Chapter 5

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Who is responsible for the invention of the Pearson product-moment correlation coefficient?

Karl Pearson

When interested in examining how one variable changes in relation to another, which of the following descriptive statistics would you want to use?

correlation

Which of the following is an example of a correlation?

phi coefficient

Correlation coefficients are used to describe

. A group
. The correlation coefficient is used to indicate the relationship of two random variables

Which of the following refers to a correlation between two variables?

Bivariate

Which of the following illustrates the range of possible values of Pearson's product-moment correlation coefficient?

-1.0 to 1.0

If variables change in the same direction, what type of correlation is this called?

positive correlation

If variables change in the opposite direction, what type of correlation is this called?

negative correlation

The correlation between variable X and variable Y is represented by which of the following?

R x y

Pearson's product-moment correlation coefficient is represented by the following letter:

r

What would you use to represent a correlation visually?

scatter plot

When data points group together in a cluster from the lower left-hand side of the xy axis to the upper right-hand side, what is this?

positive slope

When data points group together in a cluster from the upper left-hand side of the xy axis to the lower right-hand side, what is this?

negative slope

If the correlation between variables is .70, what percent of the variance is shared variance?

49%

If the correlation between variables is .70, what percent of the variance is not shared variance?

51%

If the correlation between variables is .80, what is the coefficient of determination?

.64

If the correlation between variables is .60, what is the coefficient of alienation?

.64

Which of the following correlations would be interpreted as a very strong relationship?

.80
.8 to .1

Which of the following correlations would be interpreted a strong relationship?

.79
.6 to .8

Which of the following correlations would be interpreted a moderate relationship?

.45
.4 to .6

Which of the following correlations would be interpreted as a weak relationship?

-.26
.2 to .4

Which of the following is the strongest correlation?

-.92

Which of the following is the weakest correlation?

.19

This is another word for a positive correlation:

direct correlation

This is another word for a negative correlation:

indirect correlation

This is a correlation that is best expressed as a straight line:

linear correlation

This is a situation in which the correlation between two variables begins as a direct correlation, then becomes an indirect correlation, or vice versa.

curvilinear relationship

The coefficient of determination is equal to:

the square root of the pearson product moment correlation coefficient
. is the percentage of variance in one variable that is accounted for by the variance in the other variable.

The amount of unexplained variance in a relationship between two variables is called:

coefficient of alienation also called coefficient of nondetermination

A positive correlation between two variables would be represented in a scatterplot as

line sloping upwards
. all the data points are aligned along a straight line with a positive slope

A negative correlation between two variables would be represented in a scatterplot as:

a line sloping downwards
. data points would align themselves in a straight line as well, but from the upper left hand corner of the chart to the lower right.

If the correlation between two variables was equal to 0, the scatterplot between these two variables would be represented as:

a horizontal line

This is used to summarize the correlations between a set of variables.

correlation matrix

If the range of one or both of the variables is restricted, the correlation will be:

reduced

If you wanted to compute the correlation between two interval level variables, which type of correlation should you use?

pearson

If you wanted to compute the correlation between two nominal level variables, which type of correlation should you use?

phi

If you wanted to compute the correlation between two ordinal level variables, which type of correlation should you use?

spearman rank

If you wanted to compute the correlation between one nominal level variable and one interval level variable, which type of correlation should you use?

Point biserial

If the coefficient of determination between two variables is .81, what is the Pearson correlation coefficient?

.90

If the coefficient of determination between two variables is .81, what is the coefficient of alienation?

.19

What is the numerical index that describes the relationships between two variables?

correlation coefficient

The Pearson product-moment correlation examines the relationship between what type of variables?

continuous

This measure is equal to the percentage of variance in one variable that is accounted for by the variance in a second variable.

coefficient of determination

If X increases in value as Y decreases in value, what type of correlation exists

negative

If X decreases in value as Y increases in value, what type of correlation exists

negative correlation

If X decreases in value as Y decreases, what type of correlation exists?

positive

If X increases in value as Y increases, what type of correlation exists?

positive correlation

The better your time management skills are, the more work you are able to do is an example of a ____________.

positive correlation

The more oatmeal you eat, the lower your blood cholesterol level is an example of a ____________.

negative correlation

You can use Pearson's correlation coefficient if one or more of your variables are ordinal or nominal. T/F

false

When you have a direct correlation, both variables change in the same direction. T/F

True
In a direct or positive relationship, the values of both variables increase together or decrease together. That is, if one increases in value, so does the other; if one decreases in value, so does the other.

A negative correlation indicates that variables change in opposite directions. T/F

True

In an inverse or negative relationship, the values of the variables change in opposite directions. That is, if the independent variable increases in value, the dependent variable decreases; if the independent variable decreases in value, the dependent variable increases.

Correlation coefficients describe every individual person in your data set. T/F

??

The coefficient of determination is more precise than using a correlation coefficient alone. T/F

True
page 89

If two variables are correlated, this implies that one variable causes the other.T/F

false
correlation does not imply causation
ex on page 91

In certain cases, Pearson's product-moment correlation coefficient can have values greater than 1.T/F

false?
page 77

It is better to find a positive correlation as opposed to a negative correlation.

false
page 79

What is a correlation coefficient and what is its range?

. A correlation coefficient is a numerical index that reflects the relationship between two variables.
. Values for the correlation coefficient range between -1 and +1

How is a direct correlation different from an indirect correlation?

A direct relationship is a relationship between two variables in which they both increase or decrease in conjunction.
A indirect relationship is in which one variable decreases as another increases.

Is a correlation of 0.6 stronger than a correlation of -0.9? Why or why not?

no
page 79 ( the sign do not influence the strength of the correlation the absolute value is what matters)
. the absolute vale of the coefficients reflects the strength of the correlation.

A correlation coefficient comparing exercise and body mass is -.67. What does this say about the relationship between exercise and weight?

when one variable increases, the other variable decreases
ex: as study time increases, the number of errors on an exam decreases.

A correlation coefficient comparing study time to grades is a +.80. Can one then conclude that greater study time causes good grades?

. more of one, more of the other
. as the value of one variable increases, so does the other. For example, on average, as height in people increases, so does weight.
. positive correlation

What is the difference between the sum of a set of values squared and the sum of the squared values?

page 82
sum of a set of values squared: taking values such as 2,3 summing them (5) and then squaring that (25)
. the sum of the squared values: taking values such as 2,3 squaring them (4,9) and then adding those together (13)

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