Common Core Standards: Math
4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
Sometimes, we can look at a situation and conclude—incorrectly—that one thing causes another. For example, a child might look at the moon each night, listen to the sound of the crickets outside, and think that the moon caused the sound. In fact, he might be able to give a hundred examples of the moon and the sound coexisting. But having two things happen at the same time doesn't necessarily mean that one causes the other.
Statistics can be funny like that. They can sometimes be confusing, misleading, and even downright wrong. Of course, there might also be a legitimate tie between two seemingly unrelated pieces of information. Statisticians can experiment enough to find that connection, even if they might not be able to explain it.
Students should know that statistical data can be shown a number of ways, from frequency tables to bar graphs to scatter plots to make the information easier to understand. This depends on the different types of data collected and how it's meant to be interpreted—in totals or in frequencies. Students should know how to construct these tables and how to read them.
Students should also know that depending on the data, tables, charts, or scatter plots could make the connections easier to see. But before coming to any conclusions about how these factors interact, students should know to consider any and all factors that might affect the data.
For instance, a study shows that kids who have earlier curfews usually do more chores around the house. While the two might be linked, students should know that having more chores doesn't cause earlier curfews. Is it because of strict parents? Rowdy kids being punished? Or maybe they like mowing the lawn and doing the dishes. (Yeah, right!)
While students can come up with different ways to explain the trends they see in statistical data, they should know that they cannot conclusively determine that one causes another without examining all other factors involved.