Question

identifying correlation and causation
(a) a piano instructor examined student progress. he noticed that when students spend less time playing video games, their memorization ability tends to increase. what can he conclude?

• there is no correlation between amount of time spent playing video games and memorization ability.
• there is a correlation between amount of time spent playing video games and memorization ability. there may or may not be causation. further studies would have to be done to determine this.
• there is a correlation between amount of time spent playing video games and memorization ability. there is probably also causation. this is because there is an increase in memorization ability with a decrease in the amount of time spent playing video games.

(b) an environmental study was conducted. it reported that houses with more inhabitants do not necessarily produce more or less trash. what can be determined?

• there is no correlation between number of inhabitants and amount of trash produced. however, there is no causation. this is because there is
• there is a correlation between number of inhabitants and amount of trash produced. however, there is probably an increase in the amount of trash produced with an increase in the number of inhabitants.
• there is a correlation between number of inhabitants and amount of trash produced. there may or may not be causation. further studies would have to be done to determine this.

(c) data was collected at a pool. it showed that being older does not imply that a swimmer will stay for a shorter or longer amount of time. what is likely true?

• there is no correlation between age and length of stay.
• there is a correlation between age and length of stay. there may or may not be causation. further studies would have to be done to determine this.
• there is a correlation between age and length of stay. however, there is no causation. this is because there is likely an increase in the length

Explanation:

For (a):

The instructor observed an inverse trend: less video game time links to better memorization, which shows a correlation. But correlation does not equal causation—other factors could explain the trend, so causation can't be confirmed without further study.

For (b):

The study found no consistent link between number of inhabitants and trash production, meaning there is no correlation between the two variables.

For (c):

The data shows age does not relate to length of stay at the pool, so there is no correlation between these two variables.

Answer:

(a) There is a correlation between amount of time spent playing video games and memorization ability. There may or may not be causation. Further studies would have to be done to determine this.
(b) There is no correlation between number of inhabitants and amount of trash produced.
(c) There is no correlation between age and length of stay.