1. 4.2 Relationships between Categorical Variables and Simpson’s Paradox

2. Categorical Variables
two-way table—describes 2 categorical variables; each entry can only appear once
Instagram
Twitter
Snapchat
Other
Total
Boys
Girls
Sex and Social Media are the 2 categorical variables

3. Which is a two way table? Died TOTAL Hospital A 30 100 Hospital B 3868
200
Hospital vs Result of Life
Gender vs Type of Car

4. Marginal Distribution
describes only one of the categorical variables (look at MARGINS) % are better for marginal distributions
Instagram
Twitter
Snapchat
Other
Total
Boys
Girls
Ex: Percent on social media

5. Conditional Distributions
finding percents for just one row or a column
Instagram
Twitter
Snapchat
Other
Total
Boys
Girls
Percent of Boys on: Instagram/Twitter/Snapchat/Other

6. Categorical Variables
1. What % of girls like Instagram?
2. What % of Twitter fans are boys?
3. What % of boys are Twitter fans?

7. Simpson’s Paradox
1st Half
2nd Half
Total
Player A
4/10
.400
25/100
.250
29/110
.264
Player B
35/100
.350
2/10
.200
37/110
.337
Simpson’s Paradox—an association or comparison that holds for all or several groups can reverse direction when combined to form a single group

9. Simpson’s Paradox LP RP Avg Andre Dawson .346 .283 .299 Lee Lacy .336
.266
.302
Dawson had a higher average against both left handed pitchers and right handed pitchers, but together had a lower average for the year. This is another example of Simpson’s Paradox

10. Exit Slip
Create a side by side bar graph of the two way table “Sex vs Social Media”

11. HW: pg 301 #29; pg 303 #36-38