Warm Up We are designing an experiment to determine the best growing conditions for carrots. We will plant the seeds in locations with full sun or partial sun. We will also water the seeds every day, every other day or every third day. 1) Define the factors, levels and treatments in this experiment. 2) What would be a good choice for the response variable? 3) If we want to have 20 seeds receive each treatment, how many seeds do we need to plant for the experiment? 4) List at least 3 other factors that should be controlled.

Experimental Design - Blocking Blocks are “groups” of experimental units with a similar characteristic that is expected to be influential on the outcome of the experiment. We use blocking so that we can compare results within each “block” or group. This improves the sensitivity of the experiment. Without blocking the results may be dominated by the differences between these groups.

Experimental Design - Blocking Imagine an experiment to test the effect of a new fitness program on the number of push-ups high school PE students can do. Create blocks of men and women before randomizing the subjects. Group 1 New Fitness Men Random Assignment Compare Results Group 2 Control Group Subjects Group 1 New Fitness Women Random Assignment Compare Results Group 2 Control Group Creating blocks of men and women allows us to compare results between men and women separately.

Experimental Design - Blocking Why not block for everything you can think of? Each block reduces the number of units in each treatment group. Too many blocks will eliminate the benefits of randomization and replication. There is always a trade-off between blocking and replication in any experimental design.

Practice - Blocking You plan to design an experiment to determine if listening to music during a test affects a student’s score on that test. For this experiment you have 80 student volunteers. Some students will listen to their favorite music using earbuds while taking a math test while others will take the test in silence. 1) Explain how you would design this experiment using random assignment. Be sure to indicate the treatments, the response variable and how you will conduct the random assignment. Draw a diagram. 2) You believe that the amount of sleep students had the night before the test will have a large impact on the results. Explain how you would design a randomized blocking experiment blocking for sleep. Be sure to indicate the treatments, the response variable and how you will conduct the random assignment. Draw a diagram.

Experiment – Investigate A 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 determine if a calcium supplement will increase bone density in dogs. Treatments for this experiment: Calcium supplement Control group The response variable is bone density (in units of g/cm3)

Experiment – Investigate A Treatment for Bone Density Loss in Dogs We will use a total of 35 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 Treatment for Bone Density Loss in Dogs Akita Beagle Collie Dalmatian

Experiment – Investigate A 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 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 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 Treatment for Bone Density Loss in Dogs Experiment #1: Random Assignment We will randomly assign dogs to one of the 2 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 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 2 different treatments?

Experiment – Investigate A 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 to a treatment 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. Write your dog’s bone density under the header for your block and treatment group on the board.

Experiment – Investigate A 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 within your block. Look at the mean and standard deviation for each treatment group within the 4 blocks. Is there a statistically significant difference in the results for the 2 different treatments?

Experiment – Investigate A 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 to a treatment 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. Write your dog’s bone density under the header for your block and treatment group on the board.

Experiment – Investigate A 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 within your block. Look at the mean and standard deviation for each treatment group within the 4 blocks. Is there a statistically significant difference in the results for the 2 different treatments?

Experiment – Investigate A 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?