Drawing conclusions based on data from a statistical experiment
• Given data from a statistical experiment, create a randomization distribution.
• Use a randomization distribution to determine if there is a significant difference between two experimental conditions.
A good description of how this section might play out in the classroom can be found on pp. 10–12 of Progressions for the Common Core State Standards in Mathematics: High School Statistics and Probability.
This section focuses on using data from statistical experiments to determine if there is a significant difference between two experimental conditions. By investigating what group differences might be expected due to chance alone when subjects are randomly partitioned into two groups, students are able to determine if chance alone is a plausible explanation for an observed difference. It is important that students understand that when a single group is partitioned into two groups, the two groups will tend to differ just by chance. This idea is fundamental in distinguishing “significant differences” from differences that might be due only to chance.
In this section, students should use data from an experiment to create a randomization distribution as a way of exploring group differences that are consistent with chance. This distribution is then used to determine if an observed difference is consistent with chance or whether the difference is large enough to indicate a significance difference due to the effects of the experimental conditions. Both physical and technology assisted simulations can be used to develop randomization distributions.
WHAT: This activity illustrates the process of using data from a randomized experiment to create a randomization distribution and to use that distribution to draw a conclusion based on the data (S-IC.B.5). The activity uses data from a real experiment on the effect of sleep deprivation, which is a topic that most students find interesting.
WHY: As well as addressing the standard, this activity makes good use of physical simulation that leads to technology-assisted simulation.
WHAT: This activity links the previous section and the use of simulation to the topic of the current section: drawing conclusions based on data from experiments. Students use given simulation results to reach a conclusion about whether dolphins can communicate and then independently carry out a simulation to draw a conclusion based on data from a similar experiment (S-IC.B.5).
WHY: This activity first walks students through a complete simulation, so it is a good way to help students understand the steps in a simulation. The context is of interest to many students, and that motivates them to want to complete the simulation in order to see the conclusion. The activity makes good use of physical simulation as well as technology-assisted simulation.