The student includes one of the two The correct false positives and false negatives for Test S are included (Test S: false positive: 20%, false negative:20%). The false positives and false negatives given for Test R are incorrect (test R: false positive: 10%, false negative: 30%). The numbers are reversed. Part C: Score Point 0 This response receives no credit. The student includes neither of the two An incorrect statement of relative frequency is included (test S because there was a less false % for test S). The response does not identify which false percentage it refers to. A consideration for error in context is missing.

21 A8 Part B: Score Point 0 Part C: Score Point 1

22 Annotation Anchor Paper 8 Part B: Score Point 0 This response receives no credit. The student includes neither of the two required elements with a mathematical imprecision. The false positives and false negatives for Test R are incorrect [.665 false positive (r),.005 false negative (r)]. The false positives and false negatives for Test S are incorrect [.76 false positive (s),.01 false negative (s)]. Note that answers given as probability when percentages are asked for is considered mathematically imprecise. Had this been a top score response (2/2), one score point would have been deducted from Part B. As this is not a top score response, no points are deducted from the score here. Part C: Score Point 1 This response receives partial credit. The student includes one of the two A correct statement of relative frequency based on incorrect information given in Part B is included (test R because it had both less false positives and less false negatives). A scoring decision was made stating that if an error is made in an earlier part (Part B) but is used correctly in a later part (Part C) credit can still be given to the later part (Part C) since the point was already deducted from the earlier part (Part B) wherein the error occurred. A consideration for error in context is missing.

23 A9 Part B: Score Point 0 Part C: Score Point 0

24 Annotation Anchor Paper 9 Part B: Score Point 0 This response receives no credit. The student includes neither of the two The false positives and false negatives for Test R are incorrect (false positive in R = 28.5%, false negative in R = 0.5%). The false positives and false negatives for Test S are incorrect (false positive in S = 19%, false negative in S = 1%). Part C: Score Point 0 This response receives no credit. The student includes neither of the two An incorrect statement of relative frequency is included (I will choose S which 20% error). This statement demonstrates a lack of understanding of the task by adding the percentage of false positives to the percentage of false negatives. A comparison to Test R is implied, however. A consideration for error in context is missing.

25 A10 Part B: Score Point 0 Part C: Score Point 0

26 Annotation Anchor Paper 10 Part B: Score Point 0 This response receives no credit. The student includes neither of the two The false positives and false negatives for both tests are incorrect (.3%,.1%). Only two percentages are given and neither is identified as being a false positive or a false negative or as being the result of a particular test. Part C: Score Point 0 This response receives no credit. The student includes neither of the two An incorrect statement of relative frequency is included (Test R because it seems to be more accurate). The response does not specify how Test R is more accurate than Test S. A consideration for error in context is missing.

27 Practice Set P101 - P105 No Annotations Included

28 P101

29 P102

30 P103

31 P104

32 P105

33 Practice Set Paper Score P101 2,0 P102 0,0 P103 1,0 P104 1,2 P105 1,2