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.

 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.

Group of 32 dogs Group 1: 16 dogs Treatment 1: Dogs eat new food for 6 weeks Group 2: 16 dogs Treatment 2: Dogs eat “safe” food for 6 weeks Compare health of dogs, to be evaluated by veterinarian completely NO BLOCKING ALLOWED!!! Remember: completely randomized experiment means NO BLOCKING ALLOWED!!!

 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?

incorporating blocking. 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.

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

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

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 Matched pairs a special type of block design

randomly Next, randomly assign one unit from a pair to Treatment A. The other unit gets Treatment B. Treatment A Treatment B 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). Pair according to specific characteristics Pair experimental units according to specific characteristics.

Treatment A 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”“heads”, #1 will get treatment A (and #2 will get treatment B) “tails”“tails”, #2 will get treatment A (and #1 will get treatment B) 1 2 Just make sure you flip a coin for EACH pair! Do not write: ALLIf we flip “heads”, then ALL of the #1’s get treatment A (and ALL of the #2’s get treatment B) … fair chance of going either wayYou must give each #1 (and #2) a fair chance of going either way. Do not write: ALLIf we flip “heads”, then ALL of the #1’s get treatment A (and ALL of the #2’s get treatment B) … fair chance of going either wayYou must give each #1 (and #2) a fair chance of going either way.

(shampoo worksheet)

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

Slide The Three Rules of Data Analysis The three rules of data analysis won’t be difficult to remember: 1. Make a picture 1. Make a picture — things may be revealed that are not obvious in the raw data. These will be things to think about. 2. Make a picture 2. Make a picture — important features of and patterns in the data will show up. You may also see things that you did not expect. 3. Make a picture 3. Make a picture — the best way to tell others about your data is with a well-chosen picture.

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Slide Launched: 31st May 1911 Builders: Harland and Wolff, Belfast Port of Registry: Liverpool Passengers Lost: 818 (62%) Crew Lost: 684 (77%) Total Lost: 1,502 (68%)

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

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

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

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

Slide 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. spaces For bar charts (with categorical data), be sure to leave spaces between the bars !!!

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

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

Slide 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. What Can Go Wrong?

Slide 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? percentages make sure the percentages add up to 100%!!! if you are making a pie chart with percentages (or proportions), make sure the percentages add up to 100%!!!

back to the Titanic…

Slide contingency table A contingency table allows us to look at two categorical variables together. FirstSecondThirdCrewTotal Alive Dead Total Class Survival marginal distributions

Slide 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%

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

Slide 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:

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

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

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

Slide Here’s a look at gender versus level of education in the fictitious town of Podunk (home of Podunk University!) Not High School Graduate High School Graduate* College GraduateTotal Male % % % % Female % % % % Total % % % % Level of Education Gender The distributions for each gender are the same, so gender independent level of education gender is independent of level of education. The distributions for each gender are the same, so gender independent level of education gender is independent of level of education. *and not a college graduate (no association)

Slide Podunk – Level of Education by Gender Not High School Graduate High School Graduate* College Graduate Total Male % % % % Female % % % % Total % % % % Not High School Graduate MaleFemale High School Graduate (but not college grad) College Graduate Not High School Graduate High School Graduate (but not college grad) College Graduate independent no Gender is independent of level of education (no association)

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

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

Slide 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.”

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

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