Question 1

Which of the following is NOT a reason to explain why infant mortality increased with the number of physicians?
A) More physicians would lead to greater rates of reporting infant deaths.
B) Physicians go where the problems are.
C) Both variables are under the control of some third variable.
D) All of these answers are possible.

Accepted Answer

The statement that infant mortality increased with the number of physicians can be explained by all the provided options: A) increased reporting due to more physicians, B) physicians being more present in areas with higher problems, including infant mortality, and C) a third variable influencing both the number of physicians and infant mortality rates.

Question 2

An intercorrelation matrix is one that
A) presents the correlations of each variable with each other variable.
B) is symmetric.
C) has as many rows as it does columns.
D) all of the above

Accepted Answer

An intercorrelation matrix presents the correlations of each variable with each other variable, is symmetric, and has as many rows as it does columns. Therefore, all of the above options are correct.

Question 3

If the correlation between two variables is .76, and the sample size is large, we can conclude that
A) there is 76% of a relationship between the two variables.
B) there is a strong positive relationship between the two variables.
C) there is no relationship between the two variables.
D) both a and b

Accepted Answer

A correlation of .76 indicates a strong positive relationship between the two variables, meaning as one variable increases, the other tends to increase as well. The value does not represent a percentage of the relationship but rather the strength and direction of the relationship.

Question 4

If one of our variables is a dichotomy, the correlation we compute is A) Spearman's r _S. B) a rank correlation. C) a point-biserial correlation. D) a tetrachoric correlation.

Accepted Answer

When one of the variables is a dichotomy (binary variable with only two levels), the appropriate correlation to compute is a point-biserial correlation. This measures the relationship between a continuous variable and a dichotomous variable.

Question 5

If we look at the correlation between college admissions test scores and subsequent performance in college for all admitted applicants, we are likely to
A) underestimate the degree of correlation between test score and potential performance.
B) overestimate the relationship.
C) do quite a good job of estimating the relationship if our sample is sufficiently large.
D) not know much more than when we began.

Accepted Answer

This phenomenon occurs because of the restriction of range: only students with higher test scores are typically admitted to college, which limits the variability of the test scores in the sample and can lead to an underestimation of the true correlation between test scores and college performance in the broader population.

Question 6

Which of the following is the formula for the covariance?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Which of the following is the formula...

Question 7

The correlation in the population is denoted by
A) r
B) 
C) R
D) f

Accepted Answer

The correlation in the population is typically denoted by the symbol "r".

Question 8

The covariance will always
A) be a positive number.
B) be larger than the variance.
C) reflect the direction of the relationship.
D) be less than 1.0.

Accepted Answer

The covariance reflects the direction of the relationship between two variables. It can be positive (both variables move in the same direction), negative (one variable moves up while the other moves down), or zero (no relationship). The covariance can be any number (positive or negative) and is not limited to being less than 1.0 or larger than the variance.

Question 9

When we have a relationship that is continually rising, but the line showing the relationship is not necessarily straight, we call this a _______ relationship.
A) linear
B) reclining
C) bivariate
D) monotonic

Accepted Answer

A monotonic relationship means that the relationship between the two variables is consistently increasing or decreasing, but not necessarily at a constant rate. This allows for the line representing the relationship to be curved or have patterns, rather than a straight line (which would be a linear relationship). Reclining and bivariate are not commonly used terms in describing relationships between variables.

Question 10

A newspaper headline writer found that the more adjectives she put in the titles of her articles, the greater the number of newspapers that were sold that day. This relationship between numbers of adjectives and newspaper sales must be
A) significantly positive.
B) significantly negative.
C) monotonic.
D) positive.

Accepted Answer

The relationship described indicates that as the number of adjectives increases, newspaper sales also increase, which is a positive relationship.

Question 11

When the data are in the form of ranks we
A) need a special formula that Spearman derived.
B) can just apply the standard formula to the ranks.
C) need to convert the ranks to raw scores before computing the correlation.
D) cannot do anything with the data.

Accepted Answer

The answer of When the data are in the form...

Question 12

For a given set of data the covariance between X and Y is .80. The standard deviation of X is 2.0, and the standard deviation of Y is 3.0. The resulting correlation is closest to
A) .00
B) .15
C) .80
D) -.30

Accepted Answer

The formula for correlation is:
Correlation = Covariance / (Standard deviation of X * Standard deviation of Y)
Substituting the given values we get:
Correlation = 0.80 / (2.0 * 3.0) = 0.1333
The answer closest to this value is option B, 0.15. Therefore, the answer is B.

Question 13

The covariance between height and running speed on the State College track team was equal to -28.21. This tells us that the
A) relationship between height and speed is significant.
B) relationship between height and speed is negative.
C) the correlation is equal to the square root of -28.21.
D) the correlation is equal to -28.21.

Accepted Answer

The negative value of the covariance (-28.21) indicates a negative relationship between height and running speed. However, the covariance value itself cannot be interpreted as the correlation coefficient, so choices C and D are incorrect. Additionally, the significance of the relationship is not determined by the covariance value alone, so choice A is also incorrect.

Question 14

If high scores on X are paired with low scores on Y , the covariance is going to be
A) positive.
B) negative.
C) zero.
D) There is no way to tell.

Accepted Answer

When high scores on X are paired with low scores on Y, it indicates an inverse relationship between X and Y. In such cases, the covariance is negative.

Question 15

For the following data, S XY is equal to
 
X              2               4               5
Y              2               3               4
​
A) 11
B) 9
C) 99
D) 36

Accepted Answer

S XY = Σ(XY) - ((ΣX)(ΣY))/n
= (2 x 2) + (4 x 3) + (5 x 4) - ((2+4+5)(2+3+4))/3
= 4 + 12 + 20 - (11 x 3)/3
= 36 - 33
= 3. Therefore, the correct option is D.

Question 16

We can often use a Pearson correlation even when a relationship is curvilinear. This is because
A) a straight line will often fit the data remarkably well.
B) you can always calculate a correlation with any set of data.
C) the correlation coefficient doesn't care if the relationship is curvilinear.
D) there is no alternative.

Accepted Answer

A Pearson correlation can still be useful in determining the strength and direction of the relationship between two variables, even if the relationship is curvilinear. In some cases, a straight line can still fit the data well and provide a good estimate of the correlation coefficient. However, it is important to also examine the scatterplot of the data to confirm that a linear relationship is appropriate before using a Pearson correlation.

Question 17

In testing the significance of a correlation coefficient, the degrees of freedom are
A) N
B) N - 1
C) N - 2
D) N - 3

Accepted Answer

The degrees of freedom for testing the significance of a correlation coefficient are calculated as N - 2, where N is the sample size. This accounts for the two parameters estimated in correlation analysis (the slope and intercept of the line of best fit).

Question 18

A _______ refers to the degree of the relationship between two or more variables.
A) regression
B) correlation
C) relative frequency
D) matched sample

Accepted Answer

Correlation refers to the degree of relationship between two or more variables. Regression is a statistical technique used to analyze the relationship between variables by fitting a line or curve on a scatter plot. Relative frequency refers to the proportion of times an event occurs in relation to the total number of times the event could occur. Matched sample refers to a sample in which each participant is matched with another participant who has similar characteristics.

Question 19

Which of the following pairs go together?
A) dependent variable : criterion variable
B) dependent variable : predictor variable
C) independent variable : criterion variable
D) independent variable : Y variable

Accepted Answer

The dependent variable and criterion variable are interchangeable terms as they both refer to the variable being predicted or explained by the independent variable. The independent variable is the variable that is manipulated or controlled by the researcher, while the dependent variable is the outcome variable that is being measured. Therefore, choice A is the correct pair as the dependent variable and criterion variable are synonymous.

Question 20

When we say that a correlation coefficient is statistically significant, we mean that
A) we have reason to believe that it reflects an important relationship between variables.
B) we have reason to believe that the relationship is positive.
C) we have reason to believe that the true correlation in the population is not 0.0.
D) we have strong support for a causal statement about the relationship.

Accepted Answer

When a correlation coefficient is statistically significant, it means that the probability of obtaining that correlation coefficient by chance is low (typically less than 5%). Therefore, we can conclude that there is a relationship between the variables in the sample, and that this relationship is likely to be present in the population as well. While we cannot make causal statements about the relationship based on correlation alone, we can infer that there is a true correlation between the variables.

Quiz 9: Correlation

Which of the following is NOT a reason to explain why infant mortality increased with the number of physicians?

An intercorrelation matrix is one that

If the correlation between two variables is .76, and the sample size is large, we can conclude that

If one of our variables is a dichotomy, the correlation we compute is

If we look at the correlation between college admissions test scores and subsequent performance in college for all admitted applicants, we are likely to

Which of the following is the formula for the covariance?

The correlation in the population is denoted by

The covariance will always

When we have a relationship that is continually rising, but the line showing the relationship is not necessarily straight, we call this a _______ relationship.

A newspaper headline writer found that the more adjectives she put in the titles of her articles, the greater the number of newspapers that were sold that day. This relationship between numbers of adjectives and newspaper sales must be

When the data are in the form of ranks we

For a given set of data the covariance between X and Y is .80. The standard deviation of X is 2.0, and the standard deviation of Y is 3.0. The resulting correlation is closest to

The covariance between height and running speed on the State College track team was equal to -28.21. This tells us that the

If high scores on X are paired with low scores on Y , the covariance is going to be

For the following data, S XY is equal to X 2 4 5 Y 2 3 4 ​

We can often use a Pearson correlation even when a relationship is curvilinear. This is because

In testing the significance of a correlation coefficient, the degrees of freedom are

A _______ refers to the degree of the relationship between two or more variables.

Which of the following pairs go together?

When we say that a correlation coefficient is statistically significant, we mean that

For the following data, S XY is equal to X 2 4 5 Y 2 3 4