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<p>Some key takeaways from this lesson are that finding relationships with the help of the correlation coefficient is a very good way to notice that there is a connection between variables. To determine whether the relationship is causal, the next step is usually to carefully design an experiment that isolates and precisely controls only one of the variables to determine how it affects the other variable.</p>
<p>Here are some questions for discussion.</p>
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“How can you determine if there is a causal relationship between two variables? Be prepared to show your reasoning.” (To determine a causal relationship, you need to think about the context and determine if a change in one variable causes the other variable to change. One way to help determine whether there is a causal relationship is to design an experiment that controls one of the variables.)
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“Mai states that the relationship between the number of miles driven in a taxi and the price of the taxi ride is a causal relationship. Do you agree with Mai? What other information would help further convince you one way or the other?” (I agree with her. It makes sense that the farther you go in a taxi, the more you will be charged. It might help convince me to take several taxi rides of the same length, but with different starting points or destinations, and see if the cost is the same.)
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“Jada states that the relationship between the size of a pasture and the number of cows kept at various farms is a causal relationship. Do you agree with Jada? Be prepared to show your reasoning.” (I do not agree. The increase in pasture size does not cause an increase in the number of cows [nor does an increase in number of cows make the pasture larger]. The increase in land might mean there is more food for the cows, but it is the farmer who decides how many cows there are on a farm.)
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<p>Tell students that one common mistake people tend to make using statistics is to think that all relationships between variables are causal. Scatter plots can only show a relationship between the two variables. To determine if change in one of the variables actually causes a change in the other variable, or has a causal relationship, the context must be better understood and other options ruled out.</p>