1. 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)

2. 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%

3. (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?
FREQUENCY
S.A.T. MATH SCORES

4. Hey! I’m Approximately SYMMETRIC. HI! I’m SKEWED to the LEFT
Warm – Up
COMPARE these two distributions:
Hey! I’m Approximately SYMMETRIC.
HI! I’m SKEWED to the LEFT
FREQUENCY
FREQUENCY
S.A.T. MATH SCORES
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

5. 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.

6. 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!

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

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
Survived
Given the patients were at a particular hospital, what % died?
3% %
Good Condition
Poor Condition
Hospital A Hospital B
Died
Survived
Hospital A Hospital B
Died
Survived
1% %
3.8% 4%

9. 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

12. 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
Failed
Given the particular High schools, what % Passed TAKS?
90% %
What are some ways that you can divide up the population?
Regular Students
AP Students
Jamestown Springfield
Passed
Failed
Jamestown Springfield
Passed
Failed
88% %
85% 86%