Question

(a) a researcher measured the shoe size and reading ability of a large group of children. she found that, as shoe size increases, so does reading ability. what does her analysis show?
there is no correlation between shoe size and reading ability.
there is a correlation between shoe size and reading ability. there may or may not be causation. further studies would have to be done to determine this.
there is a correlation between shoe size and reading ability. there is probably also causation. this is because there is an increase in reading ability with an increase in shoe size.

Explanation:

1. Analyze the first option: The researcher found that as shoe size increases, reading ability also increases, so there is a correlation, so the first option is wrong.
2. Analyze the second option: A positive correlation (both increasing) is found between shoe size and reading ability. But correlation does not imply causation. Just because two variables change together doesn't mean one causes the other (e.g., both could be related to age, with older children having larger shoes and better reading ability). So further studies are needed to determine causation, which matches this option.
3. Analyze the third option: Assuming causation just from correlation is incorrect, as explained above.

Answer:

The correct option is: There is a correlation between shoe size and reading ability. There may or may not be causation. Further studies would have to be done to determine this.