1. Quick review of last time~
In 2007, deaths of a large number of pet dogs and cats were ultimately traced to contamination of some brands of pet food. The manufacturer NOW claims that the food is safe, but before it can be released, an experiment to test whether the food is now safe for dogs and cats to eat must be conducted.

2. Quick review of last time~
A group of 32 dog owners have volunteered their pets for this experimental study. Of the 32 dogs, 16 are poodles and 16 are German shepherds. The dogs will eat the assigned food for a period of 6 weeks.
We believe that because of differences in body size, the two different breeds may be affected differently by potential contaminants in the dog food.
Explain how you would carry out a completely randomized experiment to see if the new food is safe for dogs to eat.

3. Completely* randomized experiment: What is the FIRST thing we do?
Remember: completely randomized experiment means NO BLOCKING ALLOWED!!!
Group 1:
16 dogs
Treatment 1:
Dogs eat new food for 6 weeks
Group 2:
Treatment 2:
Dogs eat “safe” food for 6 weeks
Compare health of dogs, to be evaluated by veterinarian
RANDOM ASSIGNMENT
Group of 32 dogs

4. Remember: you MUST explain how units were randomly assigned to treatment groups!!!
We will number the dogs from 01 to 32, then use a random number generator (or table) to select 16 dogs (ignoring repeated numbers) for treatment group 1 (new food from the company). The rest of the dogs will be placed in treatment group 2 (“safe” food).
AP Grading Criteria: If two knowledgeable statistics users read your description, will they use the same method to assign experimental units to treatments?

5. Of the 32 dogs, 16 are poodles and 16 are German shepherds (we believe different breeds may react differently to contaminants in the food). Explain the changes you would make to your previous design by incorporating blocking.

6. Randomized Block Experiment
Group 1:
8 dogs
Treatment 1
Dogs eat new food for 6 weeks
RANDOM
Block A:
16 poodles
Compare health of dogs
Treatment 2
Dogs eat “safe” food for 6 weeks
Group 2:
8 dogs
BLOCK BY
BREED
32 dogs
Group 3:
8 dogs
Treatment 1
Dogs eat new food for 6 weeks
RANDOM
Block B:
16 German shepherds
Compare health of dogs
Group 4:
8 dogs
Treatment 2
Dogs eat “safe” food for 6 weeks

7. One last major point:
NEVER call your subjects a “random sample” unless you KNOW for a FACT that they really were a random sample of the population.
With experiments, you are almost always dealing with VOLUNTEERS (think about it!)
Treatment 1:
Patient takes the new pill
Group 1:
20 patients
RANDOM ASSIGNMENT
Group of 40 volunteers
Compare numbers of headaches…
Group 2:
20 patients
Control:
Patient gets placebo

8. Matched pairs a special type of block design
pair up experimental units according to similar characteristics
randomly assign one to one treatment & the other automatically gets the 2nd treatment
Or have each unit do both treatments in random order (such as before/after, or a taste test with Coke/Pepsi)
the assignment of treatments is dependent

9. Pair experimental units according to specific characteristics.
Treatment A
Treatment B
Next, randomly assign one unit from a pair to Treatment A. The other unit gets Treatment B.
Pair experimental units according to specific characteristics.
This is one way to do a matched pairs design – another way is to have each individual unit do both treatments (as in a taste test).

10. Treatment A
Do not write:
If we flip “heads”, then ALL of the #1’s get treatment A (and ALL of the #2’s get treatment B)…
You must give each #1 (and #2) a fair chance of going either way.
Treatment B
In each pair, assign one unit the number “1” and the other the # “2”.
In each block (pair), we will flip a fair coin such that if the side of the coin facing up is…
“heads”, #1 will get treatment A (and #2 will get treatment B)
“tails”, #2 will get treatment A (and #1 will get treatment B)
Just make sure you flip a coin for EACH pair!

11. (shampoo worksheet)

12. Displaying and Describing
Categorical Data
Chapter 3
grade level?
color of hair
types of cars
gender

13. The Three Rules of Data Analysis
The three rules of data analysis won’t be difficult to remember:
Make a picture — things may be revealed that are not obvious in the raw data. These will be things to think about.
Make a picture — important features of and patterns in the data will show up. You may also see things that you did not expect.
Make a picture — the best way to tell others about your data is with a well-chosen picture.

16. Launched:. 31st May 1911 Builders:. Harland and Wolff,
Launched: 31st May 1911 Builders: Harland and Wolff, Belfast Port of Registry: Liverpool   Passengers Lost: 818 (62%) Crew Lost: (77%) Total Lost: 1,502 (68%)

17. Frequency Tables: Making Piles
Records counts and category names.

18. Relative Frequency Tables
Percentages (proportions) instead of counts.

19. Distribution: name of categories and how frequently each occurs
Both describe the distribution of a categorical variable.
Distribution: name of categories and how frequently each occurs
Frequency distribution
Relative frequency distribution

20. this is a Violation of the “Area Principle”
What do you see?
this is a Violation of the “Area Principle”
When we look at each ship, we see the area taken up by the ship, instead of the length of the ship.

21. Bar Charts
A bar chart displays the distribution of a categorical variable, showing the counts for each category next to each other for easy comparison.
A bar chart stays true to the area principle.
For bar charts (with categorical data), be sure to leave spaces between the bars!!!

22. Bar Charts
A relative frequency bar chart displays the relative proportion of counts for each category.

23. Pie Charts When you are interested in parts of the whole,
a pie chart might be your display of choice.

24. What Can Go Wrong?
While some people might like the pie chart on the left better, it is harder to compare fractions of the whole, which a well-done pie chart does.

25. What Can Go Wrong?
This plot of the percentage of high-school students who engage in specified dangerous behaviors has a problem. Can you see it?
if you are making a pie chart with percentages (or proportions), make sure the percentages add up to 100%!!!

26. back to the Titanic…

27. Class Survival marginal distributions
A contingency table allows us to look at two categorical variables together.
Class
First
Second
Third
Crew
Total
Alive
203
118
178
212
711
Dead
122
167
528
673
1490
325
285
706
885
2201
Survival
marginal distributions

28. What percent of the people on the Titanic died?
What percent of the people were surviving crew?
*What percent of the survivors were First class?
*What percent of First class survived?
1490/2201 = 67.7%
212/2201 = 9.6%
203/711 = 28.6%
203/325 = 62.5%

29. A conditional distribution shows the distribution of one variable for just the individuals who satisfy some condition on another variable.

30. Conditional Distributions
The conditional distributions tell us that there is a difference in class for those who survived and those who perished.
Pie charts
of the two distributions:

31. so class and survival are associated (they are dependent).
We see that the distribution of Class for the survivors is different from that of the non-survivors…
so class and survival are associated (they are dependent).

32. independent = no association dependent = association
The variables would be considered independent if the distribution of one variable were the same for all categories of the other variable.
independent = no association
dependent = association

33. Segmented Bar Charts
A segmented bar chart displays the same information as a pie chart, but in the form of bars instead of circles.
Proportion

34. Level of Education Gender gender is independent of level of education.
Here’s a look at gender versus level of education in the fictitious town of Podunk (home of Podunk University!)
The distributions for each gender are the same, so
gender is independent of level of education.
(no association)
Level of Education
Not High School Graduate
High School Graduate*
College Graduate
Total
Male
318
29.3%
603
55.5%
165
15.2%
1086
100%
Female
212
402
110
724
530
1005
325
1800
Gender
*and not a college graduate

35. Podunk – Level of Education by Gender
College
Graduate
College
Graduate
Not High School Graduate
High School Graduate*
College Graduate
Total
Male
318
29.3%
603
55.5%
165
15.2%
1086
100%
Female
212
402
110
724
530
1005
325
1800
High
School
Graduate
(but not
college
grad)
High
School
Graduate
(but not
college
grad)
Gender is independent of level of education (no association)
Not High
School
Graduate
Not High
School
Graduate
Male
Female

36. In which region do the greatest number of people wear seatbelts?

37. Note: we are using the word “proportion” (or “percentage”)… …NOT the word “number”
Overall, the bar chart shows that all four regions of the country have more than 60% of car drivers wearing seat belts.
The Midwest has the smallest proportion of car drivers wearing seat belts (about 62%) where the South and West have the largest proportion (about %).

38. What Can Go Wrong? Be sure to use enough individuals!
Do not make a report like “We found that
66.67% of the rats improved their performance with training.
The other rat died.”

39. What Can Go Wrong? (cont.)
Don’t use unfair or silly averages~

40. we need data for next time!
(average hair length)