Warm Up One day Dr. Lutze decides he wants to randomly assign his first period students to 2 groups for an experiment on time management. In order to save time he decides he will flip a coin as each student enters the room; if the coin is heads the student will be assigned to group 1, if the coin is tails the students will be assigned to group 2. There are 34 students in the class so Dr. Lutze will continue the coin flipping until one group has 17 students. At that point he will assign all the remaining students to the other group. Is this an effective method for random assignment? Explain why or why not.

Scope of Inference Random Assignment Not Random Assignment Random Generalize to Generalize to Selection Population Population Cause and Effect No Cause and Effect Not Only conclude about Only conclude about Random sample sample Selection (Volunteers) Cause and Effect No Cause and Effect

Scope of Inference Imagine a botanist with the city of San Jose wants to test a new treatment for mildew using the roses in the Rose Garden. She randomly selects a group of 30 rose bushes and randomly assigns 15 of them to receive the new treatment and 15 to receive the standard treatment. At the end of the experiment the new treatment is found to be significantly better at preventing mildew. What conclusion can we make? The new treatment causes fewer roses to get mildew and we can apply the results to all roses in the Rose Garden. The new treatment causes fewer roses to get mildew and we can apply the results to all roses. There may be lurking variables, we cannot assume cause and effect. The new treatment causes fewer roses to get mildew but only applies to the roses tested.

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs Older dogs lose bone density and are susceptible to disease and bone fractures. We plan to conduct an experiment to investigate 4 possible treatments for this condition: Calcium supplement Exercise routine Both calcium and exercise Control group with no supplement The response variable is bone density (in units of g/cm3)

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs We will use a total of 32 dogs in this experiment. The dogs are from 4 breeds: Akita Beagle Collie Dalmatian In addition the dogs come from 4 different clinics: Barking Lot Pooch Palace Paw Prince Treehouse

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs Akita Beagle Collie Dalmatian

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs For this simulation you will each be given a card with a dog’s name, breed and clinic specified. The card also contains information on the bone density for your dog: Mean value + change due to breed + change due to clinic Example: Fido Beagle Paw Prince Bone Density: 105 – 22 + 3 = 86

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs You will be asked to track the performance of your dog as we simulate 3 possible experimental designs. For each experiment you will be randomly assigned a treatment. You will receive a treatment card that will specify the bone density change due to that treatment. You will also generate a random integer to be used to calculate your overall bone density change. Original Card + Treatment + Random Integer = Bone Density for Your Dog for that experiment

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs Example: Original Card for Fido + Treatment + Random Integer = Bone Density for Your Dog for that experiment 86 + 14 + 3 = 103 bone density (in g/cm3)

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs Experiment #1: Random Assignment We will randomly assign dogs to each of the 4 treatment groups. Get a treatment card. Generate a random integer between 0 and 3. Sum all 3 values to determine your dog’s bone density. Write your dog’s bone density under the header for your treatment group on the board.

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs Experiment #1: Random Assignment Calculate the mean and standard deviation for the bone density for each treatment group. Is there a statistically significant difference in the results for the 4 different treatments?

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs Group 1 Treatment 1 Blocks Group 2 Treatment 2 Akita Random Assignment Compare Results Group 3 Treatment 3 Beagle Group 4 Treatment 4 Subjects Blocking by breed creates groups of only 2 dogs each. To improve our statistics we will compare each dog to the mean of his/her block. Collie Dalmatian

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs Experiment #2: Block by Breed We will create 4 blocks based on the breed of each dog. Dogs are randomly assigned treatments within each block. Join the other dogs in your block. Get a treatment card. Generate a random integer between 0 and 3. Sum all 3 values to determine your dog’s bone density. Determine the mean bone density within your block. On the board write the difference between your individual dog’s value and the mean under the header for your treatment.

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs Experiment #2: Block by Breed Calculate the mean and standard deviation for the bone density for each treatment group. Is there a statistically significant difference in the results for the 4 different treatments?

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs Experiment #3: Block by Clinic We will create 4 blocks based on the clinic of each dog. Dogs are randomly assigned treatments within each block. Join the other dogs in your block. Get a treatment card. Generate a random integer between 0 and 3. Sum all 3 values to determine your dog’s bone density. Determine the mean bone density within your block. On the board write the difference between your individual dog’s value and the mean under the header for your treatment.

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs Experiment #3: Block by Clinic Calculate the mean and standard deviation for the bone density for each treatment group. Is there a statistically significant difference in the results for the 4 different treatments?

Experiment – Investigate a new Treatment for Bone Density Loss in Dogs Conclusions: 1) Which experiments had a statistically significant result and which did not? 2) Why do you think some experiments had a significant result and others did not? 3) What does this tell you about the importance of choosing effective blocks for an experiment?