Question 1

What (approximate) correlation is shown in the following scatterplot:

A) 0.50
B) 1.00
C) Impossible to say without the data.
D) 0.00

Accepted Answer

D

Question 2

A researcher wants to examine the relationship between students' height, and the size of a box that they can jump over. Unfortunately, some of the students can't jump over the smallest box. This is an example of:
A) A floor effect.
B) A ceiling effect.
C) Outliers.
D) Measurement error.

Accepted Answer

A floor effect occurs when a measure is not able to capture lower levels of a variable. In this case, the box size is too small for some students to jump over, creating a lower limit to the measurement of their jumping ability. This is a floor effect, rather than a ceiling effect (where a measure is not able to capture higher levels of a variable, such as when a test is too easy for high-achieving students), outliers (which are extreme values that do not represent the typical pattern of the data), or measurement error (which refers to inaccuracies in measuring a variable).

Question 3

If we find a negative relationship between owning a cat and being a victim of a burglar (such that people who have cats are less likely to have their possessions stolen), what can we conclude:
A) Thieves like cats.
B) If you have a cat, your home is less likely to be robbed.
C) If you get a cat, your home is less likely to be robbed.
D) Cats don't like thieves.

Accepted Answer

(We don't know what it is about homes with cats, but getting a cat will not necessarily mean your home has the characteristics that deter thieves).

Question 4

A researcher finds that orchestra conductors tend to die at an older age than other members of the orchestra. What can they conclude?
A) Conducting orchestras is good for your health (swinging arms is good exercise).
B) Healthy people become conductors.
C) People who enjoy leading a healthy lifestyle like conducting orchestras.
D) None of these.

Accepted Answer

(In order to be a conductor, you need to live to be fairly old and still healthy, as it is a senior position. If you are not healthy at an older age, you cannot become a conductor.)

Question 5

We should be concerned about possible outliers because:
A) Outliers mean that we have a non-linear relationship.
B) Outliers mean that our data is skewed.
C) Outliers might represent an error in our measurement.
D) Outliers mean that someone has not told the truth when they responded to our questions.

Accepted Answer

Outliers can indicate errors in measurement or data entry, and can impact the accuracy of our analysis. We should investigate and potentially remove outliers before drawing conclusions from our data.

Question 6

Using Cohen's criteria, we would describe a correlation of 0.1 as:
A) Not statistically significant.
B) Small.
C) Interesting.
D) Medium.

Accepted Answer

According to Cohen's criteria, a correlation of 0.1 is considered small.

Question 7

Using Cohen's criteria we would describe a correlation of r = 0.48 as:
A) Significant.
B) Large.
C) Medium.
D) Causal.

Accepted Answer

The answer of Using Cohen's criteria we would describe a...

Question 8

Which of the following sets of values could occur with a real dataset:
A) r = 0.7; 95% CIs = 0.4, 1.1; p = 0.001
B) r = 0.0; 95% CIs = -0.2, 0.2; p = 0.03
C) r = 0.1, 95% CIs = -0.1, 0.3; p = 0.20
D) r = 0.1, 95% CIs = 0.0, 0.2; p = 0.01

Accepted Answer

The confidence interval (CI) for a correlation coefficient (r) must fall between -1 and 1, as these are the limits for correlation coefficients in real datasets. Options A, B, and D are incorrect because: A) the upper limit of the CI exceeds 1, which is not possible; B) a p-value of 0.03 with a correlation coefficient of 0.0 and such narrow CIs is unlikely; D) a p-value of 0.01 with a correlation coefficient of 0.1 and those CIs seems inconsistent. Option C is plausible because the CI is within the valid range and the p-value aligns reasonably with the correlation coefficient and CI range.

Question 9

Which of the following is true:
A) If I have two variables, and they are both normally distributed, I will have bivariate normality.
B) If I have two variables and they are both normally distributed, I may have bivariate normality, or I may not.
C) If I have two variables and they are both normally distributed, I will not have bivariate normality.
D) If I have two variables, and they are not normally distributed, I still could have bivariate normality.

Accepted Answer

Bivariate normality occurs when two variables have a joint normal distribution. While having two normally distributed variables increases the likelihood of bivariate normality, it is not a guarantee. Other factors such as the correlation between the two variables can also impact whether bivariate normality exists.

Question 10

You should use a Spearman correlation, rather than a Pearson correlation, if:
A) Your data are measured on an interval scale.
B) Your data have no outliers.
C) Your data do not have a normal distribution.
D) You are not interested in statistical significance.

Accepted Answer

Spearman correlation is a non-parametric test which doesn't assume a normal distribution in the data, unlike Pearson correlation. It is used when the data is measured on an ordinal scale or when it is not possible to meet the assumptions of normality and linearity required for Pearson correlation. Therefore, it is best to use Spearman correlation when the data does not have a normal distribution.

Question 11

Regression analysis, rather than correlation might be used when:
A) We don't know if there is a third variable that is the cause of both our variables.
B) We want to establish causation.
C) We don't care about causation.
D) We want to make predictions.

Accepted Answer

Regression analysis is used when we want to make predictions. Correlation helps us to understand the relationship between two variables, but regression analysis helps us to predict how one variable changes in response to changes in another variable. Regression does not establish causation, but rather the relationship between variables.

Question 12

Which of the following is true:
A) It is usually worth testing the intercept in a regression equation for statistical significance.
B) We should never test the intercept in a regression equation for statistical significance.
C) The intercept in a regression equation is never interesting.
D) The intercept in a regression is often an arbitrary value.

Accepted Answer

The answer of Which of the following is true:
A) It...

Question 13

Two researchers look at the relationship between the number of visits to the doctor with flu, and the temperature in different cities. They use the same data, but one researcher uses the Fahrenheit scale of temperature, and one uses the Celsius (centigrade scale). What would you expect:
A) Same correlation, same slope, different intercept.
B) Same correlation, different slope, different intercept.
C) Different correlation, different slope, different intercept.
D) Same correlation, same slope, same intercept.

Accepted Answer

Since both researchers are using the same data set, the correlation between the number of visits to the doctor with flu, and the temperature in different cities should be the same. However, since the two researchers are using different temperature scales, the slope of the regression line will be different. This is because Celsius and Fahrenheit scales have different units of measurement and different zero points. Therefore, the intercepts will also be different.

Question 14

A standardized regression line (in a bivariate regression) is:
A) Rarely useful.
B) Always worth looking at, even if you don't report it.
C) Another name for the correlation.
D) Easy to calculate if you know the slope and intercept.

Accepted Answer

A standardized regression line in a bivariate regression is essentially the correlation between the two variables, as it represents the relationship when both variables are standardized to have a mean of zero and a standard deviation of one.

Question 15

A researcher looks at the relationship between the scores for reading and age (in years) , for children in primary (elementary) school. The reading has 20 questions, so a score between 0 and 20 is possible. They find that the intercept = -5 and the slope = 2. What should they conclude?
A) Older children get higher scores on the test.
B) The predicted score of a 3 year old child would be 6.
C) You can't score -5 on the test, so they have made a mistake.
D) If they gave a 12 year old the test, they would expect a score of 24.

Accepted Answer

The positive slope of 2 indicates that as age increases, the reading score also increases, suggesting older children tend to score higher.

Question 16

The standard error of a correlation coefficient is:
A) A mistake that is commonly made by students.
B) A mistake that is rarely made by professors.
C) Not really a thing that is talked about.
D) Usually small.

Accepted Answer

(Correlations do not have symmetrical distributions, so they do not have a standard error unless they are transformed.)

Question 17

A researcher assesses the smoking and drinking habits of a group of retired ex-coal miners, and also assesses their grip strength. The researcher finds that the miners who smoke and drink more have higher strength. What can they conclude:
A) Smoking and drinking make you stronger.
B) People who exercise more smoke and drink more.
C) This can't be true.
D) There is probably a third variable that we have not accounted for.

Accepted Answer

(The third variable is age - younger ex-miners smoke and drink more and are stronger. Ex-miners who smoke a lot and drink are less likely to get old.)

Question 18

Ladislaus Bortkiewicz famously looked at the number of Prussian soldiers who had been kicked to death by horses over about 200 years. He found a distribution that looked like this:
 In most years (109) no Prussian soldiers were killed by horses. In 65 years, only one soldier died this way, until in one particularly bad year, 4 Prussian soldiers were killed by horses. If you wanted to predict this variable, what would you use?
A) Spearman correlation.
B) Non-linear regression.
C) Poisson regression.
D) Logistic regression.

Accepted Answer

The distribution of the number of Prussian soldiers killed by horses follows a Poisson distribution, as the data involves counting events (number of soldiers killed by horses) in a specific time period (200 years) with a low probability of occurrence. Poisson regression is the appropriate tool to use for predicting counts in this scenario.

Question 19

I asked students to measure their heights in inches, and then their heights in centimeters. I recorded the two measures and calculated the correlation between them. What do you think I would be most likely to find?
A) r = 0.5 (a large correlation).
B) r = 1.0 (a perfect correlation).
C) r = 0.95
D) r = 0.3

Accepted Answer

It is likely that there would be a strong positive correlation between height measured in inches and height measured in centimeters, as they are both measures of the same attribute (height) and are linearly related by a conversion factor. Therefore, it is reasonable to expect an r value close to 1.0, but not necessarily a perfect correlation due to measurement error or individual variation in height. A positive correlation (r>0) is expected, as taller heights measured in inches should correspond to taller heights measured in centimeters. Option A is possible, but it is unlikely to be as high as 0.5 because height is a highly reliable and valid measure. Option D is also possible, but it is unlikely as a correlation of 0.3 would suggest a relatively weak relationship between the two measures.

Question 20

Then I used the same data to do a regression. I predicted height in centimeters, using height in inches as the predictor. What would I be most likely to find:
A) Intercept = 0, slope = 1.
B) Intercept = 1, slope = 2.5
C) Intercept = 2.5, slope = 0.4
D) Intercept = 0, slope = 2.5

Accepted Answer

Since the predictor is height in inches and the outcome is height in centimeters, we know that the slope of the regression line must be converting inches to centimeters (2.54 cm per inch). Also, if someone is 0 inches tall, they would still have a height in cm, so we would expect a non-zero intercept. Therefore, the best choice is D, with an intercept of 0 and a slope of 2.54 (or approximately 2.5).

Quiz 18: Correlation and Regression

What (approximate) correlation is shown in the following scatterplot:

A researcher wants to examine the relationship between students' height, and the size of a box that they can jump over. Unfortunately, some of the students can't jump over the smallest box. This is an example of:

If we find a negative relationship between owning a cat and being a victim of a burglar (such that people who have cats are less likely to have their possessions stolen) , what can we conclude:

A researcher finds that orchestra conductors tend to die at an older age than other members of the orchestra. What can they conclude?

We should be concerned about possible outliers because:

Using Cohen's criteria, we would describe a correlation of 0.1 as:

Using Cohen's criteria we would describe a correlation of r = 0.48 as:

Which of the following sets of values could occur with a real dataset:

Which of the following is true:

You should use a Spearman correlation, rather than a Pearson correlation, if:

Regression analysis, rather than correlation might be used when:

Which of the following is true:

Two researchers look at the relationship between the number of visits to the doctor with flu, and the temperature in different cities. They use the same data, but one researcher uses the Fahrenheit scale of temperature, and one uses the Celsius (centigrade scale) . What would you expect:

A standardized regression line (in a bivariate regression) is:

A researcher looks at the relationship between the scores for reading and age (in years) , for children in primary (elementary) school. The reading has 20 questions, so a score between 0 and 20 is possible. They find that the intercept = -5 and the slope = 2. What should they conclude?

The standard error of a correlation coefficient is:

A researcher assesses the smoking and drinking habits of a group of retired ex-coal miners, and also assesses their grip strength. The researcher finds that the miners who smoke and drink more have higher strength. What can they conclude:

I asked students to measure their heights in inches, and then their heights in centimeters. I recorded the two measures and calculated the correlation between them. What do you think I would be most likely to find?

Then I used the same data to do a regression. I predicted height in centimeters, using height in inches as the predictor. What would I be most likely to find: