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2010

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Statistics2 ppt Statistics2 ppt Presentation Transcript

  • Determining RCHS Superiority in AP Test Scores Katherine Hobbs Elle Law
  • RCHS students often do better than students in the state/nation…
    • Ranked 20th in the nation among top high schools
    • Champions of Wake County Psychology Bowl
    • 2009 Science Olympiad Nationals 10th Place
    • Undefeated Quiz Bowl State Champions in the history of Quiz Bowl
    • 2009 Ocean Science Bowl Nationals 7th Place
    • Etc.
    • … does this apply to AP exam scores as well?
  • Did RCHS students score higher on the AP Calculus AB exam than other students in the nation in 2009?
    • Is the distribution of scores on the AP Calculus AB exam achieved by RCHS students in 2009 the same or different from the distribution for all students who took it in 2009?
    • Data
    Did RCHS students score higher on the AP Calculus AB exam than other students in the nation in 2009? Total: 47 students 0 1 0 2 7 3 7 4 33 5 # of Students at Raleigh Charter Score on AP Calculus AB 1.50 Standard Deviation 2.99 Mean Grade 59.5 137,265 3 or Higher / % 230,588 # of Students Total 24.9 57,480 1 15.5 35,843 2 17.9 41,204 3 18.7 43,140 4 23.0 52,921 5 % at # of students nationwide Score on AP Calculus AB
    • H 0 : The score distribution for RCHS students and for students nationwide on the 2009 AP Calculus AB exam is the same.
    • H A : The score distribution for RCHS students and for students nationwide on the 2009 AP Calculus AB exam is not the same.
    Did RCHS students score higher on the AP Calculus AB exam than other students in the nation in 2009?
    • Hypothesis
        • 1. Counted Data Condition: We have counts of the number of RHCS students in categories.
        • 2. Randomization Condition: We are not inferring beyond RCHS AP Calculus AB students taking the AP Calculus AB test in 2009, so randomization isn’t necessary to draw conclusions about the RCHS AP Calculus AB test- takers.
        • 3. Expected Cell Frequency Condition: All of the expected cell frequencies are greater than 5.
        • 4. Independence Assumption: We assume that students’ scores are independent.
    Did RCHS students score higher on the AP Calculus AB exam than other students in the nation in 2009?
    • Assumptions/Conditions
    <---- no cheating!
    • Conditions are met!!!!!!
    • Under these conditions, the sampling test statistic is χ 2 with 5 – 1 = 4 degrees of freedom.
    • We will do a chi-squared goodness-of-fit test!
    Did RCHS students score higher on the AP Calculus AB exam than other students in the nation in 2009?
  • Chi-squared goodness-of-fit test = 65.140 for all 5 scores P = P (χ 2 > 65.140) = 2.405 * 10 -13
  • Conclusion:
    • With the low P-value of 2.405x10 -13 we reject our null hypothesis and conclude the score distribution for RCHS on the 2009 AP Calculus AB exam is different from the distribution for all of the students nationwide who took the 2009 AP Calculus AB test.
    In a parallel universe where correlation = causation , this would mean Mr. Wajima/Felder are superior teachers.
    • Is the distribution of scores on the AP English and Language exam achieved by RCHS students in 2009 is the same or different from the distribution for all students who took it in 2009?
    Did RCHS students score higher on the AP English and Language exam than other students in the nation in 2009?
    • Data
    Did RCHS students score higher on the AP English Language exam than other students in the nation in 2009? Total: 69 students 0 1 1 2 11 3 22 4 35 5 # of Students at Raleigh Charter Score on AP English Language 1.16 Standard Deviation 2.88 Mean Grade 59.7 201,446 3 or Higher / % 337,441 # of students 11.9 40,256 1 28.4 95,739 2 30.2 101,995 3 19.0 64,138 4 10.5 35,313 5 % at # of students nationwide Score on AP English Language
    • H o : The score distribution for RCHS students and that of students nationwide on the 2009 AP English Language exam is the same.
    • H A : The score distribution for RCHS students and that of students nationwide on the 2009 AP English Language exam is not the same.
    Did RCHS students score higher on the AP English and Language exam than other students in the nation in 2009?
    • Hypothesis
  • Did RCHS students score higher on the AP English and Language exam than other students in the nation in 2009?
  • Did RCHS students score higher on the AP English and Language exam than other students in the nation in 2009?
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  • Question 2: Did RCHS students score better in the AP English Language or AP Calculus AB exam in 2009?
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    • You may have noticed earlier that the RCHS accomplishments listed earlier were mostly science/math related. How do RCHS students score on AP Calculus AB compared to AP English and Language?