5E correlation and causality

what is a negative correlation

Negative correlation means that two variables tend to change in opposite​ directions, with one increasing while the other decreases.

How do we determine the strength of a​ correlation?

The more closely two variables follow the general​ trend, the stronger the correlation​ (which may be positive or​ negative).

For the following pair of​ variables, state whether you believe the two variables are correlated. If you believe they are​ correlated, state whether the correlation is positive or negative. The time it takes to run 100 meters and the order of finish in the 100 meter dash

to measure fertility rate of women , the unit children per woman might be used

Decide whether each of the following statements makes sense​ or does not make sense​. If causality has been established beyond reasonable​ doubt, then we can be 100 %100% confident that the causality is real.

The statement does not make sense. If causality has been established beyond reasonable​ doubt, then there is a physical model that is so successful in explaining how one thing causes another that it seems unreasonable to doubt the​ causality, but beyond reasonable doubt does not mean beyond all doubt.

what is a correlation

A correlation exists between two variables when higher values of one variable consistently go with higher or lower values of another variable. amount of smoking and lung​ cancer, height and weight of​ people, price of a good and demand of the good

There is a strong correlation between tobacco smoking and incidence of lung​ cancer, and most physicians believe that tobacco smoking causes lung cancer.​ However, not everyone who smokes gets lung cancer. Briefly describe how smoking could cause cancer when not all smokers get cancer.

Not all smokers get cancer because cancer is caused by cell​ mutation, and while smoking increases the chances of such a mutation​ occurring, the mutation does not occur in every smoker.

Briefly describe each of the six guidelines for establishing causality.

The first guideline states that one should look for situations where the effect is correlated with the suspected​ cause, even when other factors vary. When checking to see if smoking causes​ cancer, let groups of smokers and​ non-smokers be completely random to see if lung cancer occurs more in the smoking group than the​ non-smoking group. The second guideline states that among groups that differ only in the presence or absence of the suspected​ cause, one should check that the effect is similarly present or absent. When checking to see if smoking causes​ cancer, look at two groups as identical as​ possible, with one group being smokers and the other group being​ non-smokers. The third guideline states to look for evidence that larger amounts of the suspected cause produce larger amounts of the effect. When checking to see if smoking causes​ cancer, look at those who smoke a lot and those who only smoke a little and compare the incidents of lung cancer. The fourth guideline states that if the effect might be produced by other potential​ causes, make sure the effect still remains after accounting for these other potential causes. When checking to see if smoking causes​ cancer, let the group of smokers vary between people of different ethnicities and genetic background to see if lung cancer is still more prevalent among smokers than​ non-smokers. The fifth guideline states that the suspected cause should be tested with an experiment. When checking to see if smoking causes​ cancer, test the effects of cigarettes on lung tissue or animals. The sixth guideline states that the physical mechanism by which the suspected cause produces the effect should be determined. When checking to see if smoking causes​ cancer, try to find what it is in cigarettes that causes cells to mutate and cause cancer.

Determine whether the statement makes sense​ or does not make sense . There is a strong negative correlation between the price of tickets and the number of tickets sold. This suggests that in order to sell a lot of​ tickets, the price should be lowered.

The statement makes sense. To increase the ticket​ sales, the price should be decreased since there is a strong negative correlation.

Consider the following statement about a correlation. State the correlation clearly​ , then state whether the correlation is most likely due to​ coincidence, a common underlying​ cause, or a direct cause. In the past three​ decades, levels of atmospheric carbon dioxide have increased while the number of pirates worldwide has decreased.

There is a negative correlation between the levels of atmospheric carbon dioxide and the number of pirates worldwide. This is a coincidence since there is no reason that levels of atmospheric carbon dioxide should affect the number of pirates worldwide.

Consider the following statement about a correlation. State the correlation clearly​ , then state whether the correlation is most likely due to​ coincidence, a common underlying​ cause, or a direct cause. Over the past 30​ years, data show that the number of games won by Major League baseball teams increased with team payroll.

There is a positive correlation between a​ team's payroll and games won. This could be a direct cause since a baseball team is likely to get paid more the better they do.

Consider the following statement about a correlation. State the correlation clearly​ , then state whether the correlation is most likely due to​ coincidence, a common underlying​ cause, or a direct cause. Automobile gas mileage decreases with tire pressure.

There is a positive correlation between gas mileage and tire pressure. This correlation is due to a direct cause because more gasoline is needed to roll a tire with lower pressure.

Consider the following statement about a correlation. State the correlation clearly​ , then state whether the correlation is most likely due to​ coincidence, a common underlying​ cause, or a direct cause. In a large resort​ city, the crime rate increased as the number of taxi cabs increased.

There is a positive correlation between the crime rate and the number of taxi cabs. This correlation is due to a common underlying cause because it is possible​ that, with an increase in​ tourism, both the crime rate and the number of cabs increase.

For the following pair of​ variables, state the units that might be used to measure each variable. Then state whether you believe that the two variables are correlated. Positive, negative, or no correlation? Average property tax in a school district and the average number of computers in each school

To measure average property​ tax, the unit dollars To measure average number of computers in each​ school, the unit number of computers There is a positive correlation because the average number of computers in each school tends to increase when average property tax in a school district increases.

For the following pair of​ variables, state the units that might be used to measure each variable. Then state whether you believe that the two variables are correlated. Positive, negative, or no correlation? Fertility rate of women and life expectancy in a country

To measure fertility rate of​ women, the unit children per woman To measure life​ expectancy, the unit years There is a negative correlation because life expectancy tends to increase when fertility in women decreases.

Decide whether the following statement makes sense​ or does not make sense​. I had originally suspected that an increase in variable E would cause a decrease in variable​ F, but I no longer believe this because I found no correlation between the two variables.

the statement makes sense. Originally, a negative correlation was suspected. Since no correlation was found, there is apparently no relationship between the variables

For the following pair of​ variables, state the units that might be used to measure each variable. Then state whether you believe that they are correlated. If you believe they are​ correlated, state whether the correlation is positive or negative. Latitude and the average high temperature in June

to measure latitude, use the degrees of latitude to measure temperature, use the degrees fahrenheit there is a negative correlation because the average high temperature in June tends to increase when latitude decreases

For the following pair of​ variables, state the units that might be used to measure each variable. Then state whether you believe that they are correlated. If you believe they are​ correlated, state whether the correlation is positive or negative. The year a state joined the Union and the land area of the state

to measure the year a state joined the union, the unit year may be used to measure the land area of a state, the unit sq. miles may be used there is a positive correlation because as the year a state joined the union increases, the land area of that state tends to increase

For the following pair of​ variables, state the units that might be used to measure each variable. Then state whether you believe that they are correlated. If you believe they are​ correlated, state whether the correlation is positive or negative. Weight and how frequently a person attends rock concerts

to measure weight, the unit pounds might be used to measure the frequency a person attends rock concerts, the unit of number of attendances might be used the variables are not correlated

For the following pair of​ variables, state the units that might be used to measure each variable. Then state whether you believe that they are correlated. If you believe they are​ correlated, state whether the correlation is positive or negative. Wind speed and air temperature along the route

to measure wind speed, the unit kilometers per hour to measure air temperature, the unit degrees Fahrenheit there is a negative correlation because air temperature tends to increase when wind speed decreases

Suppose that people living near a particular​ high-voltage power line have a higher incidence of cancer than people living farther from the power line. Can you conclude that the​ high-voltage power line is the cause of the elevated cancer​ rate? If​ not, what other explanations might there be for​ it? What other types of research would you like to see before you conclude that​ high-voltage power lines cause​ cancer? What other types of research would you like to see before you conclude that​ high-voltage power lines cause​ cancer?

You cannot conclude that the power line is the cause of the elevated cancer rate because the cause cannot be established until a mechanism is confirmed. A study that determines the effect of electricity on a​ cell's growth mechanism.

A famous study concluded that the mean lifetime of conductors of major orchestras was 73.4​ years, about 5 years longer than that of all American males at the time. The author claimed that a life of music causes a longer life. Evaluate the claim of causality and propose other explanations for the longer life expectancy of conductors.

It is probably not true that a life of music causes a longer life. People do not decide to become conductors until relatively late in life. Having survived this many​ years, a person has a longer than average life expectancy.

what is no correlation

No correlation means that there is no apparent relationship between the two variables.

what is a positive correlation

Positive correlation means that both variables tend to increase​ (or decrease) together.

For the following pair of​ variables, state whether you believe the two variables are correlated. If you believe they are​ correlated, state whether the correlation is positive or negative. The time it takes to run 100 meters and the order of finish in the 100 meter dash

positive correlation because running it in less time will result in a lower finish order

Consider the following statement about a correlation. State the correlation clearly​ , then state whether the correlation is most likely due to​ coincidence, a common underlying​ cause, or a direct cause. Over the past three​ decades, the number of miles of freeways in Los Angeles has​ grown, and traffic congestion has worsened.

there is a positive correlation between the number of miles of freeways and the traffic congestion in Los Angeles. The correlation is most likely due to the common underlying cause of Los Angeles having a very large population.

For the following pair of​ variables, state the units that might be used to measure each variable. Then state whether you believe that the two variables are correlated. If you believe they are​ correlated, state whether the correlation is positive or negative. The age of a person and time spent on social networking sites

to measure age the unit years since birth might be used to measure time the unit hours might be used there is a negative correlation because time spent on social sites rends to increase when age decreases