Does a high correlation between two quantitative variables prove that changes in one of the variables causes changes in the other variable? Explain and use a new example if possible.
Not necessarily. For example, even though a town's human population increases with the town's population of storks, this does not prove the stork bring babies. In the book, a chapter seven, page 157, you can see a scatterplot of the number of storks in a town in Germany over seven years. It is clear that the number of storks and the number of humans both increase, but the book later explains that more people means more houses and more storks, since storks like to nest on chimneys.
No it dosen't. For example As more cars tune into the radio the more accidents there are, but tunning into the radio dosent neccisarilly cause the crash. It could be that as more people tune into the radio more cars are on the road which would result in an incresse of accidents because the roads are crowded.
NO this isnt always true. for example a track team who wins TCals every year, over the coarse of 4 years slowly decreases in size. if the first year they had 100 participants then every year they lost ten. by the end of the fivth year they would have half of the participants. This doesnt mean that they wont win. The causation of participants graduating and leaving and no freshmin each year join does not cause the track team to loose. Rather its the lurking variables in the background that have causation. since track is a team and individual sport it matters on the talent and how well the track participants do each year.not the decrease in the attendance/ participation.
No, it is not always true, an example would be to look at how fast a person ran and how tall they are. Just because some one is tall( or short) doesn't mean that they will run fast or slow, there could be the lurking variables of family medical history, injury or lifestyle.
Just because two variables are highly correlated with one another, it doesn't necessarily mean that changes in one vriable will cause changes in the other. For example,we could examine the correlation between GPA and SAT scores. Although a highre GPA may be highly correlated with a higher SAT score, this isn't always the case. A change in a person's GPA wouldn't necessarily cause a change in their SAT score. There are many lurking variables that aren't taken into account, such as attendance or being a nervous test-taker.
A high correlation between two quantitative variables doesn't always mean that changes in one variable cause changes in another. A new example would be that car crashes happen to occur more when store sales jump up in a specific. Now some explanation's could be that the weight of all the stuff people buy at said stores weights the car down and the driver looses control, or it is rainier and snowier at this time because the specific month is December. The causation all depends on the lurking variables that hide just beneath the surface.
A high correlation does not necessarily prove that changes in one variable cause changes in the other. For example, height and weight. There are a number of lurking variables such as genetics, dietary/eating habits, and if a person exercises.
Just because two variables have a strong correlation, does not mean that a change in one variable will CAUSE a change in the other. We can use the variables strong correlation to PREDICT a change in one variable due to a change in the other variable but this gives no proof of causation. For example the more often you dont floss your teach the more likey you will get caveties, but this does not mean that not flossing your teeth causes caveties, a lurking variable could be that people who don't floss enough also don't brush their teeth as often as they should.
A high correlation between two quantitative variables does not always prove that changes in one of the variables causes changes in the other variable. For example, as more people play video games and more people receive seizures, it does not mean people are more likely to get a seizure when more people play video games or vice versa. There may be another factor affecting the amount of people playing video games or getting seizures such as the amount of time spent playing video games or the interest of the video game. This factor can be described as a lurking variable.
No, just because two variables have a high correlation does not make one change when the other does. One example would be between the association of age and wearing glasses. It seems that there is a correlation between age and wearing glasses, but this is not always true. If there was a change in the amount of glasses worn, this does not necessarily mean a change in the age of people who wear glasses. There could be lurking variables, such as people who start wearing contacts at a certain age, or something of that sort.
hmm..not all the time like say if ball was orange and bounced really high...say it turned purple(ooo my faorite color) doesnt mean it will bounce any higher or shorter. Many lurking varibles are present here like how much air is in the ball which would have a big impact on how high the balls bounced (duh!) haha
It doesn't prove it. There may be a hight correlation, but changes in both could be caused by another variable (or several other variables). Shower times and water usage have some correlation, but someone who spends ten minutes taking a shower may use as much water as someone who takes six minutes if they turn the water off between rinses.
Okay, okay, your examples are all very convincing. So why are correlation analyses useful? Is there some way to get closer to a true picture of causation by looking at correlations?
The best way to get to showing causation is through the use of an experiment. In an experiment we control the variables (lurking or otherwise) and thus the changes that we might see in a scatterplot's y data can be exclusively attributed to changes in x. Of course making a foolproof, ethical or managable experiment is not so easy...Strictly looking at only correlations will not get us closer to determining causation, as others have stated.
Can't correlations give us an indication of whether or not to explore further? Correlation studies are fairly simple to design, so they offer a first pass at investigating a problem. If a correlation study reveals there is a significant relationship between homework and test scores in statistics, we might want to design another study to probe this more carefully. Ethically, we can't create a true experimental study, because we already have info. that suggests homework and scores are related, so we couldn't, for example, randomly assign students to "homework" and "no homework" groups, because we may be harming those in the "no homework" group. But we might create a survey, do a case study, etc., that teases out the connection between homework and test scores more specifically.
On the other hand, if a correlation study shows NO correlation between homework and scores, that's a strong indicator there's no causal connection.
Not always because there can be lurking variables. for example the # of drownings and the ice cream sale example. there are more people on a hot day at the beach so there for the ice cream sales go up and the drownings go up.
A high correlation 'tween two quantitative variables does not prove that changes in one of the variables caused changes in the othuh variable. duh! For example, it has been shown that, on a beach, ice cream sales and the number of people who drown are highly correlated. However, this don't mean that buyin' ice cream could cause a person to drown (It's a good thing that I, MizzJuliah, can swim, but i digress...). There is a lurking variable of temperature. As it gets mo' hotter, mo' people go to the beach, therefore mo' peoples is gonna buy ice cream, and its possible that more people will drown. You should always consider any possible lurking variables. Correlation does not equal causation. [Errors intended.]
19 comments:
Not necessarily. For example, even though a town's human population increases with the town's population of storks, this does not prove the stork bring babies. In the book, a chapter seven, page 157, you can see a scatterplot of the number of storks in a town in Germany over seven years. It is clear that the number of storks and the number of humans both increase, but the book later explains that more people means more houses and more storks, since storks like to nest on chimneys.
No it dosen't. For example As more cars tune into the radio the more accidents there are, but tunning into the radio dosent neccisarilly cause the crash. It could be that as more people tune into the radio more cars are on the road which would result in an incresse of accidents because the roads are crowded.
NO this isnt always true. for example a track team who wins TCals every year, over the coarse of 4 years slowly decreases in size. if the first year they had 100 participants then every year they lost ten. by the end of the fivth year they would have half of the participants. This doesnt mean that they wont win. The causation of participants graduating and leaving and no freshmin each year join does not cause the track team to loose. Rather its the lurking variables in the background that have causation. since track is a team and individual sport it matters on the talent and how well the track participants do each year.not the decrease in the attendance/ participation.
No, it is not always true, an example would be to look at how fast a person ran and how tall they are. Just because some one is tall( or short) doesn't mean that they will run fast or slow, there could be the lurking variables of family medical history, injury or lifestyle.
Just because two variables are highly correlated with one another, it doesn't necessarily mean that changes in one vriable will cause changes in the other. For example,we could examine the correlation between GPA and SAT scores. Although a highre GPA may be highly correlated with a higher SAT score, this isn't always the case. A change in a person's GPA wouldn't necessarily cause a change in their SAT score. There are many lurking variables that aren't taken into account, such as attendance or being a nervous test-taker.
A high correlation between two quantitative variables doesn't always mean that changes in one variable cause changes in another. A new example would be that car crashes happen to occur more when store sales jump up in a specific. Now some explanation's could be that the weight of all the stuff people buy at said stores weights the car down and the driver looses control, or it is rainier and snowier at this time because the specific month is December. The causation all depends on the lurking variables that hide just beneath the surface.
A high correlation does not necessarily prove that changes in one variable cause changes in the other. For example, height and weight. There are a number of lurking variables such as genetics, dietary/eating habits, and if a person exercises.
Just because two variables have a strong correlation, does not mean that a change in one variable will CAUSE a change in the other. We can use the variables strong correlation to PREDICT a change in one variable due to a change in the other variable but this gives no proof of causation. For example the more often you dont floss your teach the more likey you will get caveties, but this does not mean that not flossing your teeth causes caveties, a lurking variable could be that people who don't floss enough also don't brush their teeth as often as they should.
A high correlation between two quantitative variables does not always prove that changes in one of the variables causes changes in the other variable. For example, as more people play video games and more people receive seizures, it does not mean people are more likely to get a seizure when more people play video games or vice versa. There may be another factor affecting the amount of people playing video games or getting seizures such as the amount of time spent playing video games or the interest of the video game. This factor can be described as a lurking variable.
No, just because two variables have a high correlation does not make one change when the other does. One example would be between the association of age and wearing glasses. It seems that there is a correlation between age and wearing glasses, but this is not always true. If there was a change in the amount of glasses worn, this does not necessarily mean a change in the age of people who wear glasses. There could be lurking variables, such as people who start wearing contacts at a certain age, or something of that sort.
hmm..not all the time like say if ball was orange and bounced really high...say it turned purple(ooo my faorite color) doesnt mean it will bounce any higher or shorter. Many lurking varibles are present here like how much air is in the ball which would have a big impact on how high the balls bounced (duh!) haha
It doesn't prove it. There may be a hight correlation, but changes in both could be caused by another variable (or several other variables). Shower times and water usage have some correlation, but someone who spends ten minutes taking a shower may use as much water as someone who takes six minutes if they turn the water off between rinses.
This does not cause anything. One must take into consideration lurking variables. Without these we can't say a high correlation causes anything. Later
Okay, okay, your examples are all very convincing. So why are correlation analyses useful? Is there some way to get closer to a true picture of causation by looking at correlations?
The best way to get to showing causation is through the use of an experiment. In an experiment we control the variables (lurking or otherwise) and thus the changes that we might see in a scatterplot's y data can be exclusively attributed to changes in x. Of course making a foolproof, ethical or managable experiment is not so easy...Strictly looking at only correlations will not get us closer to determining causation, as others have stated.
Can't correlations give us an indication of whether or not to explore further?
Correlation studies are fairly simple to design, so they offer a first pass at investigating a problem. If a correlation study reveals there is a significant relationship between homework and test scores in statistics, we might want to design another study to probe this more carefully. Ethically, we can't create a true experimental study, because we already have info. that suggests homework and scores are related, so we couldn't, for example, randomly assign students to "homework" and "no homework" groups, because we may be harming those in the "no homework" group. But we might create a survey, do a case study, etc., that teases out the connection between homework and test scores more specifically.
On the other hand, if a correlation study shows NO correlation between homework and scores, that's a strong indicator there's no causal connection.
Not always because there can be lurking variables. for example the # of drownings and the ice cream sale example. there are more people on a hot day at the beach so there for the ice cream sales go up and the drownings go up.
A high correlation 'tween two quantitative variables does not prove that changes in one of the variables caused changes in the othuh variable. duh!
For example, it has been shown that, on a beach, ice cream sales and the number of people who drown are highly correlated. However, this don't mean that buyin' ice cream could cause a person to drown (It's a good thing that I, MizzJuliah, can swim, but i digress...). There is a lurking variable of temperature. As it gets mo' hotter, mo' people go to the beach, therefore mo' peoples is gonna buy ice cream, and its possible that more people will drown. You should always consider any possible lurking variables.
Correlation does not equal causation.
[Errors intended.]
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