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a correlation indicates a relationship between two variables. That relationship may or may not be a cause-effect relationship, which is called causation.

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the relationship between two variables

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A correlation is a relationship. If you hear that two variables have a strong correlation, then you know they have a strong relationship. But you do not know if one causes the other. It is important to understand that a correlation is not necessarily a causation.
For some time, eggs were associated with high cholesterol and were considered somewhat unhealthful to eat. This situation occurred because studies showed a correlation between egg consumption and cholesterol levels, and researchers had jumped to the conclusion that eating eggs caused a person’s cholesterol levels to increase. Future studies concluded that although eggs do have some cholesterol, they were not as bad as first thought. Researchers noticed that people who ate eggs often had bacon or sausage on the side, and those foods are high in cholesterol. In this case, the side dish is a lurking variable. A lurking variable is a third variable that is affecting the relationship between the two variables being studied.

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a variable that is unobserved (the researcher is unaware of it) but may be the actual cause of an observed response

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That said, sometimes a correlation actually is a causation. For years, tobacco companies argued that smoking and lung cancer were simply a correlation, and perhaps lurking variables were to blame. But several long-term studies have proven there to be a causal relationship: Smoking does indeed cause lung cancer.

Think About It: If there is a cause-effect relationship between two variables, it is not always clear which variable causes which. For example, suppose there is a moderate positive relationship between the number of years employees work at a company and their happiness level with their jobs. Do the jobs make them happy, or do happy people stay with their jobs longer?

Finally, a correlation can be purely coincidental. Suppose a correlation is found between the number of running races a city holds and the number of broken parking meters in the city. This correlation is likely to be just a coincidence. There’s no reason to think one would have any effect on the other, and there are no apparent lurking variables.

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If there's a lurking variable, then a third variable is responsible for the relationship.

First statement: The lurking variable is population. Cities with greater populations will have greater cell phone sales and greater numbers of people who have cavities to be filled.

If there's a causation, then there's a cause-effect relationship between the variables.

Second statement: Plants need water. Using more water creates a more expensive water bill.

Third statement: Warm temperatures melt snow. This is causation.

If there's neither a causation nor a lurking variable, choose coincidence.

Fourth statement: There is no reason for a cause-effect relationship and no reasonable lurking variable.

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A researcher finds a positive correlation between the number of ice-cream bars sold on a day and the number of sandals sold on the same day. Eating ice cream does not make people buy sandals, and buying sandals doesn't give people a craving for ice cream.Which variable is most likely the lurking variable that explains the correlation?

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A researcher finds a positive correlation between the number of ice-cream bars sold on a day and the number of sandals sold on the same day. Eating ice cream does not make people buy sandals, and buying sandals doesn't give people a craving for ice cream.Which variable is most likely the lurking variable that explains the correlation?

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temperature

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Think about what the variables have in common.

The warmer it is, the more people eat ice cream and the more people wear sandals.

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In a basketball study, a positive correlation is found between how many baskets a child can make and the child's reading level. Being a good reader does not make a child a good basketball player, and being a good basketball player does not make a child good reader.Which variable is most likely the lurking variable that explains the correlation?

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In a basketball study, a positive correlation is found between how many baskets a child can make and the child's reading level. Being a good reader does not make a child a good basketball player, and being a good basketball player does not make a child good reader.Which variable is most likely the lurking variable that explains the correlation?

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age

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Think about what could relate an athletic skill to an academic skill.

The older a child is, the more capable the child is at sports and the more education the child received in reading.

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When two variables have a correlation, it does not mean that changes in one variable necessarily caused changes in the other variable. A lurking variable may be responsible for the association. A lurking variable is a third variable that is affecting the relationship between the two variables being studied.

The distance a hiker travels is a lurking variable. It seems reasonable that the greater the distance a hiker hikes, the longer he is exposed to bugs that may bite him. Answer True for this potential variable.

The hiker’s favorite music does not affect the number of granola bars he consumes or the number of bug bites he may receive. It is not even clear if the hiker listens to music while hiking. Answer False for this potential variable.

The type of hiking boots a hiker wears does not affect the number of granola bars he consumes or the number of bug bites he may receive. Answer False for this potential variable.

The amount of time the hiker travels is a lurking variable. The longer a hiker is exposed to bugs, the more bug bites the hiker is likely to receive. Answer True for this potential variable.

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Correlation is another term for linear association. Remember that when two variables correlate, it does not imply that changes in one variable caused changes in the other variable.

A correlation is an association. It is sometimes a cause-effect relationship. There may also be lurking variables.

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There is a strong positive correlation between the number of umbrellas sold in a town and the water levels in nearby rivers.What is a possible reason for why this correlation exists?

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There is a strong positive correlation between the number of umbrellas sold in a town and the water levels in nearby rivers.What is a possible reason for why this correlation exists?

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high levels of rainfall

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n a strong positive correlation between two variables, it is expected that an increase in one of the variables usually indicates an increase in the second variable. A lurking variable may be responsible for an unlikely correlation between variables.

Determine the most likely lurking variable in the strong positive correlation between the number of umbrellas sold and the water level in nearby rivers.

A melting glacier upstream would not lead to an increase in umbrella sales but may lead to an increase in water levels in nearby streams. This choice is not a lurking variable.

A large number of tourists in the area may lead to an increase in umbrella sales but is not related to a change in water levels in nearby streams. This is not a lurking variable.

Rainfall would affect both the number of umbrellas sold and the water level of nearby streams. As the number of umbrellas sold increases, the level of rainfall would likely increase and the water levels of nearby streams would increase.

The correct answer is high levels of rainfall.

A new shopping mall in the area may lead to an increase in umbrella sales but is not related to a change in water levels in nearby streams. This is not a lurking variable.

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There's a positive correlation between the amount of fertilizer a homeowner uses and the height of the plants in her garden.Which statement is true?

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There's a positive correlation between the amount of fertilizer a homeowner uses and the height of the plants in her garden.Which statement is true?

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The correlation is most likely a causation.

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A correlation between two variables does not necessarily indicate that a change in one variable caused the change in the second variable. A lurking variable may be responsible for the correlation or the relationship may be coincidence.

It seems reasonable that an increase in the amount of fertilizer a homeowner uses leads to an increase in the height of plants in her garden and that the increase in fertilizer caused this relationship. The correlation is most likely a causation.

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There's a moderate positive correlation between the length of a child's hair and the amount of time it takes for the child to run 100 m.Which statement is true?

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There's a moderate positive correlation between the length of a child's hair and the amount of time it takes for the child to run 100 m.Which statement is true?

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The correlation is most likely due to a lurking variable.

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There's a moderate negative correlation between the number of toasters and the number of fishing poles sold in a store.Which statement is true?

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There's a moderate negative correlation between the number of toasters and the number of fishing poles sold in a store.Which statement is true?

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The correlation is most likely a coincidence.