WARM – UP Eye Color Blue Brown Hazel 3 or below 14.0% 61.0% 25.0% 4+ 13.5% 60.8% 25.7% Blue Brown Hazel 3 or below 129 561 230 4+ 73 330 139 GPA 920 542 Determine if an association exists between ones eye color and ones GPA at a large school. Justify your answer by examining the conditional distribution of eye color among the two levels of GPA. Since the Distribution of eye color is relatively the same for each GPA level, eye color had little to do with your GPA. (No Association = Independent variables)

3rd Perioid 4th Period 5th Period A 22 64.7% 20 69.0% 66.7% B 8 23.5% 5 17.2% 8 24.2% ≤ C 4 11.8% 4 13.8% 3 9.1%

(12) students were asked their SAT Math scores: Warm – Up 2016 (12) students were asked their SAT Math scores: 600, 650, 505, 520, 800, 480, 740, 540, 630, 590, 400, 550 Construct And Describe the Histogram : HI! I’m SKEWED. …RIGHT? 0 1 2 3 4 5 FREQUENCY 400 480 560 640 720 800 880 S.A.T. MATH SCORES

Hey! I’m Approximately SYMMETRIC. HI! I’m SKEWED to the LEFT Warm – Up - 2016 COMPARE these two distributions: Hey! I’m Approximately SYMMETRIC. HI! I’m SKEWED to the LEFT 0 1 2 3 4 5 FREQUENCY 0 1 2 3 4 5 FREQUENCY 400 480 560 640 720 800 880 S.A.T. MATH SCORES 300 380 460 540 620 700 780 S.A.T. VERBAL SCORES SAT Math scores have a higher center than Verbal scores. They both have equal spread. MATH VERBAL Center: 700 > 600 Unusualness Nothing Nothing Spread: 480 = 480

Independence vs. Association Categorical Variables Ch.3 (continued) Independence vs. Association of Categorical Variables If two variables are independent then one would expect to see relatively the same distribution on the first variable among all levels of the second variable.

Gender did NOT matter = Independence = No Association! Ex.) Does Gender have any influence on Color preference? 160 people were asked to choice a color among Blue, Green, and Red. The results are shown below: Blue Green Red Male 60 24 36 Female 20 8 12 120 40 80 32 48 160 Blue Green Red All 160 50% 20% 30% Blue Green Red Male 50% 20% 30% Blue Green Red Female 50% 20% 30% Gender did NOT matter = Independence = No Association!

EXAMPLE: Which gender favors Red more Males or Females? 84 13 Blue 616 87 700 100 12% 13% Grades K - 5 Grades 6 - 12 Male Female Red 65 1 Blue 500 12 Male Female Red 19 12 Blue 116 75 565 13 11.5% 7.7% 135 87 14.1% 13.8%

SIMPSON’S PARADOX 3% 2% 1% 1.3% 3.8% 4% Simpson’s Paradox refers to a reversal of the direction of a comparison or an association when data from several groups are combined to form a single group. (and vise versa) EXAMPLE: Hospital A Hospital B Died 63 16 Survived 2037 784 Given the patients were at a particular hospital, what % died? 2100 800 3% 2% Good Condition Poor Condition Hospital A Hospital B Died 6 8 Survived 594 592 Hospital A Hospital B Died 57 8 Survived 1443 192 600 600 1% 1.3% 1500 200 3.8% 4%

Simpson’s Paradox HW: Page 40: 26,27,31,34,38 28/500 = 5.6% 30/500 =6% 3% 16% 2% 7% 28/500 = 5.6% 30/500 =6% Simpson’s Paradox

Ex.2 A concerned parent wants to send his child to a school with a great TAKS passing rate so that his child will succeed. What school should the parent consider? Jamestown HS Springfield HS Passed 1440 1760 Failed 160 240 Given the particular High schools, what % Passed TAKS? 1600 2000 90% 88% What are some ways that you can divide up the population? Regular Students AP Students Jamestown Springfield Passed 1056 810 Failed 144 90 Jamestown Springfield Passed 340 950 Failed 60 150 1200 900 88% 90% 400 1100 85% 86%