The mathematical purpose of this lesson is for students to collect and use data from a simulation to compare 2 treatments, and to understand the importance of randomness in experimental design. The work of this lesson connects to previous work because students estimated the population mean with a margin of error using sample means from random samples. The work of this lesson connects to upcoming work because students will conduct an experiment, and analyze their results using a simulation. Students encounter the term treatment in this lesson which is defined as the value of the variable that is changed between the two groups in an experiment.
Students also encounter a kind of simulation that is used to analyze data from experiments. Students create a randomization distribution from the data by grouping together all of the data, then randomly reassigning the data into different groups, then finding the difference between the means of these new groups. This process is repeated several times to create a distribution of the differences between the means for the treatment groups containing randomly redistributed data. The mean difference from the experiment is then compared to this randomization distribution to determine whether or not it likely occurred by chance. When students make connections between the results of the simulation and the chance that an experimental result occurred at random they are looking for and making use of structure (MP7).
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
- Describe (orally and in writing) the importance of randomness in experimental design.
- Use data from a simulation to compare data from experimental groups.
- Let’s do an experiment.
Cut slips from the blackline master for the activity Randomizing Satisfaction and place in a bag for a demonstration. Be prepared to use a chance process to split the class into two groups such as having names of students on slips of paper placed into a paper bag. If possible, do the random assignment in front of the class so that they can observe the chance process. Students may wish to calculate some standard deviations for which statistical technology is helpful.
- I can find the difference between two treatment means and use a randomization distribution to determine whether or not the result occurred by random chance.
- I understand why randomization is important in the design of a study.
In an experiment where you are comparing two groups, one of which is being given a treatment and the other of which is the control group without any treatment, the treatment is the value of the variable that is changed for the treatment group.