Chapter 5

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Karl Pearson

correlation

phi coefficient

Correlation coefficients are used to describe

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

Bivariate

-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

R x y

r

scatter plot

positive slope

negative slope

49%

51%

.64

.64

.80
.8 to .1

.79
.6 to .8

.45
.4 to .6

-.26
.2 to .4

-.92

.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

reduced

pearson

phi

spearman rank

Point biserial

.90

.19

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

correlation coefficient

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

negative

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

negative correlation

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

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.

??

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

false?
page 77

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)

Example: