This chapter discusses correlation and correlation analysis. It defines correlation as a measure of the strength of the relationship between two variables. The Pearson correlation coefficient is the most common measure used and ranges from -1 to 1, with -1 indicating a perfect negative correlation and 1 indicating a perfect positive correlation. For the Pearson correlation, the data must be interval or ratio scaled and from normally distributed populations with similar distributions. A scatterplot can help visualize the relationship between two variables by plotting their scores. Stronger correlations have less scatter in the plot.
1. chapter 9
Correlation
Learning Objectives
After reading this chapter, you will be able to. . .
1. explain the hypothesis of association.
2. interpret the correlation coefficient.
3. list the Pearson correlation requirements.
4. describe what the coefficient of determination explains.
5. explain the variables involved in the point-biserial
correlation.
6. describe the applications for the Spearman rho correlation.
7. present the data based on correlational output using SPSS.
8. interpret and report results of Pearson correlation and
Spearman rho correlation in APA format.
iStockphoto/Thinkstock
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CHAPTER 9Section 9.1 The Hypothesis of Association
Correlation is a concept that transcends statistical analysis. The
study of relationships, which is what correlation involves, has
many applications: Cloudy days are related
to (correlated with) cooler temperatures. Natural disasters are
related to declines in the
stock market. An impending test is related to the need to study,
and grinding noises in the
engine compartment of a car are usually related to repair bills.
Some relationships are stronger than others, so statistical
procedures have been developed
to quantify, or provide a numerical indicator of, the strength of
the relationship between
two variables. The numerical indicators are called correlation
coefficients, and one of the
most common is the Pearson correlation coefficient. The name
Pearson refers to Karl
Pearson, whose impact not just on studying correlation but also
on statistical analysis
generally may be unparalleled by that of any other individual.
In the early years of the 20th century, Pearson founded the first
3. department of statisti-
cal analysis, at University College London. Under Pearson’s
direction, the department
attracted, among others, William Sealy Gosset of t-test fame;
Ronald A. Fisher, who pro-
duced analysis of variance; and Charles Spearman, who
developed another correlation
approach as well as an elegant statistical procedure called factor
analysis. It is difficult to
overstate the impact that Pearson had on the evolution of
statistical analysis.
A man of fierce independence, Pearson’s education at
Cambridge was directed at religion
and philosophy rather than mathematics. As a student of
religion, he sued the university
over the compulsory chapel attendance required of all
undergraduates. Winning his suit
brought a change to university rules about compulsory
attendance, after which Pearson
chose to attend chapel! His graduate work (in Germany)
emphasized literature, and it is
a testimony to his extraordinary breadth of talent that his
greatest contributions would
be in statistical analysis. Pearson was a contemporary of
Einstein. Just as Einstein sought
a grand theory that would unite all of physics, Pearson sought a
grand theory to unite
all of mathematics. Both men were disappointed in these
endeavors, but that should not
detract from what Pearson did accomplish. Although Pearson’s
associations with his col-
leagues were not always harmonious, he and the other
statisticians who found an aca-
demic home in his department virtually defined modern
quantitative analysis. No one
4. who “crunches” numbers for any length of time can be
unaffected by the procedures and
the analytical techniques these men developed.
9.1 The Hypothesis of Association
Previous chapters concentrated on tests of significant
difference. The z-test, the inde-pendent samples t-tests, and
analysis of variance are tests of the differences between
groups. They all fall under a general assumption referred to as
the hypothesis of dif-
ference. However, some kinds of analyses do not involve
questions about significant
differences.
If a psychologist asks about the relationship between birth order
and achievement moti-
vation or about the connection between the amount of time
children read and their
school grades, the question is about relationships rather than
differences. Those ques-
tions call for procedures connected to the hypothesis of
association, and when results
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5. suk85842_09_c09.indd 326 10/23/13 1:42 PM
CHAPTER 9Section 9.1 The Hypothesis of Association
are statistically significant, it means that the relationship, rather
than the difference, prob-
ably is not random.
Correlation Versus Causation
Before pursuing correlation, it is important to make a
distinction between correlation and
causation. Because two characteristics covary, or vary together,
does not presume that one
necessarily causes the other. Although there may be a causal
relationship, it usually cannot
be determined just from studying the correlation. One of your
author’s statistics profes-
sors addressed the risk of confusing correlation with causation
this way.
Someone drinks on three successive nights. The first night it is
scotch and water, on the
second night it is bourbon and water, and on the third he drinks
vodka and water. All
three mornings after are accompanied by hangovers. Because
the water is common to
each experience, one might erroneously conclude that water
must be the cause.
There is a classic study that demonstrates, among other things, a
correlation between the
sale of ice cream by vendors on city streets and burglaries in the
same city. Someone rush-
6. ing to judgment about cause might wish to curb ice cream sales
in order to reduce the
number of burglaries, or check the criminal records of ice cream
vendors, not recognizing
that hotter weather (and the open windows that result) probably
drives both. It is not
unusual for some third variable to explain an association
between a first and a second.
Although correlation values provide some evidence for
causation, correlation alone is
rarely sufficient to demonstrate causality.
Picturing Correlation
If the word correlation is broken down—co-relation—it
expresses what is meant: The char-
acteristics are related, and the evidence for the relationship is
that they vary together, or
covary. As the level of one variable changes, the other changes
in concert. This happens
because both variables contain some of the same information.
The higher the correlation,
the more information they have in common.
A correlation can be represented visually in what is called a
scatterplot. A researcher
wishes to study the relationship between verbal ability and
intelligence and gathers scores
on both of those characteristics for 12 participants. The data is
as follows:
Participant 1 2 3 4 5 6 7 8 9 10 11 12
Verbal ability 20 35 42 48 55 60 63 66 72 76 78 85
Intelligence 80 95 90 100 100 100 110 115 120 115 110 125
7. The first participant has a verbal ability score of 20 and an
intelligence score of 80. The
data appears to suggest that as the values of one increase, so do
the values of the other;
there appears to be a positive correlation. But the relationship is
easier to see in a scatter-
plot, a graph plotting the scores of one variable on the
horizontal axis, and the other on the
vertical axis with dots indicating the intersection of each pair of
scores. There is an Excel
scatterplot of the verbal ability/intelligence data in Figure 9.1.
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CHAPTER 9Section 9.1 The Hypothesis of Association
Figure 9.1: The relationship between verbal ability and
intelligence
In the scatterplot, intelligence scores are plotted on the vertical/
ordinate or y-axis and the verbal ability scores are plotted on
the
horizontal/abscissa, or x-axis, with a dot representing where
the two scores for each participant intersect; each dot repre-
sents an intelligence score and a verbal ability score.
The plot indicates that the hunch about a positive relation-
ship was accurate. The general trend is from lower left to
upper right. As the value of one variable increases, the value of
the other tends to do like-
wise. The incline is not dramatic, but there is a general rise in
the data points.
8. Less-than-Perfect Relationships
The relationship certainly is not perfect. The fourth, fifth, and
sixth participants all have
the same level of intelligence but different levels of verbal
ability. The same is true of
participants 8 and 10, as well as participants 7 and 11. Still,
there is a general lower-left
to upper-right relationship, which is what might be expected.
Smarter people often have
more complex language patterns, perhaps evidenced by higher
verbal ability scores.
However, it also is not surprising that the relationship between
intelligence and verbal
ability (as demonstrated in school performance) is less than
perfect. Almost everyone
knows someone who is very bright but did not excel in school.
Or, at the other extreme,
there was that person of fairly average intelligence who
performed brilliantly in school.
There are names for these exceptions to the general correlation
tendency: underachievers
and overachievers.
A A single point
in a scatterplot
represents how many raw
scores?
Try It!
0
80
9. 100
120
40
60
20
140
0 20 40 60 80 100
Verbal Ability
In
te
lli
g
e
n
ce
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CHAPTER 9Section 9.1 The Hypothesis of Association
The exceptions point to the fact that people are very complex.
Human behavior is rarely
explained by one or two variables. Although intelligence is
10. related to verbal aptitude, so
are a number of other variables, such as how much the
individual reads, how easily the
individual is distracted, and how much experience the person
has had. One of the reasons
correlation values are calculated is to determine the level of
agreement when the relation-
ships are less than perfect, as they almost always are with
people.
The issue for questions under the hypothesis of association is
not whether the relationship
is perfect, because it would be extremely rare if it was, but
rather whether the relationship
is statistically significant. Statistically significant correlations
tend to reemerge every time
new data is gathered and the correlation calculated.
Although perfect correlations are rare when dealing with
people, that is not necessarily
the case in some disciplines. Mathematicians enjoy the stability
of perfect relationships.
For example, the formula for the area of a circle, A 5 πr2 (pi
times the square of the radius),
works for circles of any size because there is a perfect
relationship between a circle’s radius
and its area.
But even imperfect correlations can be very important. For
example, health professionals,
knowing that there is a correlation, even a weak one, between
the exposure to secondhand
smoke and the development of respiratory problems, warn the
public against exposure. In
this case, as exposure to secondhand smoke increases so too the
incidence of respiratory
11. problems increases. The research concerning secondhand smoke
and respiratory prob-
lems demonstrates a relationship or association between these
variables that is not causal
but that may, upon further experimental investigation, show a
causal element. In a similar
example, suppose educators know there is a correlation between
the amount of time stu-
dents spend on homework and their success on a high school
exit exam; as the number of
hours spent on homework goes up, high school exit exam scores
increase. Based on such a
correlation, the educators could encourage students to study
more in the expectation that
pass rates may rise if they do.
These two examples each illustrate a positive correlation that
simply means that as the
value of one variable increases (or decreases), the value of the
related variable likewise
increases (or decreases). In basic terms, the values of the two
variables move in the same
direction and, when the data is plotted, the slope will be
positive; that is, upward to the
right (Figure 9.2). The term positive does not imply a value
judgment as to whether the
outcome is desirable.
A negative correlation is one in which the values of two
correlated variables move in
opposite directions. As the value of one variable increases, the
value of the other decreases
and vice versa. When the data is plotted, the slope will be
negative; that is, downward
to the right (Figure 9.2). Just as a positive correlation does not
mean that the relationship
12. between two variables is somehow “good,” neither does a
negative correlation suggest
that the relationship between two variables is “bad.” Consider
the case of a drug reha-
bilitation program that demonstrates a negative correlation
between the amount of time
spent in the program and the rate of recidivism. As the number
of days spent in rehabilita-
tion increases, the rate of occurrence of relapse decreases.
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CHAPTER 9Section 9.1 The Hypothesis of Association
Figure 9.2: Degrees of correlational strength
Source: The New Spalding Grammar School,
www.sgspsychology.webs.com. Retrieved from
http://sgspsychology.webs.com
/METHODS/correlation.gif
The Amount of Scatter
The amount of scatter in a scatterplot suggests the strength of
the correlation. Scatterplots
for strong correlations have very little scatter. The points
coalesce around what can appear
to be almost a line. More scattered points and a less well-
defined line indicate weaker
relationships.
Strong Positive
Weak Positive
13. Strong Negative
Moderate Negative
None Weak Negative
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www.sgspsychology.webs.com
http://sgspsychology.webs.com/METHODS/correlation.gif
http://sgspsychology.webs.com/METHODS/correlation.gif
CHAPTER 9Section 9.1 The Hypothesis of Association
What Correlations Provide
Calculating a correlation produces a single number that
indicates the
strength of the relationship between the variables involved.
Correla-
tion values of either 21 or 11 indicate perfect relationships. A
correla-
tion of 0 indicates no relationship. Values less than the absolute
value
of 1 indicate an imperfect relationship, with the strength of the
rela-
tionship declining as the value approaches 0 from either
extreme. The
sign that precedes the value (1 or 2) indicates whether the
correla-
tion is positive or negative. In terms of hypothesis testing, the
further
the value is away from 0, the higher the correlation and the
lower the
14. p-value. An indication of p , .05 indicates a 5% probability that
there
is a significant difference away from 0 (i.e., a significant
correlation).
Correlating two variables does not require that they both
measure the same characteristic.
Often, entirely different kinds of things are correlated. The
example of secondhand smoke
and respiratory issues involves two completely different
variables, but the strength of
the relationship between them can be calculated nevertheless.
As long as the two vari-
ables can be quantified—reduced to a number—the strength of
the relationship can be
determined. This is also termed a bivariate analysis indicating
two variables. As a result,
bivariate outliers should be detected when performing these
analyses as described in the
next section.
Requirements for the Pearson Correlation
There are several different correlation procedures. The
appropriate procedure for a par-
ticular problem is determined by characteristics such as the
scale of the data involved. The
Pearson correlation, for example, requires variables of either
interval or ratio scale. Nomi-
nal or ordinal scale data involves other procedures. In addition
to the need for interval or
ratio data, the Pearson correlation has the following
requirements:
• In their populations, the characteristics are assumed to be
normally distributed.
15. Normal distributions can never be reflected in relatively small
samples, but
there must be reason to believe that the samples come from
populations that are
normal.
• The distributions from which the samples come must be
similarly distributed.
• The two samples are assumed to be randomly selected from
their populations.
• The relationship between the variables must be linear.
• Bivariate outliers should be detected and dealt with to account
for their influence.
Normality is indicated when the standard deviation is about
one-sixth of the range, the
measures of central tendency all have about the same value, and
other sophisticated
methods such as the Shapiro-Wilks or Kolmogorov-Smirnov
tests (Chapter 2). The nor-
mality of the two variables involved in a correlation is also
suggested by the way data is
distributed in the scatterplot. When both variables are normal,
the points in the plot will
be distributed from left to right with the number of points
gradually increasing until they
reach their greatest frequency in the middle of the graph and
then decreasing gradually
to the right extreme. If the relationship is positive, that scatter
is generally from lower left
B If two
variables are
normally distributed
but uncorrelated,
what pattern will their
16. data points make in a
scatterplot?
Try It!
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CHAPTER 9Section 9.1 The Hypothesis of Association
to upper right. If it is negative, the pattern is from upper left to
lower right. If there is no
correlation between the variables, the points make a circular
pattern in the middle of the
graph with the greatest density in the middle of the circle. The
greater frequency in the
middle of the circle reflects central tendency in data
distributions.
The similar-distribution requirement does not mean that the
standard deviations should
be the same. That is not likely to happen unless both variables
are measured along the
same range. It means that the standard deviations should
account for similar proportions
of their respective ranges.
The strength of a correlation is affected by range attenuation.
When the range of scores
in either variable is artificially abbreviated, the correlation
value will be artificially low.
Range attenuation can be indicated by a standard deviation that
is substantially smaller
than we know it to be in the population. If we were correlating
intelligence scores with
17. reading comprehension, and the intelligence scores have a
standard deviation of 8 points
when we know that the population standard deviation is 15
points, we can expect any
resulting correlation value to be artificially low. One of the
advantages of random selec-
tion is that random samples of a reasonable size tend to mirror
their populations reason-
ably well. Range restriction problems are much less likely to
occur with randomly selected
samples.
Different Types of Correlations
When the relationship between two variables is linear, it means
that the degree to which
they change in concert with each other is consistent throughout
their ranges; if it is low
and positive, it is low and positive at low levels of both
variables and at higher levels of
both variables. Consider the correlation between anxiety and
performance on an achieve-
ment test. For someone preparing for an important test, a little
anxiety is probably a good
thing. It prompts the individual to take the test seriously, to
prepare study notes, to spend
more time reading the textbook, and so on. If there is not any
anxiety at all, the test might
be disregarded. It seems likely that, at least in the early going,
achievement increases with
anxiety.
However, there is a point when if the level of anxiety continues
to increase, the individual’s
performance reaches a plateau and then may even begin to
diminish. The test-taker can
18. become so anxious that concentration is difficult and
performance no longer improves.
Beyond that point, increasing anxiety probably inhibits
achievement. These conditions
describe a relationship that is curvilinear. It is illustrated in the
following data, where anxi-
ety is gauged as a function of someone’s increasing pulse rate in
beats per minute, and
achievement as the number of problems per minute the
individual completes successfully.
Anxiety 52 54 58 62 64 67 72 73 75 78 82 86 88
Achievement 3 5 6 6 8 8 9 7 5 5 4 3 1
The scatterplot illustrating the relationship between anxiety and
achievement is Fig-
ure 9.3.
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CHAPTER 9Section 9.1 The Hypothesis of Association
Figure 9.3: The relationship between achievement and anxiety
Initially, there is a positive relationship between anxiety and
perfor-
mance. The first few pairs of data have points that rise from left
to
right. However, a positive relationship becomes negative when
as
anxiety increases, performance falls off. The correlation is
curvilinear.
After performance reaches 9 problems completed successfully
19. per
minute, more anxiety does not boost this individual’s
performance.
The scatterplot also reveals some of the danger associated with
range
restriction. If someone collected data for only the first half of
the sample, so that the first
six pairs of scores were the sample, those scores provide very
different indicators of the
relationship between anxiety and performance than the last six
pairs of scores. The first
part of the distribution makes the relationship look linear and
positive. The latter part
of the data makes the relationship look linear but negative. An
accurate picture of the
relationship requires data throughout the entire ranges of the
two variables. Since a curvi-
linear relationship is detected in this example, specifically a
quadratic curve, a Pearson cor-
relation cannot be used as this violates the assumption of
linearity. Testing for a quadratic
curve can be estimated using the following SPSS steps:
Analyze S Regression S Curve Estimation
Such analyses is beyond the scope of this book, but curve
estimation theory, steps, and out-
put can be interpreted with the help of most advanced graduate-
level statistics textbooks.
Understanding Correlation Values
It is important not to confuse the sign of the correlation with its
strength. A correlation
of 2.50 contains the same amount of information about the two
20. variables as does a cor-
relation of 1.50. The sign makes a great deal of difference to
how the relationship is
C What impact
does range attenua-
tion have on a
correlation?
Try It!
0
4
5
6
2
3
1
9
8
7
0 50 55 60 65 70 75 80 85 90
Anxiety
A
21. ch
ie
ve
m
e
n
t
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CHAPTER 9Section 9.2 Calculating the Pearson Correlation
interpreted, but it has nothing to do with the strength of the
relationship. With positive
correlations, as the value of one variable increases so does the
value of the other. When
correlations are negative, increasing values of one variable are
associated with decreasing
values of the other.
Earlier we noted that different scales of data require different
types of correlation proce-
dures. Different correlation procedures are also needed
depending on the number and
arrangements of the variables involved:
• Bivariate correlations indicate the relationship between two
variables. Bivariate
correlations are the focus of this chapter.
• Multiple correlation gauges the relationship between one
22. variable and a combi-
nation of others.
• Canonical correlation measures the relationship between two
groups of
variables.
• Partial correlation measures the relationship between two
variables, controlling
for the influence of a third variable on both of the first two.
• Semipartial correlation allows one to gauge the relationship
between two vari-
ables, controlling for the influence of a third on either of the
first two.
• Point-biserial correlation allows a correlation with one of the
variables having
dichotomous data and the other variable with continuous data.
• Tetrachoric correlation allows a correlation when both
variables are dichoto-
mous data.
All the correlations in this bulleted list, except bivariate
correlations, are beyond the scope
of this book. Just note that correlation can involve several
different configurations and
scales of variables.
9.2 Calculating the Pearson Correlation
Also called the Pearson product-moment correlation coefficient,
the Pearson correla-tion, or because its symbol is typically a
lowercase r, “Pearson’s r” is probably the
most often calculated of any correlation value. Thumbing
23. through statistics books and
online sources will reveal several formulas. All the formulas
provide the same answer, but
some are easier to follow than others. Visually, Formula 9.1 is
probably simplest:
rxy 5
a 3 1zx2 1zy2 4
n 2 1
Formula 9.1
Note that the r has the subscripts x and y, which refer to the
correlation of the x variable
with the y variable. Because there is no assertion of cause, it
does not matter which vari-
able is labeled x and which y. Formula 9.1 indicates that
1. if the x scores are transformed into z scores (Formula 3.1: z 5
x 2 M
s
)
2. and the y scores are also transformed into z scores,
3. the value of rxy is the sum of the products of the x and y z
scores for each
participant,
4. divided by the number of participants in the data group minus
1.
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24. CHAPTER 9Section 9.2 Calculating the Pearson Correlation
5. The n 2 1 signifies that this is a correlation formula for
sample, rather than popu-
lation, data. It is the same adjustment for sample data made with
the standard
deviation calculation in Chapter 1.
• Formula 9.1 can be used to calculate the correlation value of
the verbal ability
and intelligence scores from the earlier example.
• Transforming the verbal ability and intelligence scores into
their equivalent z
values with Formula 3.1 produces the following z equivalents
for the original
raw scores:
Verbal
ability (x)
21.991 21.212 2.848 2.537 2.173 0.87 .242 .398 .710 .917
1.021 1.385
Intelli-
gence (y)
21.902 20.761 21.141 2.380 2.380 2.380 .380 .761 1.141 .761
.380 1.522
Here, each pair of z scores is multiplied and the products
summed:
(21.991 3 21.902) 1 (21.212 3 20.761) 1 … 1 (1.385 3 1.522) 5
10.313
25. rxy 5
a 3 1zx2 1zy2 4
n 2 1
Because n (the number of pairs of scores) 5 12, n 2 1 5 11:
rxy 5
10.313
11
5 .938
With a maximum possible correlation value of 1.0, rxy 5 .938
indicates a strong relation-
ship between verbal ability and intelligence, something that is
reflected in the fact that
many intelligence measures include measures of verbal ability.
Although Formula 9.1 is visually simple, the need to turn
everything into z scores before
calculating rxy makes the calculations very time-consuming and
tedious. It is the long
way around. Formula 9.2 is the formula we will use, and it also
turns out to be the for-
mula programmed into many hand-calculators. It is visually
more complex but much
easier to execute.
rxy 5
n a xy 2 ( a x)( a y)
Å e cn a x
2 2 ( a x)
2 d cn a y2 2 ( a y)2 d f
26. Formula 9.2
Where
x 5 one of the scores in each pair
y 5 the other score in each pair (the designation of the x and y
pairs must
be consistent)
n 5 the number of participants for whom there are scores, or the
number
of pairs of scores
suk85842_09_c09.indd 335 10/23/13 1:42 PM
CHAPTER 9Section 9.2 Calculating the Pearson Correlation
a xy indicates that the two scores for each participant are
multiplied and then
summed (This value is referred to as the sum of the cross
products.)
a x
2 indicates that each x score is squared, and then the squares
summed
( a x)
2 indicates that the x scores are all totaled, and then that total
squared
a y
2 indicates that each y score is squared, and then the squares
summed
27. ( a y)
2 indicates that the y scores are all totaled, and then that total
squared.
The formula is not as daunting as it seems. After calculating a
problem or two, the process
will become familiar. Probably most of the statistical heavy-
lifting will be done with Excel
or a hand-calculator that has a built-in correlation function, but
it is helpful to prepare
for that occasional time when there is no computer and the
calculator has no correlation
function.
A Correlation Example
A researcher is duplicating a classic experiment by psychologist
E. L. Thorndike. The
experiment is related to Thorndike’s law of effect, which
maintains that behaviors fol-
lowed by a satisfying state of affairs are likely to be repeated.
In the experiment, the
researcher sets up a cage equipped with a door that opens if a
cat placed in the cage bats
a string suspended inside the cage. According to the law of
effect, if batting the string is
followed by something satisfying, that behavior should occur
more frequently than other
behaviors in future trials. A hungry cat is placed in the cage and
food is placed outside
where it is inaccessible from the inside of the cage. The data
represents the several trials
and the amount of time in minutes that elapse each time before
the cat releases itself. This
experiment is repeated 10 times over as many days. The data is
28. as follows:
Trial number 1 2 3 4 5 6 7 8 9 10
Elapsed time 5.0 5.5 4.75 4.5 4.25 3.5 2.75 2.0 1.0 .25
The scatterplot for this data is in Figure 9.4. The data suggests
that the relationship is prob-
ably negative and quite strong.
suk85842_09_c09.indd 336 10/23/13 1:42 PM
CHAPTER 9Section 9.2 Calculating the Pearson Correlation
Figure 9.4: The relationship between number of trials and
elapsed time
The correlation value offers a check of both conclusions. Verify
that
n 5 10
a xy 5 137.25
ax
2 5 385
( a x)
2 5 (55)2
ay
2 5 141
( a y)
29. 2 5 (33.5)2
Now, use Formula 9.2:
rxy 5
n a xy 2 ( a x)( a y)
Å e cn a x
2 2 ( a x)
2 d cn a y2 2 ( a y)2 d f
Substituting the relevant values provides
rxy 5
101137.152 2 1552 133.52
"531013852 2 1552 2 4 31011412 2 133.52 2 46
rxy 5
1372.5 2 1842.5
"3 13850 2 30252 4 3 11410 2 1122.252 4
rxy 5
2470
"1825 3 287.752
5 2.965
0
4
5
30. 2
3
1
6
0 2 4 6 8 1210
Number of Trials
E
la
p
se
d
T
im
e
in
M
in
u
te
s
suk85842_09_c09.indd 337 10/23/13 1:42 PM
31. CHAPTER 9Section 9.2 Calculating the Pearson Correlation
Interpreting Results
The relationship is indeed negative and because the maximum
correlation is 61.0, the
relationship is also substantial, but neither of those conclusions
indicates whether it is
statistically significant. As with z, t, and F, significance is
determined by comparing the
calculated value to a table value. For the Pearson correlation, it
is Table 9.1 (also Table E
in the Appendix).
Table 9.1: The critical values of rxy
Number of xy
Pairs (n)
Degrees of
Freedom (n 2 2)
Alpha (A) Level
0.10 0.05 0.01
3 1 0.988 0.997 1.000
4 2 0.900 0.950 0.990
5 3 0.805 0.878 0.959
6 4 0.729 0.811 0.917
7 5 0.669 0.754 0.875
33. Source: Brighton Webs Ltd. Statistical and Data Services for
Industry. (2006). Critical values of correlation coefficient R.
Retrieved from
http://www.brighton-webs.co.uk/statistics/critical_values_r.aspx
suk85842_09_c09.indd 338 10/23/13 1:42 PM
http://www.brighton-webs.co.uk/statistics/critical_values_r.aspx
CHAPTER 9Section 9.2 Calculating the Pearson Correlation
Like the t and F values, the correct critical value for r is
determined by the degrees of free-
dom. They are the number of pairs of data minus 2. Be careful
not to confuse the number
of pairs with the number of scores.
Table 9.1 has columns for a 5 .1, a 5 .05, and a 5 .01. The
columns for .05 and .01 are
quite typical; the column for a 5 .1 occurs in statistical tables
less often. For 8 degrees of
freedom (the number of pairs of data minus 2) and with a 5 .05,
the critical value is .632,
which is written this way:
rxy .05(8) 5 .632
The subscripts help distinguish the table value from the
calculated correlation value.
If the calculated value equals or exceeds the table value, the
result is statistically sig-
nificant. In two-tailed tests, the sign of the correlation value—
whether it is positive or
34. negative—is not relevant to whether it is significant. Some
tables also include the critical
values for one-tailed correlations, which are relevant for
determining whether a value
with a specified sign is significant. Table 9.1 has only the
values for two-tailed tests.
The Relationship Between Degrees of Freedom and Significance
Even with a correlation value as extreme as .956, checking the
table for significance is
important. In both the t-test and ANOVA, the magnitude of the
critical values declines as
degrees of freedom (and sample size) increase. It is the same
with correlation, but here the
decline in critical values is more dramatic. Note from Table 9.1,
for example, that if n 5 3
(and, therefore, df 5 1) the correlation would need to be at least
rxy 5 .997 (nearly perfect)
to be statistically significant. At the other extreme, if n 5 25 (so
that df 5 23) a correlation
of just rxy 5 .396 is statistically significant!
The Statistical Hypotheses
The null and alternate hypotheses take on different forms with
correlation than they had
for the difference tests. The null hypothesis is that there is no
relationship between the
variables. Symbolically, it is written this way:
H0: r 5 0
The r is the Greek letter rho (as in “row your boat”) and is the
equivalent of r, the symbol
for a Pearson correlation. So the null hypothesis says in effect r,
35. or the correlation, equals
0. More specifically, it means that there is no statistically
significant relationship, which
is one that is likely to emerge every time data is collected and
analyzed. The alternate
hypothesis states that the correlation does not equal 0; in this
case, there is a statistically
significant relationship:
Ha: r ? 0
suk85842_09_c09.indd 339 10/23/13 1:42 PM
CHAPTER 9Section 9.2 Calculating the Pearson Correlation
The Coefficient of Determination
One of the recurring themes in this book is the distinction
between statistical significance
and practical importance. Measures of practical importance
were the reason for calculat-
ing Cohen’s d and eta-squared for significant t-test and ANOVA
results.
Effect sizes may be even more important for correlation results
because relatively small
correlations can be statistically significant when the sample
sizes are large enough. The
effect size for the Pearson correlation is the coefficient of
determination (rxy
2). As the
notation suggests, the coefficient of determination is simply the
square of the correlation
36. coefficient. Squaring the correlation indicates how much of the
variance in y is explained
by x (or vice versa because there is no judgment about cause).
In the problem about number of trials and elapsed time,
rxy 5 2.965, so
rxy
2 5 .931
For that problem, the coefficient of determination is interpreted
this way: 93.1% of the
variance in time elapsed can be explained by the number of
trials, which would be a very
important finding with implications for many kinds of
performance tasks, except that the
numbers were contrived to begin with. Consequently, the
coefficient of nondetermina-
tion is 1 2 rxy
2, which indicates variance due to unexplained causes or error.
In this case
it would be
1 2 .931 5 . 069 or 6.9%
The Interpretive Value of rxy
2
The statistic can also indicate how unimportant some low
correlations are, even when
they are statistically significant. For example, with 23 degrees
of freedom, a correlation
of rxy 5 .396 is statistically significant. The coefficient of
determination for that value is
37. rxy
2 5 .157. One variable in such a relationship explains just 16%
of the variance in the
other. The other 84% of the variability is related to other
factors.
When the variables describe the behavior of people, small
coefficients of determination
do not surprise us. This is just part of the complexity of human
subjects. It is not unusual
to expect relatively low values when people are the subjects and
only two variables are
involved.
However, low correlations and low rxy
2 values are sometimes quite important. If research
revealed that the correlation between the age of first exposure
to illegal narcotics and the
development of an addiction was rxy 5 2.3 (the younger the
subject is at first exposure,
the more likely the individual is to develop an addiction), the
resulting rxy
2 value would
be just .09. But even if just 9% of the variance in addiction was
somehow related to age
of exposure, because the consequences are so dramatic for the
individual and indeed for
society, the value would probably be thought of as important.
The importance of an rxy
2
value has to be discussed within the context of consequences.
38. suk85842_09_c09.indd 340 10/23/13 1:42 PM
CHAPTER 9Section 9.2 Calculating the Pearson Correlation
Comparing Correlation Values
In isolation, correlation coefficients can be difficult to interpret
because correlation strength
does not increase or decrease in consistent increments. The
change from rxy 5 .2 to rxy 5 .3
is a less dramatic increase in strength than the increase from rxy
5 .75 to rxy 5 .85, for
example. Although the Pearson r requires equal interval data, in
the coefficients that are
the result, an increase in correlation strength of .1 reflects a
very different change when it
is from .8 to .9 than it does from .2 to .3. It takes a much
stronger increase in the relation-
ship to increase by .1 in the upper ranges of correlation values
than in the lower ranges,
something suggested by the distance between tenths in this
number line:
rxy 5 .1 .2 .3 .4 .5 .6 .7 .8 .9
Squaring the correlation coefficient makes the intervals
consistent. A change in the coef-
ficient of determination from .35 to .5, for example, represents
the same increase in pro-
portion of variance explained as an increase from .7 to .85, as
the following line suggests.
Squaring of the r (or r2) indicates the magnitude or effect size.
As seen in previous chap-
39. ters, effect size is a statistic that is used to interpret the degree
of influence of the IV on the
DV. In the case of a correlation, it is the magnitude or strength
of the association between
two variables. Cohen’s (1988) guidelines for the magnitude of a
correlation coefficient are
.1 is small, .3 is moderate, and .5 is large.
r2xy 5 .1 .2 .3 .4 .5 .6 .7 .8 .9
Another Correlation Problem
A consultant is asked to solicit political contributions for a
politician’s campaign commit-
tee. The consultant reviews some of the data available and notes
that age appears to be
related to the number of dollars donated. To test this
observation, a sample is randomly
selected from a list of national donors, which yields the
following:
Donor 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Age 25 27 32 32 35 38 43 45 45 47 48 52 63 65 66
Amount 20 20 35 25 100 50 75 45 100 150 100 200 50 100 125
The problem is completed in Figure 9.5.
• The correlation of the donor’s age with the amount the donor
contributed is rxy 5 .564.
• The critical value at p 5 .05 for 13 degrees of freedom is .514.
• Because rxy . r.05(13), the correlation is statistically
significant.
• The coefficient of determination (rxy
40. 2 5 .318) indicates that
about 32% of the variability in how much donors contribute
can be explained by their age.
D What is
the relationship
between degrees
of freedom and
statistical significance in
correlation?
Try It!
suk85842_09_c09.indd 341 10/23/13 1:43 PM
CHAPTER 9Section 9.3 Correlating Data When One Variable Is
Dichotomous
Figure 9.5: The Pearson correlation for age and political
contribution amount
9.3 Correlating Data When One Variable Is Dichotomous
If the question about donor contributions had been about the
relationship between the amount donated and the gender of the
donor, the Pearson approach will still provide the
answer, but the correlation procedure is called a point-biserial
correlation(rpb). The word
point refers to the continuous variable, the amount of money
donated in this example.
The word biserial refers to the other variable, which has only
two values or dichotomous
data. The change that is required is that the gender variable has
41. to be coded in a way that
Donor’s
Age
Contribution Amount
x x2 y xyy2
25
27
32
32
35
38
43
45
45
47
48
52
63
65
46. n�xy � (�x)(�x)
�{[n�x2 � (�x)2] [n�y2 � (�y)2]}
0.514
suk85842_09_c09.indd 342 10/23/13 1:43 PM
CHAPTER 9Section 9.3 Correlating Data When One Variable Is
Dichotomous
reflects its dichotomy. To determine the correlation between the
donor’s gender and the
amount donated, gender has to be coded either 0 or 1. In terms
of the strength of the coef-
ficient, it does not matter whether females or males are coded 0
or 1. Since point-biserial is
a test of relationships or an association between two variables,
it is not the best choice for a
causal relationship with a dichotomous independent variable on
a continuous dependent
variable. For instance, if we wanted to look at the differences
between gender (dichoto-
mous data) on their level of work-family conflict, an
independent-samples t-test or Mann-
Whitney U-test will be more robust in testing significant group
differences.
The point-biserial correlation has a number of applications.
Questions about the relation-
ship between gender and income, between public versus private
school students and
achievement, between Republican versus Democrat and
optimism (assuming that opti-
47. mism is measured on at least an interval scale) are all questions
that can be analyzed with
the point-biserial correlation.
The only adjustment is to code the dichotomous variable as
either 0 or 1. When the donors
are recoded according to gender, whether the 0 indicates women
or men will not affect the
strength of the coefficient. It will affect the sign, however, so
there needs to be some care
in interpreting the result. If donors 3, 5, 6, 7, 9, 10, 11, and 14
are female, and if females are
coded 1 and males 0, the following is the result:
Donor (x) 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0
Amount (y) 20 20 35 25 100 50 75 45 100 150 100 200 50 100
125
Calculating the Point-Biserial Correlation
The amounts donated (the y values) remain the same from the
age/donor problem and
can be retrieved from Figure 9.5, where a y 5 1,195 and a y
2 5 133,425. The other val-
ues must be recalculated, although it is much simpler with the
gender (x) variable recoded
to 1s and 0s. Here is the data in columns:
Gender (x) x2 Amount (y) y2 xy
0 0 20 400 0
0 0 20 400 0
49. a x 5 8 a x
2 5 8 a y 5 1,195 a y
2 5 133,425 a xy 5 710
rxy 5
n a xy 2 ( a x)( a y)
Å e cn a x
2 2 ( a x)
2 d cn a y2 2 ( a y)2 d f
rxy 5
15(710) 2 (8)(1,195)
"5315(8) 2 (8)2 4 315(133,425) 2 (1,195)2 46
rxy 5
10,650 2 9,560
"3(120 2 64)4 3(2,001,375 2 1,428,025)4
rxy 5
1,090
"32,107,600
5 .19
Still testing at p 5 .05 and with the degrees of freedom still df 5
13,
• the critical value is still rxy .05(13) 5 .514, and
• the statistical decision will be to fail to reject H0. The
relationship between the
50. donor’s gender and the amount contributed is not statistically
significant.
• The rxy 5 .19 is probably a random correlation that is unlikely
to be significant if
new data was collected and the analysis repeated.
The interpretation of the point-biserial correlation is the same
as it is for a conventional
Pearson correlation except that whether the coefficient is
positive or negative is a function
only of which variable is coded 1. If male donors had been
coded with 1s, the correlation
would have been negative, rxy 5 2.19.
There are many applications for this procedure. Each of the
following questions can be
answered with a point-biserial correlation:
• What is the relationship between whether or not a parent
earned a college degree
and the child’s grades?
• How is whether or not a student is a native speaker of English
related to the stu-
dent’s test score?
• What is the correlation between blue-collar/white-collar jobs
and the amount of
leisure time?
suk85842_09_c09.indd 344 10/23/13 1:43 PM
51. CHAPTER 9Section 9.4 The Pearson Correlation in Excel
If both variables are dichotomous, another bivariate correlation
is involved. It is called the
phi coefficient and will be covered in Chapter 11.
“Degrees of Significance”?
At rxy 5 .19 and a table value of rxy .05(13) 5 .514, the
correlation value is not significant.
If it had been rxy 5 .50, and this correlation value was some
relationship calculated for
your senior thesis, would it be appropriate to refer to it as
“almost significant” or “nearly
significant”? It is not uncommon to see such qualifiers even in
the published literature,
but significance decisions should be treated the same way as
dichotomous variables are
treated. There are just the two possible outcomes: The
correlation is significant or it is
not significant. To try to make a statement about the nearness to
an alternative outcome
undermines the principle behind significance testing. There are
just two hypotheses, and
the outcome is couched in terms of one outcome or the other.
9.4 The Pearson Correlation in Excel
A psychologist is interested in determining the relationship
between risk taking and success in solving novel problems.
Having devised the Inventory Risk Survey Cat-
alog (the I-RiSC), the researcher gauges a group of 16-year-
olds’ willingness to do the
unconventional and then provides a series of word problems
with which the participants
are unfamiliar. Scores on the I-RiSC and the problems are as
52. follows for 10 participants:
I-RiSC 2 7 4 5 1 8 7 9 3 6
Problems 14 17 14 16 12 17 16 17 15 15
To complete the problem in Excel, it is easiest to set up the data
in two columns. Two rows
also will work, but parallel columns are visually simpler.
• Create a label in cell A1 for I-RiSC and in cell B1 ProbSolv so
that the I-RiSC
data will be in cells A2 to A11 and the ProbSolv data in B2 to
B11.
• From the Home tab at the top of the page click Data and then
Data Analysis at
the far right.
• Select Correlation, which is the second option in the window.
• In the Input Range window enter A2:B11, which indicates
where the data is
found. Note that the default is that the data is grouped in
columns. Had they
been entered in rows, this would need to be changed. Had the
Labels in First
Row box been checked, Excel would have treated the first row
in each column
(A2 and B2 because that is what is designated) as labels rather
than data. That
adjustment for the labels was made by indicating that the data
begins in A2
rather than A1.
• Enter a cell value below or to the right of the last data entry
53. for the Output
Range so that the results do not overwrite the scores—either
cell A12 or lower,
or to the right of column B.
• Click OK.
suk85842_09_c09.indd 345 10/23/13 1:43 PM
CHAPTER 9Section 9.4 The Pearson Correlation in Excel
The output is deceptively simple. The following box is called a
correlation matrix, and
it is often used to present correlation results. The intersection of
column 1 and column
2 indicates how well the data in column 1—the Excel A column,
where I-RiSC data is
located—correlates with the data in column 2—the Excel B
column, which contains the
problem-solving scores.
Column 1 Column 2
Column 1 1
Column 2 0.904203 1
The result of the analysis is a Pearson correlation of rxy 5 .904.
The 1s in the diagonal
indicate that each variable correlates perfectly with itself (rxy 5
1.0), of course. Note that
the output does not indicate whether the calculated value is
statistically significant, which
makes a check of the critical values table necessary. Table 9.1
54. indicates that rxy .05(8) 5 .632.
The relationship between risk taking and problem solving is
statistically significant. Was
this not contrived data, it would be quite important to know that
about 82% (rxy
2 5 .818)
of problem-solving success (.9042) is explained by whatever the
I-RiSC measures.
Apply It!
Investigating the Correlation Between Crime and
Unemployment
A criminal investigative analyst is interested in studying a
possible link between
crime and unemployment to help in allocating crime prevention
funds. Specif-
ically, she would like to know if murder rates and property
crime rates in her state correlate
with the state unemployment rate.
The analyst obtains the murder and property rates for her state
for the 16 years from 1990
to 2005 from the FBI Uniform Crime Reports. (These rates are
given per 100,000 inhabit-
ants.) She then consults the Bureau of Labor Statistics for the
unemployment rate (in per-
centages) in her state during that same time period.
The analyst will compute the Pearson’s r correlation between
murder rate and unemploy-
ment. She will compute a separate correlation between property
crime rate and unemploy-
55. ment. The Pearson’s r requires interval or ratio variables that
are normally and similarly
distributed. The null hypothesis is that there is no relationship
between the variables, writ-
ten H0: r 5 0.
(continued)
suk85842_09_c09.indd 346 10/23/13 1:43 PM
CHAPTER 9Section 9.4 The Pearson Correlation in Excel
Apply It! (continued)
Crime rates and unemployment rates for this state are given for
the years 1990 through
2005.
Year Murder Rate Property Crime Rate Unemployment
1990 7.1 4462 5.6
1991 6.7 5092 6.8
1992 6.4 4801 7.5
1993 6.4 4662 6.9
1994 6.2 4678 6.1
1995 5.7 4460 5.6
1996 5.8 4438 5.4
56. 1997 5.4 4279 4.9
1998 6.1 4040 4.5
1999 5.5 3852 4.2
2000 5.1 3592 4.0
2001 4.9 3456 4.7
2002 4.3 3412 5.8
2003 4.2 3289 6.0
2004 4.7 3168 5.5
2005 5.0 3081 5.1
Using Excel, the correlation value for murder rate and
unemployment is rxy 5 .386.
Using Excel, the correlation value for property crime rate and
unemployment is rxy 5 0.551.
Using 14 degrees of freedom (16 data sets 2 2) and with the risk
of type I, or alpha, error at
p 5 .05, the critical value is rxy .05(14) 5 .497.
If the calculated value equals or exceeds the table value, the
result is statistically significant.
Therefore, the correlation between murder rate and
unemployment is not statistically sig-
nificant because
rxy 5 .386 , rxy .05(14) 5 .497.
57. (continued)
suk85842_09_c09.indd 347 10/23/13 1:43 PM
CHAPTER 9Section 9.5 Nonparametric Tests: Spearman’s Rho
9.5 Nonparametric Tests: Spearman’s Rho
The Pearson correlation requires that both variables must be at
least interval scale. The point-biserial correlation requires that
one variable must be at least interval scale, and
the other must be a variable with only two levels.
Neither of those is helpful when the data is ordinal scale,
which describes much of the data that psychologists and
other social scientists encounter. Nearly everyone who goes
to the mall or answers the telephone has been asked to take a
survey, particularly if it happens to be an election year. Sur-
vey data is usually ordinal scale. It is common for the ques-
tionnaires to have a Likert-type format, where a statement is
read and the respondents are asked the degree to which they
agree with the statement by selecting from a range of choices
such as
Strongly agree
Agree
Neither agree nor disagree
Disagree
Strongly disagree
58. Although it is common enough to code the responses
(Strongly agree 5 1, Agree 5 2, and so on) and then calculate
means and standard deviations for all respondents, those sta-
tistics assume that the data is at least interval scale. Survey
data rarely is. The Likert types of responses are essentially
rankings. A response of “Strongly agree” is more positive
The links
provided below
introduce two sides of a
debate: Is Likert scaling
ordinal or interval data?
Read both sides of the
debate to formulate your
own conclusion.
Likert scaling is ordinal
data, as presented in
ASQ’s Quality Progress,
Statistics Roundtable:
http://asq.org/quality
-progress/2007/07/
statistics/likert-scales
-and-data-analyses.html
Likert scaling is interval
data, as presented in the
Shiken Research Bulletin:
http://jalt.org/test/bro
_34.htm
Try It!
Apply It! (continued)
59. However, the correlation between property crime rate and
unemployment is significant.
Therefore, the null hypothesis is rejected. There is a
relationship between these two
variables.
rxy 5 0.551 . rxy .05(14) 5 .497
The coefficient of determination is rxy
2 5 .55122 5 .303.
The coefficient of determination indicates that about 30% of the
variance in the property
crime rate can be explained by the unemployment rate. The
criminal investigative analyst
can use this information to divert more funds to preventing
property crimes during times of
high unemployment.
Apply It! boxes written by Shawn Murphy.
suk85842_09_c09.indd 348 10/23/13 1:43 PM
http://asq.org/quality-progress/2007/07/statistics/likert-scales-
and-data-analyses.html
http://asq.org/quality-progress/2007/07/statistics/likert-scales-
and-data-analyses.html
http://asq.org/quality-progress/2007/07/statistics/likert-scales-
and-data-analyses.html
http://asq.org/quality-progress/2007/07/statistics/likert-scales-
and-data-analyses.html
http://jalt.org/test/bro_34.htm
http://jalt.org/test/bro_34.htm
60. CHAPTER 9Section 9.5 Nonparametric Tests: Spearman’s Rho
than “Agree” but precisely how much more is not clear.
Besides, one respondent’s “Dis-
agree” may be another respondent’s “Strongly disagree.” This
data is more safely treated
as ordinal scale responses.
Back to Correlation
In addition to survey data, other common data also is ordinal
scale, such as class rankings
and percentile scores. Sometimes one variable is interval/ratio.
For example, a researcher
might wish to correlate a person’s annual income (ratio data)
with subjects’ optimism,
which is gauged by a Likert-type survey (ordinal data).
Although ratio scale (if your
income is 0, it really does mean you have no money), income
data is also frequently non-
normal. Income data usually has a right skew, which is why
reports refer to median rather
than mean income. The lack of normality in the ratio variable
and a second variable that is
ordinal scale both rule out a Pearson’s correlation.
Charles Spearman, Pearson’s colleague at University College
London, developed a cor-
relation procedure that is tremendously flexible. It will
accommodate two variables in a
correlation procedure that fit any of the following:
• Both are ordinal scale.
• One variable is ordinal scale and one is interval or ratio scale.
• Two variables are interval or ratio scale, but one or both fail
to meet the Pearson
61. correlation requirement for normality.
The procedure is Spearman’s rho, for which the symbol will be
rs. Spearman’s rho is a
nonparametric procedure. Nonparametric means that no
assumptions need to be made
about parameters. For our purposes, it means that rs will
accommodate nonnormal data,
or data for which normality cannot be judged. The formula is as
follows:
rs 5
1 2 6 a d
2
n(n2 2 1)
Formula 9.3
Where
d 5 the difference between the rankings for the two variables
n 5 the number of pairs of data
The 1s and the 6 are constant values. They are there every time
a Spearman’s
correlation is calculated.
The steps to calculating a Spearman’s rho follow:
1. Rank the scores for both variables separately.
2. For each pair of rankings, subtract the second ranking in the
pair from the first to
62. produce a difference score, d.
3. Square each of the d values for d2.
4. Sum the d2 values for a d
2.
5. Solve for rs.
suk85842_09_c09.indd 349 10/23/13 1:43 PM
CHAPTER 9Section 9.5 Nonparametric Tests: Spearman’s Rho
Ranking Tied Scores
There are rules to follow for the ranking procedure. If there are
multiples of some of the
scores for one of the variables, they must all receive the same
ranking. If someone were
ranking the following values, for example:
3, 5, 6, 6, 7, 8, 8, 8, 9, 10
ranking the values from smallest to largest would produce
1, 2, 3.5, 3.5, 5, 7, 7, 7, 9, 10
The two 6s and the three 8s are handled as follows:
• Because the two 6s occupy rankings 3 and 4, those two
rankings
are added together and divided by the number of tied scores,
which are two: (3 1 4) 4 2 5 3.5. Both the 6s receive rankings of
3.5, after which the next ranking must then be 5.
• The three 8s occupy rankings 6, 7, and 8. Following the same
63. procedure, (6 1 7 1 8) 4 3 5 7, after which the next ranking must
be 9.
An Example
Suppose the preceding data is a measure of economic
conservatism among a group of
investors, with higher scores indicating the most caution. If the
effort is to check for a
relationship between investors’ ages and their level of
conservatism, the following might
be the result:
Conservatism Age
3 26
5 25
6 32
6 35
7 35
8 34
8 37
8 40
9 42
10 39
E Spearman’s
64. rho requires data of
what scale?
Try It!
suk85842_09_c09.indd 350 10/23/13 1:43 PM
CHAPTER 9Section 9.5 Nonparametric Tests: Spearman’s Rho
A Spearman’s rho solution is calculated in Figure 9.6. The
Spearman’s correlation is
rs 5 .852. Table 9.2 is the table of critical values for
Spearman’s rho. It is also Table F in the
Appendix. There are no degrees of freedom for the Spearman’s
value to guide us to the
correct critical value, only the number of pairs of data. Note
that for p 5 .05 and 10 pairs
of data, the critical value is rs .05 (10) 5 .648. The relationship
between level of economic
conservatism and age in this group of investors is statistically
significant; reject H0.
Figure 9.6: The Spearman’s rho correlation: economic
conservatism with age
Age
Co
ns
er
va
tis
68. 0.25
4
0.25
9
0
4
1
4
�d2 = 24.50
1. Ranking the scores produces R1 for conservatism and R2 for
age.
2. The d score is the difference between the two rankings.
3. The square of the difference score is d2.
6�d2
n(n2 � 1)
r5 = 1 �
6(24.5)
10(102 � 1)
= 1 �
= 1 � 0.148
71. (continued)
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www.sussex.ac.uk/Users/grahamh/RM1web/Rhotable.htm
www.sussex.ac.uk/Users/grahamh/RM1web/Rhotable.htm
CHAPTER 9Section 9.5 Nonparametric Tests: Spearman’s Rho
Apply It! (continued)
These same employees are also asked to list their average one-
way commute time in min-
utes on this survey.
Because the job satisfaction data is ordinal scale, the Pearson’s
correlation is not appropri-
ate, and the HR manager will instead use Spearman’s rho to
determine the correlation.
Commute
Time
(Minutes)
Commute
Rank
Job
Satisfaction
Satisfaction
Rank
72. Difference
Between
Ranks
Difference2
2 1 vs 2 –1 1
7 2 ss 5 –3 9
11 3 vs 2 1 1
15 4 ss 5 –1 1
17 5 vs 2 3 9
23 6 ss 5 1 1
28 7 sd 7.5 –0.5 0.25
32 8 vd 9.5 –1.5 2.25
36 9 vd 9.5 –0.5 0.25
40 10 sd 7.5 2.5 6.25
ad
2 5 31
N 5 10
The Spearman’s rho formula is
rs 5
1 2 6 ad
73. 2
n(n2 2 1)
5 0.812
For rs 5 .05 and 10 pairs of data, the critical value is rs .05 (10)
5 .648
Because 0.812 . 0.648, the null hypothesis is rejected. The
relationship between job satis-
faction and average commute time is significant.
This study has shown that the longer the average commute time
employees have, the more
likely they are to be dissatisfied with their job. The human
resources manager can use this
information as one reason the company should enact a policy
that allows employees to
work from home.
Apply It! boxes written by Shawn Murphy.
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CHAPTER 9Section 9.5 Nonparametric Tests: Spearman’s Rho
The Direction of the Ranking
In the example of economic conservatism among investors, the
least
conservative value received the ranking of 1, and the most, 10.
With
respect to age, the youngest investor received the ranking of 1.
74. In
terms of the value of the statistic, it does not matter whether the
rank-
ings go from lowest to highest, or from highest to lowest, as
long as the
same is done for both variables. If we decided that because 10 is
the most
conservative score in this set that it should be ranked 1, that
would
work fine, but the same would have to be done for age—the
high-
est age would need to receive a ranking of 1. If the data in one
group
ranked from highest down and the other from lowest up, then
the cor-
relation would appear to be negative!
The Spearman’s Rho in Summary
Spearman’s correlation provides flexibility to the analyst. As
long as there is some evi-
dence of a relationship, correlations can be calculated for any
combination of ordinal,
interval, and ratio variables. But of course there has to be some
sacrifice for so much lati-
tude, and it is statistical power. Note that part of Spearman’s
process is the ranking of the
data. In the course of ranking values, the amount of difference
between any two data points
is no longer part of the analysis. When the ages of the investors
were ranked,
• the 25-year-old was 1
• the 26-year-old was 2
• and the 32-year-old was 3
75. As soon as ages are converted to rankings, the amount of age
difference between the
26- and 32-year-old was lost. The only information evident from
the rankings is that the
26-year-old is 2 and the 32-year-old is 3. That does not happen
with a procedure designed
specifically for interval or ratio data like Pearson’s r.
Consequently, although there some-
times is not much difference between their coefficients, a
Pearson correlation will some-
times be statistically significant when Spearman’s is not. Note
the following comparison
of critical values at a 5 .05:
No. of Pairs Pearson’s Critical Value* Spearman’s Critical
Value
5 .878 1.0
6 .811 .886
10 .632 .648
*For df 5 no. of pairs 2 2.
In each case, the value required for significance with a
Spearman correlation is higher
than that required for a Pearson correlation.
F If the grade
averages of 10
students who were
ranked 1 through 10
in their class were
correlated with their
class rankings and the
76. highest GPA was given a
ranking of 1, and so on,
what would the resulting
coefficient indicate?
Try It!
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CHAPTER 9Section 9.6 Presenting Results
Another limitation is that we cannot square the Spearman value
to determine the propor-
tion of variance in y explained by x. There is no equivalent of
rxy
2 for Spearman’s rho.
When the data does not meet the Pearson requirements, there is
not a choice to be made.
When it does, a Pearson’s r is going to be more precise than
Spearman’s rho. In the next
section, we will use real data for a multiple correlation with a
Pearson correlation and
Spearman rho comparison using SPSS.
9.6 Presenting Results
Using a public data set from Pew Research (2010),
YouthEconomy_dataset.sav file, a multiple correlation will be
performed between four variables, Specifically age, q1
(happiness), q5 (optimism), and q11 (job satisfaction). Both a
Pearson correlation and a
Spearman rho will be performed simultaneously using SPSS.
77. To perform the analysis, go to AnalyzeSCorrelateSBivariate.
Input age, q1 (happiness),
q5 (optimism), and q11 (job satisfaction) into the Variables box
(your screen should look
like that in Figure 9.7). Check both Pearson and Spearman
boxes below. Then click OK.
The resulting SPSS output tables are provided in Figure 9.8.
Figure 9.7: SPSS steps in a multiple correlation
Source: Pew Research Social & Demographic Trends. (2011).
Youth and Economy. Retrieved from
http://www.pewsocialtrends.org
/category/datasets/
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http://www.pewsocialtrends.org/category/datasets/
http://www.pewsocialtrends.org/category/datasets/
CHAPTER 9Section 9.6 Presenting Results
Figure 9.8: SPSS output in a multiple correlation
Source: Pew Research Social & Demographic Trends. (2011).
Youth and Economy. Retrieved from
http://www.pewsocialtrends.org/
category/datasets/
Correlations
Sig. (2-tailed)
Pearson Correlation
78. N
Sig. (2-tailed)
Pearson Correlation
N
Q1.
AGE.
Q.5
Q.11
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).
Sig. (2-tailed)
Pearson Correlation
N
Sig. (2-tailed)
Pearson Correlation
N
AGE.
9197
82. Q1.
Q.5
Q.11
**. Correlation is significant at the 0.01 level (2-tailed).
Sig. (2-tailed)
Correlation Coefficient
N
Sig. (2-tailed)
Correlation Coefficient
N
Sig. (2-tailed)
Correlation Coefficient
AGE.
9226
0.056**
0.000
9226
0.000
85. 5385
1.000
�0.019*
5385
0.000
�0.136**
suk85842_09_c09.indd 356 10/23/13 1:43 PM
http://www.pewsocialtrends.org/category/datasets/
http://www.pewsocialtrends.org/category/datasets/
CHAPTER 9Summary
9.7 Interpreting Results
Refer to the most recent edition of the APA manual for specific
detail on formatting statistics; Table 9.3 may be used as a quick
guide in presenting the statistics covered
in this chapter.
Table 9.3: Guide to APA formatting of statistics results
Abbreviation or Term Description
r Pearson’s correlation coefficient
rs Spearman’s correlation coefficient
r Rho
87. Many of the questions researchers and scholars ask are about
the relationships between
variables. To accommodate them, the discussion in this chapter
shifted to statistical pro-
cedures that fall under the hypothesis of association umbrella
(Objective 1). Three of the
many correlation procedures that respond to the hypothesis of
difference are the Pearson
correlation, the point-biserial correlation, and Spearman’s rho.
In each case, their pos-
sible values range from 21.0 to 11.0, and all their coefficients
are interpreted the same
way. Positive correlations indicate that as the values in one
variable increase, the values
in the other also increase. Negative correlations indicate that as
one increases, the other
decreases. The sign of the coefficient, however, is unrelated to
its strength (Objective 2).
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CHAPTER 9Key Terms
The differences among the correlation procedures in this
chapter are in the kinds of vari-
ables they accommodate. The Pearson correlation requires
interval or ratio variables that
are normally and similarly distributed (Objective 3). A special
application of Pearson, the
point-biserial correlation, requires an interval/ratio variable and
a second variable that
has only two manifestations, or a dichotomously scored variable
(Objective 5). Spearman’s
rho will accommodate any combination of ordinal, interval, or
88. ratio variables (Objec-
tive 6). Because the data that is used in a Pearson correlation
contains more information
than the rankings that make up the data for Spearman’s
approach, the Pearson value
provides more information about the nature of the relationship
between the variables.
This is evident because the Pearson correlation value can be
squared to produce the coef-
ficient of determination. The rxy
2 value indicates the proportion of one variable that can be
explained by changes in the other (Objective 4). Results for
both the Pearson correlation
and Spearman rho were presented with the use of SPSS
(Objective 7). The results from the
SPSS output were then interpreted and reported in proper APA
format (Objective 8).
Two variables are correlated when each contains information
common also to the other.
The amount of one explained by the other is what that rxy
2 value, the coefficient of deter-
mination, indicates. This concept provides a foundation for
regression, which is the focus
of Chapter 10. Regression allows what is known of y from
analyzing x to predict the value
of y from x. It involves calculations and thinking with which
you are already familiar, so
work the end-of-chapter problems, reread any of the sections in
Chapter 9, and prepare
for Chapter 10!
Key Terms
89. bivariate correlations All procedures that
test for significant relationships between
two variables.
canonical correlation Measure of the rela-
tionship between two groups of variables.
coefficient of determination The propor-
tion of one variable in a Pearson correlation
that can be explained by the other.
correlation matrix A box in which the vari-
ables involved are listed in rows as well as
in columns and each variable is correlated
with all variables, including itself.
dichotomous data A binary variable with
two choices such as gender (i.e., male/
female) or answer (i.e., yes/no).
hypothesis of association The umbrella
term for significance tests that deal with the
correlation between variables.
hypothesis of difference The umbrella
term for significance tests dealing with dif-
ferences between groups.
linear When the relationship between
two variables is linear, the strength of the
relationship is consistent throughout their
ranges. With curvilinear relationships, the
strength and sometimes even the nature
of the relationship (positive or negative)
changes depending upon where in the vari-
ables’ ranges they are measured.
90. suk85842_09_c09.indd 358 10/23/13 1:43 PM
CHAPTER 9Chapter Exercises
multiple correlation Gauge of the strength
of the relationship between one variable
and two or more other variables.
nonparametric Statistical procedures that
make no assumptions about data normality
or data distribution.
partial correlation Measure of the relation-
ship between two variables, controlling for
the influence of a third in both of the first
two.
Pearson correlation coefficient Indication
of the strength of the relationship between
interval- or ratio-scale variables.
point-biserial correlation A special appli-
cation of the Pearson correlation for those
instances where one of the variables, such
as gender or marital status, has just two
manifestations.
range attenuation Occurs when a vari-
able is not measured throughout its entire
range. Attenuated range artificially reduces
the strength of any resulting correlation
value.
91. scatterplot A graph representing two vari-
ables, one on the horizontal axis and the
other on the vertical axis. Each point in the
graph indicates the measure of both vari-
ables for one individual.
semipartial correlation Gauge of the rela-
tionship between two variables, controlling
for a third in just one of the first two.
Spearman’s rho A correlation procedure
for two ordinal variables, one ordinal and
one interval or ratio variable, or two inter-
val or ratio variables that fail to meet Pear-
son correlation requirements for normality.
tetrachoric correlation Allows a correla-
tion when both variables are dichotomous
data.
Chapter Exercises
Answers to Try It! Questions
The answers to all Try It! questions introduced in this chapter
are provided below.
A. A single point in a scatterplot represents two raw scores, one
for x and one for y.
B. If the two variables are normally distributed but
uncorrelated, their combined
scatterplot will be circular with greatest density in the middle of
the plot because
of the tendency for most of the data to be in the middle of either
distribution.
92. C. Range attenuation diminishes the strength of the correlation
value in linear rela-
tionships. It produces an artificially low correlation coefficient.
D. As degrees of freedom increase, the correlation value
required to reach signifi-
cance diminishes.
E. Spearman’s rho will accommodate variables that have any
combination of ordi-
nal, interval, or ratio scale.
F. The coefficient would indicate that the higher the ranking,
the lower the GPA. If
a ranking of 1, is “best,” the best (highest) GPA must also
receive a class ranking
of 1. Otherwise, the relationship looks negative when it is not.
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CHAPTER 9Chapter Exercises
Review Questions
The answers to the odd-numbered items are in the answers
appendix.
1. What values indicate the strongest and weakest values for a
Pearson’s r?
2. What is the equivalent in a Pearson correlation for h2 or
Cohen’s d?
3. What are the requirements for calculating Pearson’s r?
93. 4. What is range attenuation, and how does it affect correlation
values for linear
relationships?
5. A university counselor gathers data on students’ grades and
whether or not they
are employed. What statistical procedure will gauge that
relationship?
6. What procedure will indicate whether there is a significant
relationship between
sales representatives’ sales rank and their attitudes about the
product they sell?
7. What procedure will gauge the relationship between
university students’ grade
averages and their scores on, for example, a statistics test?
8. Refer to Question 7: What statistic will indicate the
proportion of the students’ test
scores that is a function of their GPA?
9. A forensic psychologist gathers data on the average time
juveniles go to bed and
whether or not they have an arrest record.
a. What type of correlation (Spearman, Pearson, or point-
biserial) is appropriate in
this instance?
b. What is the correlation?
c. How much of variability in arrest records can be explained
by what time the
juvenile goes to bed?
94. Retire Arrest
1 9.0 No
2 9.5 No
3 11.0 Yes
4 11.5 Yes
5 10.0 Yes
6 9.75 No
7 10.0 No
8 10.25 Yes
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CHAPTER 9Chapter Exercises
10. A group of consumers has just taken two surveys on (a)
their attitude about the
economy and (b) their attitude about those in government. In
both, higher scores
mean more optimism. The data is ordinal scale. Are the two
attitudes related?
Economy Government
1 15 10
2 5 4
95. 3 16 11
4 10 8
5 11 13
6 3 4
7 12 10
8 11 8
9 10 7
10 14 9
11. A group of students has been told that reading will help
them in a test of verbal
ability required by the university they wish to attend. The x
variable indicates the
minutes per day spent reading. The y variable is their scores on
the test.
Minutes Score
1 15 57
2 80 84
3 0 60
4 75 92
5 30 65
96. 6 10 60
7 22 75
8 15 68
a. Is the relationship statistically significant?
b. How much of the variance in test scores can be explained by
differences in the
amount of time spent reading?
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CHAPTER 9Chapter Exercises
12. An educational psychologist is working with
developmentally disabled students
in a special education setting and is curious about the
relationship between stu-
dents’ persistence on puzzle tasks (measured in the number of
minutes they
remain on task) and their number of absences from class.
Persist Absent
1 12 3
2 4 3
3 15 5
4 18 7
97. 5 12 1
6 5 4
7 8 3
8 9 4
Is the relationship between persistence and attendance
statistically significant at
p 5 .05?
13. An employer wishes to analyze the relationship between
stress and job perfor-
mance. Stress is reflected in systolic blood pressure. Job
performance is the number
of sales per day.
a. What is the appropriate correlation procedure?
b. Is the relationship statistically significant?
Sales Blood
Pressure
1 1 150
2 4 140
3 3 140
4 6 110
5 2 140
6 4 130
98. 7 0 160
8 3 110
9 5 120
10 7 160
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CHAPTER 9Chapter Exercises
14. An industrial/organizational psychologist is determining the
relationship between
workers’ willingness to embrace new manufacturing procedures,
gauged with a
dogmatism scale (higher scores indicate greater dogmatism) and
their level of job
satisfaction (higher scores indicate greater satisfaction). The
satisfaction data is at
least ordinal scale.
a. What is the relationship?
b. What is the null hypothesis?
c. Do you reject or fail to reject?
d. What is the relationship between dogmatism and job
satisfaction?
e. Is the correlation statistically significant?
Dogmatism Satisfaction
1 8 4
2 4 12
99. 3 3 14
4 5 15
5 7 5
6 2 14
7 3 15
8 1 15
Analyzing the Research
Review the article abstracts provided below. You can then
access the full articles via your
university’s online library portal to answer the critical thinking
questions. Answers can be
found in the answers appendix.
Using Pearson Correlation in a Schema Study
Bamber, M., & McMahon, R. (2008). Danger—Early
maladaptive schemas at work!: The
role of early maladaptive schemas in career choice and the
development of occu-
pational stress in health workers. Clinical Psychology &
Psychotherapy, 15(2), 96–112.
Article Abstract
The schema-focused model of occupational stress and work
dysfunctions (Bamber &
Price, 2006; Bamber, 2006) hypothesizes that individuals with
EMS (unconsciously) gravi-
tate toward occupations with similar dynamics and structures to
100. the toxic early environ-
ments and relationships that created them. They subsequently
re-enact these EMS and
their associated maladaptive coping styles in the workplace. For
most individuals, this
results in “schema healing”, but for some individuals with more
rigid and severe EMS,
schema healing is not achieved and the structures and
relationships of the workplace,
together with the utilization of maladaptive coping styles, serve
to perpetuate their EMS.
The model hypothesizes that it is these individuals who are
most vulnerable to develop-
ing occupational stress syndromes. To date, this model has been
subjected to very lit-
tle empirical investigation, so the main aim of this study was to
address this gap in the
suk85842_09_c09.indd 363 10/23/13 1:43 PM
CHAPTER 9Chapter Exercises
literature by testing out some of its main assumptions and to
provide empirical data,
which would either support or reject the model using a
population of health workers. Spe-
cifically, it was hypothesized that “occupation-specific” EMS
would be found in health
workers from a range of different healthcare professions. It was
also hypothesized that
the presence of higher levels of EMS would be predictive of
raised levels of occupational
stress, psychiatric caseness, and increased sickness absence in
those individuals. A cross-
101. sectional study design was employed and a total of 249 staff
working within a NHS Trust,
belonging to one of five occupational groups (medical doctors,
nurses, clinical psycholo-
gists, IT staff and managers), participated in the study. All
participants completed the
Young Schema Questionnaire-Short Form (Young, 1998); the
Maslach Burnout Inventory-
Human Services Form (Maslach & Jackson, 1981), and the
General Health Questionnaire-
28-item version (Goldberg, 1978). A demographic questionnaire
and sickness absence data
was also collected. The results of a between groups analysis of
variance and further post
hoc statistical analyses identified a number of occupation
specific EMS. Also, the results
of a series of multiple linear regression analyses indicated the
presence of some EMS to
be predictive of higher levels of burnout, psychiatric caseness,
and sickness absence in
health workers. In conclusion, the findings of this study provide
empirical support for the
schema-focused model of occupational stress and work
dysfunctions (Bamber & Price,
2006; Bamber, 2006), and it appears that the existence of
underlying EMS may constitute a
predisposing vulnerability factor to developing occupational
stress.
Critical Thinking Questions
1. In the study it was stated that it was estimated that a sample
size of 85 would give
an 80% power to detect a correlation of r 5 .3 (p , 0.05, two-
tailed). Define the
concept of power.
102. 2. If emotional deprivation is r 5 .15 (p , 0.05, two-tailed), what
is the direction and
significance?
3. There is a significant correlation between GHQ total, MBI,
and sickness absence.
What variable causes the other?
Using a Non-parametric Correlation in a Quality of Life Study
Arpawong, T. E., Richeimer, S. H., Weinstein, F., Elghamrawy,
A., & Milam, J. E. (2013).
Posttraumatic growth, quality of life, and treatment symptoms
among cancer
chemotherapy outpatients. Health Psychology, 32(4), 397–408.
Article Abstract
Objective: The experiences of positive adjustment and growth,
termed Posttraumatic
Growth (PTG), are commonly reported among cancer survivors
in the years after treat-
ment. However, few studies have examined PTG among patients
in active treatment for
cancer. This study examined both positive and negative
valenced change in PTG and rela-
tionships with treatment-related symptoms and mental and
physical quality of life (QOL)
among adults in active cancer treatment. Methods: In this cross-
sectional study, adult
outpatients (n 5 114) completed a self-administered
questionnaire. Hierarchical linear
regression modeling (HLM) was performed to examine unique
associations between posi-
tive and negative valenced change in PTG and QOL subscales
103. and symptom reporting,
suk85842_09_c09.indd 364 10/23/13 1:43 PM
CHAPTER 9Chapter Exercises
controlling for theoretically relevant sociodemographic
variables. Results: The majority of
participants (87%) reported at least one positive life change,
whereas half (50%) reported at
least one negative life change across PTG items. In HLM
analysis of QOL subscales, nega-
tive valence PTG scores were positively associated with
Physical Functioning and Bodily
Pain and inversely associated with General Health, Role
Physical, and Mental Health
(F(12, 71) 5 5.13; p , .0001). In HLM analysis of treatment
symptom burden, positive
valence PTG scores were inversely associated with age at
diagnosis and reports of nausea
(F(8, 83) 5 2.93; p 5 .007). Conclusions: Reports of positive and
negative life changes since
diagnosis are common among adults actively receiving
treatment for cancer. Assessments
of both valenced PTG scores can provide a broader profile of
biopsychosocial adjustment
and symptom reporting during cancer treatment.
Critical Thinking Questions
1. Why did this study use a Spearman’s test versus a Kendall’s
tau?
2. The Spearman’s correlation coefficient between anxiety and
104. BMI is (2.04). If the
significance value of this coefficient is (.001), what can be
concluded?
3. The Spearman’s correlation coefficient between dyspnea on
exertion and exercise
capacity peak is .27 with p , .01. What does this mean?
4. Why is it a good thing to check that the N value corresponds
to the number of
observations that were made in the Spearman’s correlation
output?
suk85842_09_c09.indd 365 10/23/13 1:43 PM
suk85842_09_c09.indd 366 10/23/13 1:43 PM
MKT260 - International Marketing
Table of Contents
Subject Summary
...............................................................................................
....................2
Subject Coordinator
...............................................................................................
................2
Subject Coordinator
...............................................................................................
...2
106. Schedule
...............................................................................................
.....................5
Learning
materials.................................................................................
....................6
Learning, teaching and support strategies
..............................................................6
Recommended student time commitment
.............................................................9
Assessment Items
...............................................................................................
..................10
Essential requirements to pass this
subject...........................................................10
Items
...............................................................................................
.........................10
Critical Analyses of Internat'l Marketing Issues
........................................11
Case Study on Culture and International Marketing
................................16
Weekly Workshop Discussion
Activity.......................................................21
International Marketing
Plan.....................................................................23
Assessment Information
...............................................................................................
.......29
Academic integrity
...............................................................................................
...30
Referencing.............................................................................
107. .................................30
How to submit your assessment items
..................................................................30
Online submission
process........................................................................30
Postal submission process
........................................................................30
Hand delivered submission process
.........................................................31
Alternative submission process
................................................................31
Extensions...............................................................................
.................................31
How to apply for special
consideration..................................................................31
Penalties for late
submission..............................................................................
....32
Resubmission
...............................................................................................
...........32
Feedback processes
...............................................................................................
.32
Assessment
return......................................................................................
.............32
Student Feedback & Learning Analytics
..............................................................................33
Charles Sturt University Subject Outline
MKT260 201960 S I
Version 1 - Published 12 June 2019
108. Page 1 of 34
Evaluation of subjects
.............................................................................................3
3
Changes and actions based on student feedback
.................................................33
Learning analytics
............................................................................................. ..
....33
Services & Support
...............................................................................................
................33
Develop your study skills
....................................................................................... .33
Library Services
...............................................................................................
........34
CSU Policies &
Regulations.............................................................................
......................34
Subject Outline as a reference
document..............................................................34
Subject Summary
MKT260 - International Marketing
Session 2 2019
Faculty of Business, Justice and Behavioural Sciences
School of Management and Marketing
Internal Mode
109. Credit Points 8
Welcome to a new session of study at Charles Sturt University.
Please refer to the University's
Acknowledgement of Country
(http://student.csu.edu.au/study/acknowledgement-of-
country).
Subject Coordinator
Subject Coordinator Mr Gana Pathmanathan
Email [email protected]
Phone 02 9291 9349
Consultation procedures
Any questions concerning the teaching of this subject can be
made by contacting me, your
lecturer, as below.
My name : Donna Gill
My email : [email protected] (mailto:[email protected])
Email is the best option. Please send a brief message regarding
the issue and include the
subject name and subject code in your email. If your query is
urgent then meet with the
subject coordinator
Subject Overview
Abstract
Charles Sturt University Subject Outline
MKT260 201960 S I
110. Version 1 - Published 12 June 2019
Page 2 of 34
http://student.csu.edu.au/study/acknowledgement-of-country
http://student.csu.edu.au/study/acknowledgement-of-country
mailto:[email protected]
International economic, cultural, political and legal
environments will be studied as a prelude
to planning marketing strategies for international markets. The
subject will examine the role of
marketing research, international finance, market entry and
expansion strategies and the
marketing mix in international marketing.
Learning outcomes
Upon successful completion of this subject, students should:
• be able to analyse elements of the international environment
and their inter-
relationship and demonstrate their relevance to international
marketing strategies;
• be able to identify and assess international marketing
opportunities and threats;
• be able to plan, implement and manage international
marketing strategies;
• be able to formulate effective strategies for international
marketing, including market
entry and marketing mix strategies; and
• be able to apply cultural sensitivity to create marketing
strategies aligned with global
111. citizenship principles.
Subject content
This subject will cover the following topics:
• International marketing research
• The international environment: Economic and financial;
cultural; political and legal;
technological and environmental; and competitive factors
• International marketing planning
• Market entry and expansion strategies
• Product and service strategies
• Distribution and supply logistics
• Pricing strategies and foreign exchange
• Promotional strategies
• Contemporary issues and future trends
Key subjects
Passing a key subject is one of the indicators of satisfactory
academic progress through your
course. You must pass the key subjects in your course at no
more than two attempts. The first
time you fail a key subject you will be at risk of exclusion; if
you fail a second time you will be
excluded from the course.
The Academic Progress Policy
(https://policy.csu.edu.au/view.current.php?id=00250) sets out
the requirements and procedures for satisfactory academic
progress, for the exclusion of
students who fail to progress satisfactorily and for the
termination of enrolment for students
112. who fail to complete in the maximum allowed time.
Assumed knowledge
Charles Sturt University Subject Outline
MKT260 201960 S I
Version 1 - Published 12 June 2019
Page 3 of 34
https://policy.csu.edu.au/view.current.php?id=00250
Assumed knowledge in this subject is equivalent to that covered
in MKT110.
Subject Schedule & Delivery
Prescribed text
The textbooks required for each of your enrolled subjects can
also be found via the Student
Portal Textbooks (http://student.csu.edu.au/study/study-
essentials/textbooks) page.
Fletcher, R., & Crawford, H. J. (2017). International Marketing:
An Asia Pacific perspective (7th
ed.). Frenchs Forest, NSW: Pearson Education.
This text is available in paper format from the Co-op Bookshop,
or in ebook format from the
publisher http://www.pearson.com.au/9781488611162
Class/tutorial times and location
Your class times can be found at Timetable @ CSU
(http://timetable.csu.edu.au/). Find out
113. how to use Timetable @ CSU via the Student Portal Class
Timetable
(http://student.csu.edu.au/study/study-essentials/timetable)
page.
Charles Sturt University Subject Outline
MKT260 201960 S I
Version 1 - Published 12 June 2019
Page 4 of 34
http://student.csu.edu.au/study/study-essentials/textbooks
http://www.pearson.com.au/9781488611162
http://timetable.csu.edu.au/
http://student.csu.edu.au/study/study-essentials/timetable
http://student.csu.edu.au/study/study-essentials/timetable
Schedule
Session
Week
Week
Commencing
Topics Textbook
Chapter
Learning Activities
1 15 July Globalisation and
international marketing
introduction
114. 1 & 11
2 22 July The international legal
and political
environment
2
3 29 July The international
economic/financial
environment
3
4 5 August Culture and
international marketing
4 Assessment 1 due
Friday, August 9 (11:59
pm AEST)
Census Date August 9
5 12 August Technology change &
Environmental issues
5 & 6
6 19August International market
research
7
7 26 August No class(mid-session
115. break)
8 2 september International market
selection and entry
8 Assessment 2 due
Friday, September 6
(11:59 pm AEST)
9 9 September International marketing
planning and strategy
9 & 12
10 16 Sept No class
11 23 Sept Products: goods and
services in the
international arena
13 & 17
12 30 Sept Pricing & Distribution in
the international arena
14 & 16 Assessment 3 due
Monday, 30 September
(11:59 pm AEST)
13 7 October Promotion in
international markets
15
116. Charles Sturt University Subject Outline
MKT260 201960 S I
Version 1 - Published 12 June 2019
Page 5 of 34
14 14 October Contemporary issues in
international marketing
18 Assessment 4 due
Friday, October 18
(11:59 pm AEST)
Learning materials
Details of learning materials that support your success in this
subject can be found in the
Interact2 Subject Site.
Learning, teaching and support strategies
This subject is delivered through weekly, 3 hour
workshop/lecturers.
Important assessment notes:
Week 1 We will discuss the subject outline in detail. We will
also discuss Assessment 4 in this
session.
Week 3 We will discuss Assessment 1. We will discuss your
queries regarding Assessment 1
