+- Association Sentences
A study by a prominent psychologist found a moderately strong positive association between the number of hours of sleep a person gets and the person’s ability to memorize information. Explain in the context of this problem what “positive association” means.
A positive association means in general people who had more sleep were able to memorize more information.
A study by a prominent psychologist found a moderately strong positive association between the number of hours of sleep a person gets and the person’s ability to memorize information. Hoping to improve academic performance, the psychologist recommended the school board allow students to take a nap prior to any assessment. Discuss this reasoning as a statistician.
The child psychologist is attributing association to cause and effect. There is an implication that more sleep will cause better memorization, therefore causing an increase in assessments scores. Perhaps people who had memorized more were able to sleep more restfully, or perhaps differences in brain chemistry allowed some people to memorize more and to sleep more easily.
CORRELATION IS NOT EQUAL TO CAUSATION.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
A correlation of –0.98 indicates a strong, negative association.
True. Correlation is a number between -1 and +1, with 0 being very weak and +-1 being very strong. -0.98 is very close to -1, so it is strong and negative.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
A very low correlation of –0.772 shows that there is almost no association between Gross Domestic Product (a number) and Infant Mortality Rate.
False. -0.772 is closer to -1 than it is to zero, so it is not a very low correlation. Correlation values close to zero are very low.
If a point that was far away from the trend of the other points but still followed the trend was removed, would the correlation become stronger, weaker or stay the same?
Removing a far away point that still follows the trend would make the correlation WEAKER.
A school board study found a moderately strong negative association between the number of hours high school seniors worked at part-time jobs after school hours and the students’ grade point averages. Explain in this context what “negative association” means.
Students who worked more hours tended to have lower grades.
A school board study found a moderately strong negative association between the number of hours high school seniors worked at part-time jobs after school hours and the students’ grade point averages. Hoping to improve student performance, the school board passed a resolution urging parents to limit the number of hours students be allowed to work. As a statistician, should you agree or disagree with the school board’s reasoning. Explain.
They are mistakenly attributing the association to cause and effect. Maybe students with low grades are more likely to seek jobs, or maybe there is some other factor in their home life that leads both to lower grades and to the desire or need to work.
CORRELATION IS NOT EQUAL TO CAUSATION.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
Multiplying by every value of x by 2 will double the correlation.
False. Multiplying every value of x by 2 (or any number) will not change the correlation.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
There was a correlation of 0.44 between Gross Domestic Product (GPD) and Continent.
False. Continent is not a number(not quantitative), so we cannot calculate correlation.
If a point that was far away from the trend of the other points and did not follow the trend was removed, would the correlation become stronger, weaker or stay the same?
Removing a point that is far away from the trend that does not follow the trend would make the correlation STRONGER.
A researcher notes that there is a positive correlation between the temperature on a summer day and the number of bees that he can count in his garden over a 5-minute time span. Describe what the researcher means by a positive correlation.
As the number of degrees increases, the number of bees increases in a linear manner.
A larger firm is considering acquiring a bookstore. An analyst for the firm, noting the positive association between number of sales people working and sales, suggests that when they acquire the store they should hire more people because that will drive higher sales. Is his conclusion justified? What alternative explanations can you offer? Use appropriate statistics terminology.
This conclusion is not justified. Correlation does not demonstrate causation. The analyst argues that the number of sales staff working causes sales to be higher. It is possible (perhaps more plausible) that the store hired more people as sales increased. The causation may run in the opposite direction of the analyst’s argument.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
The units of the correlation are the same as the units of y.
False. Correlation has no units.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
There was a very strong correlation of 1.22 between Life Expectancy and Gross Domestic Product (a number).
False. Correlation is a number between -1 and +1. We cannot have a correlation of 1.22, because it is not between -1 and +1.
If a point that was not far away from the trend of the other points but still followed the trend was removed, would the correlation become stronger, weaker or stay the same?
Removing a point that is not far away from the trend and still follows the trend would not change the correlation. The correlation would STAY THE SAME.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
The correlation between Fuel Efficiency (as measured by miles per gallon) and Price of 150 cars at a large dealership is r = –0.34. In general, the more you pay, the lower the fuel efficiency of your car will be.
True. r = -0.34, so the association is negative, which means overall, when x increases (the more you pay), y decreases the lower the fuel efficiency of your car will be.
A study finds that during blizzards, online sales are highly associated with the number of snow plows on the road; the more plows, the more online purchases. The director of an association of online merchants suggests that the organization should encourage municipalities to send out more plows whenever it snows because, he says, that will increase business. Comment as a statistician.
The director’s conclusion is not justified. The lurking variable is the severity of the blizzard. Particularly severe blizzards require more snowplows, and they also prevent people from leaving home, where they are more likely to make online purchases, especially since they have to leave home to go to a store.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
A correlation of 0.02 indicates a strong positive association.
False. Correlations close to +-1 are strong. Correlations close to 0 are weak. 0.02 is very close to 0, so it is very weak.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
The correlation between Age and Income as measured on 100 people is r = 0.75. In general, when Age increases, Income increases as well.
True. r is positive; a positive correlation generally means: as x "Age" increases, y "Income" tends to increase as well.
Make a scatter plot that has a point that is far away from the trend of the other points but still follows the trend that if that point was removed the correlation become weaker. Circle that point.
See "Removing Points 400" card.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
The correlation between Fuel Efficiency (as measured by miles per gallon) and Price of 150 cars at a large dealership is r = –0.34. If we measure Fuel Efficiency in kilometers per liter instead of miles per gallon, the correlation will increase.
False. Changing units to kilometers per liter instead of miles per gallon will not change the correlation.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
Since the correlation between Olympic gold medal times for the 800m hurdles and 100m dash is –0. 41, the correlation between times for the 100m dash and the 800m hurdles is +0.41.
False. Correlation does not change if we reverse the role of the x and y variables.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
Adding an outlier can dramatically change the correlation.
True. Outliers affect correlation.
Assume that the conditions for correlation are met. Determine whether each statement is true or false. Explain your answer briefly.
The correlation between Age and Income as measured on 100 people is r = 0.75. Whether we measure Age in years or months, the correlation will still be 0.75.
True. Changing units from years to months will not change the correlation.
Make a scatter plot that has a point that is far away from the trend of the other points but does not follow the trend that if that point was removed the correlation become stronger. Circle that point.
See "Removing Points 500" card.