1917Repeated Measures Designs for Interval DataKaren K.docx

191
7Repeated Measures Designs for Interval Data
Karen Kasmauski/Corbis
Chapter Learning Objectives
After reading this chapter, you should be able to do the
following:
1. Explain how initial between-groups differences affect t test
or analysis of variance.
2. Compare the independent t test to the dependent-groups t
test.
3. Complete a dependent-groups t test.
4. Explain what “power” means in statistical testing.
5. Compare the one-way ANOVA to the within-subjects F.
6. Complete a within-subjects F.
tan82773_07_ch07_191-226.indd 191 3/3/16 12:26 PM
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Section 7.1 Reconsidering the t and F Ratios

Introduction
Tests of significant difference, such as the t test and analysis of
variance, take two basic forms,
depending upon the independence of the groups. Up to this
point, the text has focused only
on independent-groups tests: tests where those in one group
cannot also be subjects in other
groups. However, dependent-groups procedures, in which the
same group is used multiple
times, offer some advantages.
This chapter focuses on the dependent-groups equivalents of the
independent t test and the
one-way ANOVA. Although they answer the same questions as
their independent-groups
equivalents (are there significant differences between groups?),
under particular circum-
stances these tests can do so more efficiently and with more
statistical power.
7.1 Reconsidering the t and F Ratios
The scores produced in both the independent t and the one-way
ANOVA are ratios. In the case
of the t test, the ratio is the result of dividing the difference
between the means of the groups
by the standard error of the difference:
t 5
M1 2 M2
SEd
With ANOVA, the F ratio is the mean square between (MSbet)
divided by the mean square

within (MSwith):
F 5
MSbet
MSwith
With either t or F, the denominator in the ratio reflects how
much scores vary within (rather
than between) the groups of subjects involved in the study.
These differences are easy to see
in the way the standard error of the difference is calculated for
a t test. When group sizes are
equal, recall that the formula is
SEd 5 Î (SEM1)
2 1 (SEM2)
2
with
SEM 5
s
√n
and s, of course, a measure of score variation in any group.
So the standard error of the difference is based on the standard
error of the mean, which in
turn is based on the standard deviation. Therefore, score
variance within in a t test has its root
in the standard deviation for each group of scores. If we reverse
the order and work from the
standard deviation back to the standard error of the difference,
we note the following:

• When scores vary substantially in a group, the result is a
large standard deviation.
• When the standard deviation is relatively large, the
standard error of the mean must
likewise be large because the standard deviation is the
numerator in the formula for SEM.
• A large standard error of the mean results in a large
standard error of the difference be-
cause that statistic is the square root of the sum of the squared
standard errors of the mean.
tan82773_07_ch07_191-226.indd 192 3/3/16 12:26 PM
Section 7.1 Reconsidering the t and F Ratios
• When the standard error of the difference is
large, the difference between the means has
to be correspondingly larger for the result to
be statistically significant. The table of critical
values indicates that no t ratio (the ratio of the
differences between the means and the stan-
dard error of the difference) less than 1.96 to 1
is going to be significant, and even that value
requires an infinite sample size.
Error Variance
The point of the preceding discussion is that the value of t in
the t test—and for F in an

ANOVA—is greatly affected by the amount of variability within
the groups involved. Other
factors being equal, when the variability within the groups is
extensive, the values of t and F
are diminished and less likely to be statistically significant than
when groups have relatively
little variability within them.
These differences within groups stem from differences in the
way individuals within the
samples react to whatever treatment is the independent variable;
different people respond
differently to the same stimulus. These differences represent
error variance—the outcome
whenever scores differ for reasons not related to the IV.
But within-group differences are not the only source of error
variance in the calculation of
t and F. Both t test and ANOVA assume that the groups
involved are equivalent before the
independent variable is introduced. In a t test where the impact
of relaxation therapy on cli-
ents’ anxiety is the issue, the test assumes that before the
therapy is introduced, the treat-
ment group which receives the therapy and the control group
which does not both begin with
equivalent levels of anxiety. That assumption is the key to
attributing any differences after the
treatment to the therapy, the IV.
Confounding Variables
In comparisons like the one studying the effects
of relaxation therapy, the initial equivalence of
the groups can be uncertain, however. What if the
groups had differences in anxiety before the therapy
was introduced? The employment circumstances of

each group might differ, and perhaps those threat-
ened with unemployment are more anxious than
the others. What if age-related differences exist
between groups? These other influences that are
not controlled in an experiment are sometimes
called confounding variables.
A psychologist who wants to examine the impact
that a substance abuse program has on addicts’
behavior might set up a study as follows. Two
groups of the same number of addicts are selected,
Greg Smith/Corbis
In a study of the impact of substance
abuse programs on addicts’ behavior,
confounding variables could include
ethnic background, age, or social class.
Try It!: #1
If the size of the group affects the size of
the standard deviation, what then is the
relationship between sample size and
error in a t test?
tan82773_07_ch07_191-226.indd 193 3/3/16 12:26 PM
Section 7.2 Dependent-Groups Designs
and one group participates in the substance-abuse program.
After the program, the psycholo-

gist measures the level of substance abuse in both groups to
observe any differences.
The problem is that the presence or absence of the program is
not the only thing that might
prompt subjects to respond differently. Perhaps subjects’
background experiences are differ-
ent. Perhaps ethnic-group, age, or social-class differences play a
role. If any of those differ-
ences affect substance-abuse behavior, the researcher can
potentially confuse the influence
of those factors with the impact of the substance-abuse program
(the IV). If those other dif-
ferences are not controlled and affect the dependent variable,
they contribute to error vari-
ance. Error variance exists any time dependent-variable (DV)
scores fluctuate for reasons
unrelated to the IV.
Thus, the variability within groups reflects error variance, and
any difference between groups
that is not related to the IV represents error variance. A
statistically significant result requires
that the score variance from the independent variable be
substantially greater than the error
variance. The factor(s) the researcher controls must contribute
more to score values than the
factors that remain uncontrolled.
7.2 Dependent-Groups Designs
Ideally, any before-the-treatment differences between the
groups in a study will be minimal.
Recall that random selection entails every member of a
population having an equal chance
of being selected. The logic behind random selection dictates
that when groups are randomly

drawn from the same population, they will differ only by
chance; as sample size increases,
probabilities suggest that they become increasingly
similar in characteristic to the population. No sample,
however, can represent the population with complete
fidelity, and sometimes the chance differences affect
the way subjects respond to the IV.
One way researchers reduce error variance is to adopt
what are called dependent-groups designs. The inde-
pendent t test and the one-way ANOVA required inde-
pendent groups. Members of one group could not also be
members of other groups in the
same study. But in the case of the t test, if the same group is
measured, exposed to a treatment,
and then measured again, the study controls an important source
of error variance. Using the
same group twice makes the initial equivalence of the two
groups no longer a concern. Other
aspects being equal, any score difference between the first and
second measure should indi-
cate only the impact of the independent variable.
The Dependent-Samples t Tests
One dependent-groups test where the same group is measured
twice is called the before/after
t test. An alternative is called the matched-pairs t test, where
each participant in the first group
is matched to someone in the second group who has a similar
characteristic. The before/after
t test and the matched-pairs t test both have the same
objective—to control the error variance
that is due to initial between-groups differences. Following are
examples of each test.

Try It!: #2
How does the use of random selection
enable us to control error variance in sta-
tistical testing?
tan82773_07_ch07_191-226.indd 194 3/3/16 12:26 PM
• The before/after design: A researcher is interested in the
impact that positive
reinforcement has on employees’ sales productivity. Besides the
sales commission,
the researcher introduces a rewards program that can result in
increased vaca-
tion time. The researcher gauges sales productivity for a month,
introduces the
rewards program, and gauges sales productivity during the
second month for the
same people.
• The matched-pairs design: A school counselor is
interested in the impact that verbal
reinforcement has on students’ reading achievement. To
eliminate between-groups
differences, the researcher selects 30 people for the treatment
group and matches
each person in the treatment group to someone in a control
group who has a similar
reading score on a standardized test. The researcher then

introduces the verbal
reinforcement program to those in the treatment group for a
specified period of time
and then compares the performance of students in the two
groups.
Although the two tests are set up differently, both cal-
culate the t statistic the same way. The differences
between the two approaches are conceptual, not math-
ematical. They have the same purpose—to control
between-groups score variation stemming from non-
relevant factors.
Calculating t in a Dependent-Groups Design
The dependent-groups t may be calculated using several
methods. Each method takes into
account the relationship between the two sets of scores. One
approach is to calculate the
correlation between the two sets of scores and then to use the
strength of the correlation
as a mechanism for determining between-groups error variance:
the higher the correlation
between the two sets of scores, the lower the error variance.
Because this text has yet to dis-
cuss correlation, for now we will use a t statistic that employs
“difference scores.” The differ-
ent approaches yield the same answer.
The distribution of difference scores came up in Chapter 5 when
it introduced the indepen-
dent t test. Recall that the point of that distribution is to
determine the point at which the
difference between a pair of sample means (M1 2 M2) is so
great that the most probable
explanation is that the samples came from different populations.

Dependent-groups tests use that same distribution, but rather
than the difference between
the means of the two groups (M1 2 M2), the numerator in the t
ratio is the mean of the dif-
ferences between each pair of scores. If that mean is sufficiently
different from the mean
of the population of difference scores (which, recall, is 0), the t
value is statistically sig-
nificant; the first set of measures belongs to a different
population than the second
set of measures. That may seem odd since in a before/after test,
both sets of measures
come from the same subjects, but the explanation is that those
subjects’ responses (the
DV) were altered by the impact of the independent variable;
their responses are now
different.
The denominator in the t ratio is another standard error of the
mean value, but in this case, it
is the standard error of the mean of the difference scores. The
researcher checks for signifi-
cance using the same criteria as for the independent t:
Try It!: #3
How do the before/after t test and the
matched-pairs t test differ?
tan82773_07_ch07_191-226.indd 195 3/3/16 12:26 PM

• A critical value from the t table, determined by degrees of
freedom, defines the point
at which the calculated t value is statistically significant.
• The degrees of freedom are the number of pairs of scores
minus 1 (n 2 1).
The dependent-groups t test statistic uses this formula:
Formula 7.1
t 5
Md
SEMd
where
Md 5 the mean of the difference scores
SEMd 5 the standard error of the mean for the difference scores
The steps for completing the test are as follows:
1. From the two scores for each subject, subtract the second
from the first to determine
the difference score, d, for each pair.
2. Determine the mean of the d scores:
Md 5
Sd
number of pairs

3. Calculate the standard deviation of the d values, sd.
4. Calculate the standard error of the mean for the difference
scores, SEMd, by dividing
sd by the square root of the number of pairs of scores,
SEMd 5
sd
Î number of pairs
5. Divide Md by SEMd, the standard error of the mean for the
difference scores:
t 5
Md
SEMd
Figure 7.1 depicts these steps.
The following is an example of a dependent-measures t test: A
psychologist is investigating
the impact that verbal reinforcement has on the number of
questions university students
ask in a seminar. Ten upper-level students participate in two
seminars where a presentation
is followed by students’ questions. In the first seminar, the
instructor provides no feedback
after a student asks the presenter a question. In the second
seminar, the instructor offers
feedback—such as “That’s an excellent question” or “Very
interesting question” or “Yes, that
had occurred to me as well”—after each question.

Is there a significant difference between the number of
questions students ask in the first
seminar compared to the number of questions students ask in the
second seminar? Problem
7.1 shows the number of questions asked by each student in
both seminars and the solution
to the problem.
tan82773_07_ch07_191-226.indd 196 3/3/16 12:26 PM
Subtract the second score
from the first for each pair
to determine d
Determine the mean of
the d score; Md
Determine Sd by taking
the standard deviation
of the d scores
Divide Sd by the square
root of the number of
pairs to determine SEMd
Divide Md by SEMd to
determine t

Problem 7.1: Calculating the before/after t test
Seminar 1 Seminar 2 d
1 1 3 22
2 0 2 22
3 3 4 21
4 0 0 0
5 2 3 21
6 1 1 0
7 3 5 22
8 2 4 22
9 1 3 22
10 2 1 1
Sd 5 211
(continued)
Figure 7.1: Steps for calculating the before/after t test
Subtract the second score
from the first for each pair
to determine d
Determine the mean of
the d score; Md
Determine Sd by taking
the standard deviation
of the d scores

Divide Sd by the square
root of the number of
pairs to determine SEMd
Divide Md by SEMd to
determine t
tan82773_07_ch07_191-226.indd 197 3/3/16 12:26 PM
The calculated value of t exceeds the critical value from Table
5.1 (Table B.2 in Appendix B).
Therefore, the result is statistically significant. Note that we are
interested in the absolute
value of the calculated t. Because the question was whether
there is a significant difference
in the number of questions, it is a two-tailed test. It does not
matter which session had the
greater number—whether Session 1 is larger than Session 2 or
the other way around. The
students in the second session, where questions were followed
by feedback, asked signifi-
cantly more questions than the students in the first session,
when no feedback was offered by
the instructor.
Degrees of Freedom, the Dependent-Groups Test, and Power
When Md 5 21.1, the two sets of scores show comparatively
little difference. What makes

such a small mean difference statistically significant? The
answer is in the amount of error
variance in this problem. When there is minimal error
variance—for example, the standard
error of the difference scores is just 0.348—comparatively small
mean differences can be
Problem 7.1: Calculating the before/after t test (continued)
1. Determine the difference between each pair of scores, d,
using subtraction.
2. Determine the mean of the difference, the d values (Md).
Md 5
Sd
10
5
11
10
5 21.1
3. Calculate the standard deviation of the d values (Sd). Verify
that
Sd 5 1.101.
4. Just as the standard error of the mean in the earlier test was
s√n, determine
standard error of the mean for the difference scores (SEMd) by
dividing the
result of step 3 by the square root of the number of pairs. Verify
that
SEMd 5

sd
Î np
5
1.101
Î 10
5 0.348
5. Divide Md by SEMd to determine t.
t 5
Md
SEMd
5 2
1.1
0.348
5 23.161
6. As noted earlier, the degrees of freedom for the critical value
of t for this test
are the number of pairs of scores, np 2 1.
t0.05(9) 5 2.262
tan82773_07_ch07_191-226.indd 198 3/3/16 12:26 PM

statistically significant. The ability to detect such small
differences, which are nevertheless
statistically significant, is the rationale for using dependent-
groups tests, which brings us
back to power in statistical testing, a topic first raised in
Chapter 6.
Table B.2 in Appendix B, the critical values of t, indicates that
critical values decline as degrees
of freedom increase. That occurs not only in the critical values
for t, but also for F in analysis
of variance and, in fact, for most tables of critical values for
statistical tests.
• For the dependent-groups t test, the degrees of freedom
are the number of pairs of
related scores, 21.
• For the independent-groups t test (Chapter 5),
df 5 n1 1 n2 22
With the smaller numerical value for df, the dependent-groups
test has the higher standard to
meet for statistical significance, even though the number of raw
scores is the same. But even a
test with a larger critical value can produce significant results
when it has less error variance.
This is what dependent-groups tests do. The central point is that
when each pair of scores
comes from the same participant, or from a matched pair of
participants, the random vari-
ability from nonequivalent groups is minimal because
scores tend to vary similarly for each pair, resulting in

relatively little error variance. The reduced error more
than compensates for the fewer degrees of freedom
and the associated larger critical value.
Recall that in statistical testing, power is defined as the
likelihood of detecting a significant difference when
it is present. The more powerful statistical test is the
one that will most readily detect a significant difference. As
long as the sets of scores are
closely related, the dependent-measures, or dependent-groups,
test is more powerful than
the independent-groups equivalent.
A Matched-Pairs Example
The other form of the dependent-groups t test is the matched-
pairs design. In this approach,
rather than measure the same people repeatedly, each
participant in one group is paired with
a participant who is similar from the other group.
For example, consider a psychologist who wants to determine
whether a video on domestic
violence will prompt viewers to be less tolerant of domestic
violence. The psychologist selects
a group of subjects, introduces them to the video which they
view, and measures their atti-
tudes toward domestic violence. A second group does not view
the video. Reasoning that age
and gender might be relevant to attitudes about domestic
violence, the psychologist selects
people for the second group who match these characteristics of
those in the first group.
Problem 7.2 shows subjects’ scores from an instrument designed
to measure attitudes about
domestic violence and the matched-pairs t solution.

Try It!: #4
What does it mean to say that the within-
subjects test has more power than the
independent t test?
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The absolute value of t is less than the critical value from Table
5.1 (or Table B.2 in Appendix
B) for df 5 9. The difference is not statistically significant.
There are probably several ways to
explain the outcome, but we will explore just three.
1. The most obvious explanation is that the video was
ineffective. Subjects’ attitudes
were not significantly altered as a result of the viewing.
2. Another explanation has to do with the matching. Perhaps age
and gender are not
related to individuals’ attitudes. Prior experience with domestic
violence may be the
most important characteristic, a factor left uncontrolled in the
pairing.
3. Another explanation is related to sample size. Small samples
tend to be more variable
than larger samples, and variability is what the denominator in
the t ratio reflects.
Perhaps if this had been a larger sample, the SEMd would have

had a smaller value and
the t would have been significant.
The second explanation points out the disadvantage of matched-
pairs designs compared to
repeated-measures designs. The individual conducting the study
must be in a position to
know which characteristics of the participants are most relevant
to explaining the depen-
dent variable so that they can be matched in both groups.
Otherwise it is impossible to know
whether a nonsignificant outcome reflects an inadequate match,
control of the wrong vari-
ables, or a treatment that just does not affect the DV.
Problem 7.2: Calculating a matched-pairs t test
Subject Viewed Did not view d
1 1.5 3 21.5
2 4 0 4
3 3 2 1
4 0 0 0
5 2 0 2
6 4.5 4 0.5
7 6 2 4
8 0 1 21.0
9 5.25 2 3.25
10 2 3 21.0
Verify that Md 5 1.125
Sd 5 2.092
SEMd 5
sd

Î np
5
2.092
Î 10
5 0.662
t 5
Md
SEMd
5 2
1.125
0.662
5 1.700
t0.05(9) 5 2.262
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Comparing the Dependent-Samples t Test to the Independent t
Test
To compare the dependent-samples t test and the independent t
more directly, we will apply both tests
to the same data to illustrate how each test deals with error

variance. Before beginning, a necessary
caution: Once data are collected, there is no situation where
someone can choose which test to use.
Either the groups are independent, or they are not. Our
comparison is purely an academic exercise.
A university program encourages students to take a service-
learning class that emphasizes
the importance of community service as a part of the students’
educational experience. Data
are gathered on the number of hours former students spend in
community service per month
after they complete the course and graduate from the university.
• For the independent t test, the students are divided
between those who took a
service-learning class and graduates of the same year who did
not.
• For the dependent-groups t test, those who took the
service-learning class are
matched to a student with the same major, age, and gender who
did not take the class.
The data and the solutions to both tests are listed in Problem
7.3.
Problem 7.3: The before/after t versus the independent t test
Student Class No class d
1 4.000 3.000 1.00
2 3.000 2.000 10
3 3.000 2.000 1.00
4 2.000 2.000 00
5 3.000 2.5.00 0.5.00

6 4.000 3.000 10
7 1.000 2.000 21.00
8 5.000 4.000 10
9 6.000 5.000 1.00
10 4.000 3.000 10
M 3.500 2.850 0.650
s 1.434 1.001 0.669
SEM 0.453 0.316 0.211
For an independent t test, the results show:
SEd 5 Î (SEM12
1 SEM2
2) 5 Î 0.4532 1 0.3162 5 0.553
t 5
M1 2 M2
SEd
5
3.50 2 2.850
0.553
5 1.175; t0.05(18) 5 2.101. The result is not significant.
For a matched-pairs t test, the results show:
t 5
Md
SEMd
5 0.650 1 0.211 5 3.081; 5 2.262. The result is significant.

tan82773_07_ch07_191-226.indd 201 3/3/16 12:26 PM
Because the differences between the scores are quite consistent,
as they tend to be when
participants are matched effectively, very little variation exists
between the individuals in
each pair. Minimal variation results in a comparatively small
standard deviation of difference
scores and a small standard error of the mean for the difference
scores. The small standard
deviation and standard error of the mean make it more likely
that t ratios with even rela-
tively small numerators will be statistically significant. Since
the independent t test does not
assume that the two groups are related, error variance is based
on the differences within the
groups of raw scores, rather than between the individuals in
each pair, and the denominator
is large enough that in that test, the t value is not significant.
Computing the Dependent-Groups t Test Using Excel
To use Excel to complete Problem 7.3 as a dependent-groups
test, follow this procedure:
1. Create the data file in Excel.
2. a. Label Column A “Class” to indicate those who had the
service learning class, and
label column B “No Class.”

b. Enter the data, beginning with cell A2 for the first group and
cell B2 for the
second group.
3. Click the Data tab at the top of the page.
4. At the extreme right, choose Data Analysis.
5. In the Analysis Tools window, select ttest: Paired Two
Sample for Means and
click OK.
6. In the blanks for Variable 1 Range and Variable 2 Range,
enter A2:A11 for
the data in the first (Class) group (cells A2 to A11), and enter
B2:B11 for the
No Class data (cells B2 to B11).
7. Indicate that the hypothesized mean difference is 0. This
reflects the value for the
mean of the distribution of difference scores.
8. Indicate A13 for the output range so that the results do not
overlay the data scores.
9. Click OK.
Widen column A so that all the output is readable. Figure 7.2
shows the resulting screenshot.
In the Excel solution, t 5 3.074 rather than the 3.081 from the
manually calculated solution.
Excel calculates the correlation between scores to find a
solution, rather than determining the
difference between scores as we did. In any event, the very
minor difference, 0.007, between
the solution shown in Problem 7.3 and the Excel solution in
Figure 7.2 is not relevant to the

outcome. The Excel output also indicates results for one-tailed
and two-tailed tests. At p 5
0.05, the outcome is statistically significant in either case.
tan82773_07_ch07_191-226.indd 202 3/3/16 12:26 PM
Figure 7.2: Excel output for the dependent-samples t test using
data from
Problem 7.3
Source: Microsoft Excel. Used with permission from Microsoft.
Comparing the Two Dependent t Tests
The before/after and matched-pairs approaches to calculating a
dependent-groups t test
have their individual advantages. The before/after design
provides the greatest control
over the extraneous variables that can confound the results in a
matched-pairs design. The
matching approach always has the chance that subjects in Group
2 are not matched closely
enough on some relevant variable to minimize the error
variance. In the service-learning
example, students were matched according to age, major, and
gender. But if marital status
affects students’ willingness to be involved in community
service and that variable is not
controlled, an imbalance of married/not-married students could

confound results. The
before/after procedure involves the same subjects, and unless
their status on some impor-
tant variable changes between measures (a rash of marriages
between the first and second
measurement, for example), that approach will better control
error variance.
Note that the matched-pairs approach relies on a large sample
from which to draw to select
participants who match those in the first group. As the number
of variables on which partici-
pants must be matched increases, so must the size of the sample
from which to draw to find
participants with the correct combination of characteristics.
tan82773_07_ch07_191-226.indd 203 3/3/16 12:26 PM
Apply It!
Repeated Measures
A research team is investigating the
impact of fixed-ratio reinforcement on
laboratory rats. Initially, the rats receive
food reinforcers each time they make a
correct turn in a maze. The control rats
receive no reinforcement. The depen-
dent variable is the amount of time in
seconds it takes each rat to complete the

maze. Table 7.1 shows the results of the
investigation.
Table 7.1: Impact of fixed-ratio reinforcement on laboratory
rats
Rat
Time(s)
With reinforcement Without reinforcement
A 112 120
B 85 82
C 103 116
D 154 168
E 65 75
F 52 51
G 85 96
H 72 79
I 167 178
J 123 141
K 142 153
Table 7.2 shows the Excel solution to the t test.

mbot/iStock/Thinkstock
tan82773_07_ch07_191-226.indd 204 3/3/16 12:26 PM
The advantage of the matched-pairs design, on the other hand,
is that it takes less time to
execute. The treatment group and the control group can both be
involved in the study at the
same time. By way of a summary, note the comparisons among t
tests in Table 7.3.
Table 7.3: Comparing the t tests
Independent t Before/after Matched-pairs
Groups Independent groups One group measured
twice
Two groups: each subject
from the first group matched
to one in the second
Denominator/
error term
Within-groups and
between-groups
variability

Within-groups variability
only
Within-groups variability
only
Table 7.2: Summary statistics from the Excel t test
Variable 1 Variable 2
Mean 105.45 114.45
Variance 1428.67 1736.27
Observations 10 10
Pearson Correlation 0.99
Hypothesized Mean Difference 0.00
df 9
t Stat 24.817
P(T�t) one-tail 0.0003
t Critical one-tail 1.8331
P(T�t) two-tail 0.0007
t Critical two-tail 2.2622
The magnitude of the calculated value of t 5 24.817 exceeds the
critical two-tail value from
the table of tcrit 5 2.26. The result indicates that providing
reinforcement for correct decisions

has a statistically significant effect on the time it takes a rat to
complete the maze.
Apply It! boxes written by Shawn Murphy
tan82773_07_ch07_191-226.indd 205 3/3/16 12:26 PM
Section 7.3 The Within-Subjects F
7.3 The Within-Subjects F
Sometimes two measures of the same group are not enough to
track changes in the depen-
dent variable. Maybe the researchers conducting the service-
learning study want to compare
how much time students devoted to community service the year
they graduated, one year
later, and then two years after graduation. The within-subjects F
is a dependent-groups
procedure for two or more groups of scores when the DV is
interval or ratio scale. Because
the dependent-groups t test is the repeated-measures equivalent
of the independent t test,
the within-subjects F is the repeated-measures or matched-pairs
equivalent of the one-way
ANOVA. The same Ronald Fisher who developed analysis of
variance also developed this test,
which is a form of ANOVA, and the test statistic is still F.
Here too, the dependent groups can be formed either by
repeatedly measuring the same group
or by matching separate groups of participants on the relevant

variables. When more than
two groups are involved, matching becomes increasingly
problematic, however. Although it
is theoretically possible to match the participants across any
number of groups, to match
more than one or two relevant variables across more than two or
three groups of subjects
is a highly complex undertaking. Imagine the difficulty, for
example, of matching subjects on
some measure of aptitude, their income, and their level of
optimism in three or more differ-
ent groups. Even matching these variables for two groups might
prove quite difficult. For this
reason, repeatedly measuring the same participants is much
more common than matching
across several groups.
Managing Error Variance in the Within-Subjects F
Recall from Chapter 6 that when Fisher developed ANOVA, he
shifted away from calculating
score variability with the standard deviation, standard error of
the mean, and so on and used
sums of squares instead. The particular sums of squares
computed are the key to the strength
of this procedure.
If a researcher measures a group of participants in a study on a
dependent variable at three
different intervals and records their scores in parallel columns,
the result is a data sheet simi-
lar to Table 7.4.
• The column scores for the first, second, and third
measures are treated the way
scores from three different groups were treated in a one-way
ANOVA; the differences

from column to column reflect the effect of the IV, the
treatment.
• The participant-to-participant differences, which are like
the within-group differ-
ences in a one-way ANOVA, are reflected in the differences in
the scores from row to
row. Those differences are error variance, just as they were in
the one-way ANOVA.
Table 7.4: A data sheet
1st measure 2nd measure 3rd measure
Participant 1 . . .
Participant 2 . . .
tan82773_07_ch07_191-226.indd 206 3/3/16 12:26 PM
• The within-subjects F calculates the variability between
rows (the within-
groups variance), and then, because that variance comes from
participant-to-
participant differences that will be the same in each group,
eliminates it from
further analysis.
• The only error variance that remains is that which does

not stem from initial
person-to-person differences. It will be from such sources as
inaccurate measures
of the DV, mistakes in coding the DV, or differences in how
sensitive the subjects
are to the DV that change from treatment to treatment.
In the dependent-samples t test, the within-subjects variance—
error variance—is reduced
by using subjects in two groups that are highly similar to begin
with or because they are the
same people measured before and after a treatment. In either
case, initial between-groups
differences, an important source of variance, are minimized, and
attributing differences to the
effect of the independent variable becomes easier.
In the within-subjects F, the variability within groups is
calculated and then simply discarded
so that it is no longer a part of the analysis. That cannot be done
in the one-way ANOVA
because the amount of variability within groups is different for
each group, and there is no
way to separate it from the balance of the error variance in the
problem.
A Within-Subjects F Example
A psychologist is studying practice effect in connection with the
ability of 12-year-olds to
solve a series of puzzles involving logic and reasoning. The
study has five subjects, who
solve as many puzzles as they can during a 30-minute period.
The psychologist conducts
three trials an hour apart. Although the puzzles are similar, each
trial involves different
puzzles. The researcher wants to answer the question whether

greater familiarity with
the puzzles is associated with solving more puzzles correctly.
Table 7.5 shows the study’s
results.
Table 7.5 Data from puzzle-solving study
Number of puzzles solved
1st trial 2nd trial 3rd trial
Diego 2 5 4
Harold 4 7 7
Wilma 3 6 5
Carol 4 5 6
Moua 5 8 9
tan82773_07_ch07_191-226.indd 207 3/3/16 12:26 PM
The independent variable (the IV, the treatment) is the
particular trial. The dependent vari-
able (the DV) is the number of puzzles successfully solved. The
research question is whether
the second or third trials will result in significantly more
puzzles solved than in the first trial.

In Chapter 6, the sum of squares between (SSbet) measured the
variability related to the IV.
This study gauges the same source of variance, except that it is
called the sum of squares
between columns (SScol).
The Components of the Within-Subjects F
Calculating the within-subjects F begins just as the one-way
ANOVA begins, by determining
all variability from all sources with the sum of squares total
(SStot). It is calculated the same
way as it was in Chapter 6:
1. The formula for the sum of squares total is
SStot =∑(x 2 MG)2
a. Subtract each score (x) from the mean of all the scores from
all the groups (MG),
b. square the difference, and then
c. sum the squared differences.
The balance of the problem is completed with the following
steps:
2. The equation for the sum of squares between columns (SScol)
is much like SSbet in the
one-way ANOVA. The scores in each column are treated the
same way the different
groups were treated in the one-way ANOVA. For columns 1, 2,
and through k:
Formula 7.2
SScol 5 (Mcol 1 2 MG)2ncol 1 1 (Mcol 2 2 MG)2ncol 2 1 . . . 1
(Mcol k 2 MG)2ncol k

a. calculate the mean for each column of scores (Mcol),
b. subtract the mean for all the data (MG) from each column
mean,
c. square the result, and
d. multiply the squared result by the number of scores in the
column (ncol).
3. The sum of squares between rows is also like the SSbet from
the one-way problem except
that it treats the scores for each row as a separate group. For
rows 1, 2, and through i:
Formula 7.3
SSrows 5 (Mrow 1 2 MG)2nrow 1 1 (Mrow 2 2 MG)2nrow 2 1 .
. . 1 (Mrow i 2 MG)2nrow i
a. calculate the mean for each row of scores (Mrow),
b. subtract the mean for all the data (MG) from each row mean,
c. square the result, and
d. multiply the squared result by the number of scores in the
row.
tan82773_07_ch07_191-226.indd 208 3/3/16 12:26 PM
4. The residual sum of squares is the error term in the within-
subjects F. It is the
equivalent of SSwith or the SSerr in the one-way ANOVA. With

the within-subjects F,
the person-to-person differences within each measure are
calculated and eliminated
since they are the same for each set of measures. Unexplained
variance is what
remains after the treatment effect (the effect of the IV) and the
person-to-person
differences within in each group are eliminated:
Formula 7.4
SSresid 5 SStot 2 SScol 2 SSrows
a. If from all variance from all sources (SStot),
b. the treatment effect (SScol) is subtracted
c. and the person-to-person differences (SSrows) are subtracted,
d. what remains is unexplained variance, error.
Completing the Within-Subjects F Calculations
Just as with one-way problems, the mean square values are
calculated by dividing the sums of
squares by their degrees of freedom. The degrees of freedom
values are as follows:
• df total 5 N 2 1
• df columns 5 number of columns 2 1
• df rows 5 number of rows 2 1
• df residual 5 df columns 3 df rows
Although we listed the degrees of freedom values for total and
rows, as well as for col-
umns and residuals, there are no MS values for total and rows.
The df values for
those two variance measures are listed because the sum of all df
values must equal
df for total; they allow for a quick check of df values. The next

step is to complete the
ANOVA table, including the calculation of F. We can determine
the test statistic, F, in
the within-subjects ANOVA by dividing the treatment effect
(MScol) by the error term
(MSresid); F 5 MScol / MSresid
Problem 7.4 shows the calculations and the table for the impact
of the practice-effects
study.
As with one-way ANOVA, the first step is to calculate the
SStot. It is the sum of the squared
differences between each individual score (x) and the grand
mean (MG). The SStot is followed
by the SS for the differences between columns (SScol). It is the
sum of the squared differences
between each column mean (Mcol1, for example) and the grand
mean (MG), times the number
of scores in the column (ncol1, for example). Next, calculate the
SS for the differences from row
to row. For each row, square the difference between the row
mean (Mr1, for example) and the
grand mean (MG), and then multiply the squared difference by
the number of scores in the
row (nr1, for example). Finally, find the error term—the
residual sum of squares—which is
what remains from SStot 2 SScol 2 SSrows.
tan82773_07_ch07_191-226.indd 209 3/3/16 12:26 PM

The calculated value of F exceeds the critical value of F from
the table. The number of puzzles
completed is significantly different for the different trials. The
significant F indicates that dif-
ferences of this magnitude are unlikely to have occurred by
chance.
Completing the Post Hoc Test
Ordinarily, the calculation of F leaves unanswered the question
of which set of measures
is significantly different from which. However, in this
particular problem there is only one
Problem 7.4: A within-subjects F example
Puzzles completed
1st trial 2nd trial 3rd trial Row means
Diego 2 5 4 3.667
Harold 4 7 7 6.0
Wilma 3 6 5 4.667
Carol 4 5 6 5.0
Moua 5 8 9 7.333
Column means 3.60 6.20 6.20
Grand mean (Md) 5.333
1. SStot 5 ∑(x 2 MG)2
(2 2 5.333)2 1 (4 2 5.333)2 1 . . . 1 (9 2 5.333)2 5 49.333
2. SScol 5 (Mcol 1 – MG)2ncol 1 1 (Mcol 2 – MG)2ncol 2 1 . . .
1 (Mcol k – MG)2ncol k

(3.6 2 5.333)25 1 (6.2 2 5.333)25 1 (6.2 2 5.333)25 5 22.533
3. SSrows 5 (Mr1 – MG)2nr1 1 (Mr2 – MG)2nr2 1 . . . 1 (Mri –
MG)2nri
(3.667 2 5.333)23 1 (6.0 2 5.333)23 1 (4.667 2 5.333)23
1 (5.0 2 5.333)23 1 (7.333 2 5.333)23 5 23.333
4. The residual sum of squares.
SSresid 5 SStot 2 SScol 2 SSrows 5 49.333 2 22.533 2 23.333 5
3.467
The ANOVA table
Source SS df MS F Fcrit
Total 49.333 14
Columns 22.533 2 11.267 26.0 4.46
Rows 23.333 4
Residual 3.467 8 0.433
tan82773_07_ch07_191-226.indd 210 3/3/16 12:26 PM
possibility. Because both the second trial and the third
trial measures have the same mean (M 5 6.20), they
must both be significantly different from the only other
group of measures in the problem, the first trial mea-
sures, for which M 5 3.6. As a demonstration of how

we would determine which groups were significantly
different from which were it otherwise, honestly sig-
nificant difference (HSD) is completed anyway.
The HSD procedure is the same as for the one-way test, except
that the error term is now
MSresid. Substituting MSresid for MSwith in the formula
provides
HSD 5 x Ñ
MSresid
n
where x is a value from Table B.4 in Appendix B. It is based on
the number of means, which is
the same as the number of groups of measures, 3 in the example,
and the df for MSresid, which
is 8. n 5 the number of scores in any one measure, 5 in this
instance.
For the number-of-puzzles-solved correctly study,
4.04 Ñ
0.433
5 5 1.19
A difference of 0.306 or greater between any pair of means is
statistically significant.
Using the same approach used in Chapter 6, the matrix in Table
7.6 indicates how the difference
between each pair of means helps us determine which
differences are statistically significant.

Table 7.6: Matrix of differences of means
1st trial (3.6) 2nd trial (6.2) 3rd trial (6.2)
1st trial (3.6) diff 5 0 diff 5 2.6* diff 5 2.6*
2nd trial (6.2) diff 5 0.00
3rd trial (6.2)
*Indicates a significant difference
The first trial measures are significantly different from the
second and third measures. Because
the mean values for the second and third trial measures are the
same, neither of those two is
significantly different from the other. For these 12-year-old
subjects working with this kind of
logic/reasoning puzzle, practice effect is greatest from first to
subsequent trials.
Calculating the Effect Size
The final question for a significant F is the question of the
practical importance of the result.
Using eta-squared as the measure of effect size produces the
following:
η2 5
SScol
SStot
Try It!: #5
How is the error term in the within-
subjects F different from that in the one-
way ANOVA?

tan82773_07_ch07_191-226.indd 211 3/3/16 12:26 PM
with SScol taking the place of SSbet in the one-way ANOVA.
For the problem just completed, SScol 5 22.533 and SStot 5
49.333, so
η2 5
22.533
49.333 5 0.457
The eta-squared value indicates that approximately 46% of the
variance in the number of
puzzles solved successfully by these subjects can be explained
by whether it was the first or
some subsequent trial.
Apply It!
The Meditation Pilot Program Revisited
Recall Chapter 5’s example of the middle school that adopted a
meditation program in an effort
to relieve stress among students, increase their test scores, and
improve student behavior. In
the earlier chapter, we used a one-sample t test to determine
that a statistically significant
increase in GPAs occurred among participating students. Now,
we will use a within-subject F

test to see if their stress levels have decreased over successive
intervals.
Ten randomly chosen students selected for the program filled
out questionnaires about their
stress levels. Scores ranged from 1 to 10, with 10 indicating the
most stress. The survey was
given before the start of the program and at three-month
intervals. The time elapsed repre-
sents the independent variable, the treatment effect that drives
this analysis. The dependent
variable is the stress score. This example includes four groups
of DV scores.
Results of the stress questionnaires appear in Table 7.7.
Table 7.7: Stress over time for 10 students
Student
Time (months)
0 3 6 9
1 7 6 6 6
2 9 6 5 5
3 7 5 5 4
4 5 3 3 2
5 7 6 4 4
6 8 5 7 5

7 5 4 4 3
8 7 5 6 5
9 6 6 4 4
10 7 5 5 5
Table 7.8 shows results of the within-subject F test calculations.
tan82773_07_ch07_191-226.indd 212 3/3/16 12:26 PM
Table 7.8: Within-subject F test calculations for changes in
stress over time
Source SS df MS F
Total 82.000 39
Columns 34.475 3 11.492 26.36
Subjects 35.725 9
Residual 11.775 27 0.436
f.05(3,27) 2.96
The F value of 26.36 is greater than the critical F value of 2.96,
results that are unlikely to
have occurred by chance. It seems clear that the length of time
during which students practice
meditation has a significant effect on stress levels.
The significant value of F indicates the need for a post hoc test
to determine which group(s) of stress

measures are significantly different from which others. Recall
that the HSD formula is as follows:
HSD 5 x Ñ
MSresid
n
Entering the MSresid value from the ANOVA table and relevant
value of x from the Tukey’s table
gives us
HSD 5 3.875 Ñ
0.436
10 5 0.81
A difference of 0.81 or greater between any two means indicates
that the difference between
those intervals is statistically significant. A matrix that shows
the difference between each pair
of means makes interpreting the HSD value easier, as in Table
7.9.
Table 7.9: Detecting significant differences among multiple
groups
0 month (6.8) 3 months (5.1) 6 months (4.9) 9 months (4.3)
0 month (6.8) diff 5 1.7* diff 5 1.9* diff 5 2.5*
3 months (5.1) diff 5 0.2 diff 5 0.8
6 months (4.9) diff 5 0.6
9 months (4.3)
*Indicates a significant difference

Comparing the means reveals that the greatest decrease in stress
occurs during the first three
months of the meditation program, a difference between the
means of 1.7. It is also appar-
ent that the stress scores for any interval are significantly
different from the stress recorded
before the experiment began.
To determine the practical importance of the decline in stress
measures requires an effect-size
calculation. Once again, we will use eta squared. For the
problem just completed, Icol 5 34.475,
and SStot 5 82.000. Therefore,
η2 5
34.475
82.000 5 0.42.
About 42% of the variance in stress can be explained by how
long the student has been
enrolled in the meditation program.
The within-subjects F test allowed analysis of students’ stress
levels at multiple times through-
out the year and showed that the program was reducing stress
levels by significant amounts
from the stress recorded among subjects before the program
began.
Apply It! boxes written by Shawn Murphy
tan82773_07_ch07_191-226.indd 213 3/3/16 12:26 PM

Comparing the Within-Subjects F and the One-Way ANOVA
In the one-way ANOVA, within-group variance is different for
each group because each group
is made up of different participants. With no way to distinguish
between the subject-to-
subject variability within groups from other sources of error
variance, the subject-to-subject
variance cannot be calculated and eliminated from further
analysis, as it can be in the within-
subjects F. The smaller error term that is the result in the
within-subjects test (which, remem-
ber, is the divisor in the F ratio) allows relatively small
differences between sets of measures
to be statistically significant.
The effect of eliminating some sources of error is illustrated by
using the same data in the
study of practice effect on problem solving. If those same data
were treated as the num-
ber of problems solved by separate groups, rather than by the
same group over time, the
researcher analyzes using a one-way ANOVA instead of the
within-subjects F. We caution that
this approach is for illustration only because groups are either
independent or dependent,
and one set of data cannot fit both scenarios. We use it here to
allow us to compare the error
terms for each approach.
The SStot and the SSbet will be the same as the SStot and the
SScol in the within-subjects problem.

SStot 5 49.333
SSbet 5 22.533
But with no way to isolate the participant-to-participant
differences from the balance of the
error variance in the one-way ANOVA, the SSwith amount in a
one-way ANOVA ends up the
same as SSrows 1 SSresid in the within-subjects F in Problem
7.4.
SSwith 5 ∑(xa 2 Ma)2 1 ∑(xb 2 Mb)2 1 ∑(xc 2 Mc)2 5 (2 2
3.60)2 1 (4 2 3.60)2
1 . . . 1 (9 2 6.20)2 5 26.80
From Table 7.10, we can make the following observations:
• The number of degrees of freedom for “within” changes
from the 8 for residual
to 12, which results in a smaller critical value for the
independent-groups
test, but that adjustment does not compensate for the additional
error in the
term.
Table 7.10: The within-subjects F example repeated as a one-
way ANOVA
The ANOVA table
Source SS df MS F Fcrit
Total 49.333 14
Between 22.533 2 11.267 5.045 3.89

Within 26.800 12 2.233
tan82773_07_ch07_191-226.indd 214 3/3/16 12:26 PM
• Note that the sum of squares for the error term jumps from
3.467 in the within-
subjects test to 26.80 in the independent-groups test.
• The F value is reduced from 26.0 in the within problem to
5.046 in the one-way
problem, a factor of about one-fifth.
Although calculating both one-way ANOVA and with-subjects F
results for the same data is
not realistic, the comparison illustrates what can be gained by
setting up a dependent-groups
test. That is an option that researchers do have at the planning
level.
Another Within-Subjects F Example
A psychologist working at a federal prison is interested in the
relationship between the
amount of time a prisoner is incarcerated and the number of
violent acts in which the pris-
oner is involved. Using self-reported data, inmates respond
anonymously to a questionnaire
administered one month, three months, six months, and nine
months after incarceration.
Problem 7.5 shows the data and the solution.

The results (F) indicate that there are significant differences in
the number of violent acts
documented for the inmate related to the length of time the
inmate has been incarcerated.
The HSD results indicate that those incarcerated for one month
are involved in a signifi-
cantly different number of violent acts than those who
have been in for three or six months. Those who have
been in for six months are involved in a significantly
different number of violent acts than those who have
been in for nine months. The eta squared value indi-
cates that about 37% of the variance in number of vio-
lent acts is a function of how long the inmate has been
incarcerated.
Try It!: #6
How do the eta squared values compare
for the one-way ANOVA/within-subjects F
problem?
Problem 7.5: Another within-subjects F example:
Violent acts and time of incarceration
Percentile improvement
Inmate 1 month 3 months 6 months 9 months Row means
1 4 3 2 5 3.50
2 5 4 3 4 4.0
3 3 1 1 2 1.750
4 4 2 1 3 2.50
5 2 1 2 3 2.0
Column means 3.60 2.20 1.80 3.40
MG 5 2.750

(continued)
tan82773_07_ch07_191-226.indd 215 3/3/16 12:26 PM
Problem 7.5: Another within-subjects F example:
Violent acts and time of incarceration (continued)
Verify that
1. SStot 5 ∑(x 2 MG)2 5 31.750
2. SScol 5 (Mcol 1 2 MG)2ncol 1 1 (Mcol 2 2 MG)2ncol 2 1
(Mcol 3 2 MG)2ncol 3 1 (Mcol 4 2 MG)2ncol 4
(3.6 2 2.75)25 1 (2.2 2 2.75)25 1 (1.8 2 2.75)25 1 (3.4 2
2.75)25 5 11.750
3. SSsubj 5 (Mr1 2 MG)2nr1 1 (Mr2 2 MG)2nr2 1 (Mr3 2
MG)2nr3 1 (Mr4 2 MG)2nr4 1 (Mr5 2 MG)2n5
(3.6 2 2.75)24 1 (4.0 2 2.75)24 1 (1.75 2 2.75)24 1 (2.5 2
2.75)24
1 (2.0 2 2.75)24 5 15.0
4. SSresid 5 SStot 2 SScol 2 SSsubj 5 31.75 2 11.75 2 15 5 5.0
The ANOVA table
Source SS df MS F

Total 31.75 19
Columns 11.75 3 3.917 9.393
Subjects 15.00 4
Residual 5.0 12 0.417
F0.05(3.12) 5 3.49. F is significant.
The post hoc test:
HSD 5 x0.05 Ña
MSw
n
b 5 4.20 Ña
0.417
5
b 5 1.213
M1 5 3.6 M2 5 2.2 M3 5 1.8 M4 5 3.4
M1 5 3.6 1.4* 1.8* 0.2
M2 5 2.2 0.4 1.2
M3 5 1.8 1.6*
M4 5 3.4
*The differences marked with an asterisk are significant.
n2 5
SScol
SStot

5
11.75
31.75 5 0.370% of the variance in violence witnessed is related
to how long the
inmate has been incarcerated.
tan82773_07_ch07_191-226.indd 216 3/3/16 12:26 PM
Computing Within-Subjects F Using Excel
In spite of the important increase in power that is available
compared to independent-groups
tests, a dependent-groups ANOVA is not one of the more
common tests. Excel does not offer
it as an option in the list of Data Analysis Tools, for example.
However, like many statistical
procedures the dependent-groups ANOVA involves a number of
repetitive calculations, which
Excel can simplify. We will complete the second problem as an
example.
1. Set the data up in four columns just as they appear in
Problem 7.5, but insert a blank
column to the right of each column of data. With a row at the
top for the labels, begin
entering data in cell A2.
2. Calculate the row and column means as well as a grand mean

as follows:
a. For the column means, place the cursor in cell A7 just
beneath the last value in
the first column and enter the formula =average(A2:A6), then
press Enter.
b. To repeat this for the other columns, left click on the solution
that is now in A7,
drag the cursor across to G7, and release the mouse button. In
the Home tab, click
Fill and then Right. This will repeat the column-means
calculations for the other
columns. Delete the entries that populate cells B7, D7, and F7,
which are still
empty at this point.
c. For the row means, place the cursor in cell I2 and enter the
formula
=average(A2, C2, E2, G2) followed by Enter.
d. To repeat this for the other rows, left click on the solution
that is now in I2, drag
the cursor down to I6, and release the mouse button. In the
Home tab, click Fill
and then Down. This will repeat the calculation of means for the
other rows.
e. For the grand mean, place the cursor in cell I7 and enter the
formula
=average(I2:I6) followed by Enter (the mean of the row means
will be the same
as the grand mean—the same could have been done with the
column means).
3. To determine the SStot:

a. In cell B2, enter the formula =(A222.75)^2 and press Enter.
This will square
the difference between the value in A2 and the grand mean. To
repeat this for the
other data in the column, left-click the cursor in cell B2, and
drag down to cell B6.
Click Fill and Down. Place the cursor in cell
B7, click the summation sign (∑) at
the upper right of the screen, and press Enter. Repeat these
steps for columns
D, F, and H.
b. Place the cursor in H9, type SStot=, and click Enter. In cell
I9, enter the formula
=Sum(B7,D7,F7,H7) and press Enter. The value will be 31.75,
which is the total
sum of squares.
4. For the SScol:
a. In cell A8, enter the formula =(3.622.75)^2*5 and press
Enter. This will square
the difference between the column mean and the grand mean
and multiply the
result by the number of measures in the column, 5. In cells C8,
E8, G8, repeat this
for each of the other columns, substituting the mean for each
column for the 3.60
that was the column 1 mean.
b. With the cursor in H10, type in SScol= and click Enter. In
cell I10, enter the
formula =Sum(A8,C8,E8,G8) and press Enter. The value will
be 11.75, which
is the sum of squares for the columns.

tan82773_07_ch07_191-226.indd 217 3/3/16 12:26 PM
5. For the SSrows:
a. In cell J2, enter the formula =(I222.75)^2*4 and press Enter.
Repeat this in
rows I3–I6 by left-clicking on what is now I2 and dragging the
cursor down to
cell I6. Click Fill and Down.
b. With the cursor in H11, type SSrow= and click Enter. In cell
I11, enter the formula
=Sum (J2:J6) and press Enter. The value will be 15.0, which is
the sum of
squares for the participants.
6. For the SSresid, in cell H12, enter SSresid= and click Enter.
In cell I12, enter the formula
=I102I112I12. The resulting value will be 5.0.
We used Excel to determine all the sums-of-squares values.
Now, the mean squares are
determined by dividing the sums of squares for columns and for
residual by their degrees of
freedom:
MScol 5
11.75

3
5 3.917
MSresid 5
5
12
5 0.417
F 5
MScol
MSresid
5
3.917
0.417
5 9.393, which agrees with the earlier calculations done by
hand.
To create the ANOVA table, enter the following data:
• Beginning in cell A10, type in Source; in B10 SS; df in
C10; MS in D10; F in E10; and
Fcrit in F10.
• Beginning in cell A11 and working down, type in total,
columns, rows, residual.
For the sum-of-squares values:
• In cell B11, enter =I9.

For the degrees of freedom:
• In cell C11, enter 19 for total degrees of freedom.
• In cell C12, enter 3 for columns degrees of freedom.
• In cell C13, enter 4 for rows degrees of freedom.
• In cell C14, enter 12 for residual degrees of freedom.
For the mean squares:
• In cell D12, enter =B12/C12. The result is MScol.
• In cell D14, enter =B14/C14. The result is MSresid.
For the F value in cell E12, enter =D12/D14.
In cell F12, enter the critical value of F for 3 and 12 degrees of
freedom, which is 3.49.
tan82773_07_ch07_191-226.indd 218 3/3/16 12:26 PM
The list of commands looks intimidating, but mostly because
every keystroke has been
included. With some practice, using Excel in this way will
become second nature. Figure 7.3
shows a screenshot of the result of the calculations.
Writing Up Statistics
Because of some of the strengths noted earlier, repeated-

measures designs are a fixture
in psychological research. Lambert-Lee et al. (2015) used a
before/after t test to evaluate
autistic children’s basic language progress during a 12-month
period. They concluded that
an applied behavior analysis approach to teaching basic-
language skills to autistic children
results in a statistically significant improvement in their
language skills. One of the difficul-
ties in a study such as this, however, is knowing whether factors
other than the treatment—
applied behavior analysis in this case—might have prompted the
significant improvement.
Figure 7.3: Screenshot of a within-subjects F problem
Source: Microsoft Excel. Used with permission from Microsoft.
tan82773_07_ch07_191-226.indd 219 3/3/16 12:26 PM
Summary and Resources
There is always the possibility, particularly with younger
subjects, that simply the passage of
time explains the change.
Sometimes when using the within-subjects F, the dependent
variable measure is the amount
of difference between the various measures, called “change
scores,” rather than the raw scores
upon which the researcher ordinarily relies. One of the

criticisms of repeated-measures
designs is that change scores—the amount of improvement
between measures—tend to be
unreliable. In a measurement context, this unreliability means
that the scores may not be
repeatable; someone replicating the experiment with new
subjects under similar conditions
might find substantially different amounts of score
improvement. Thomas and Zumbo (2012)
examined this criticism of change scores using a within-subjects
F (also called a repeated
measures ANOVA) and found the criticism unwarranted.
Chapter Summary
Any statistical procedure has advantages and disadvantages. The
downside of the different
independent-groups designs is that subjects within the
individual groups often respond to
the independent variable differently. Those differences are a
source of error variance that is
unique to each group. Even with random selection and fairly
large groups, there will be dif-
ferences in the way that people in the same group respond to
whatever stimulus is offered.
The before/after t and within-subjects F tests eliminate that
source of error variance by
either using the same people repeatedly or by matching subjects
on the most important
characteristics. Controlling error variance results in a test that
is more likely to detect a sig-
nificant difference (Objectives 1 and 5).
In dependent-groups designs, using the same group repeatedly
allows for a smaller number

of participants involved (Objectives 1, 2, 3, 4, and 6). One of
the downsides to repeated-
measures designs, however, is that they take more time to
complete. Unless subjects are
matched across measures, the different levels of the independent
variable cannot be admin-
istered concurrently as they can in independent-groups tests.
More time increases the
potential for attrition. If one of the participants drops out of a
repeated-measures study, all
the data measures of the dependent variable for that subject are
lost (Objectives 2 and 4).
Another potential problem stems from the “practice effect.” In
an experiment where a group is
measured multiple times, each time with an increasing amount
of the IV, early exposure may
change the way subjects respond later. Dependent-groups also
present the related problem of
carry-over effects. Exposure to a level of the independent
variable may alter the way the subject
responds later to a different level of that same variable;
exposure to a modest amount of positive
reinforcement may affect the way the same individual responds
to a substantial amount of posi-
tive reinforcement later, an effect that is not a problem for
studies involving independent groups.
Independent-groups and dependent-groups tests have important,
underlying consistencies.
Whether the test is independent t, before/after t, one-way
ANOVA, or a within-subjects F, in
each case the independent variable is nominal scale, and the
dependent variable is interval
or ratio scale (Objective 2). Furthermore, all of these test
significant differences. In the for-

mal language of statistics, they “test the hypothesis of
difference.” Sometimes, however, the
test questions the strength of the association rather than the
difference. That discussion will
introduce correlation, which is the focus of Chapter 8.
tan82773_07_ch07_191-226.indd 220 3/3/16 12:26 PM
before/after t test A dependent-groups
application of the t test in which one group
is measured before and after a treatment.
confounding variables Variables that
influence an outcome but are uncontrolled
in the analysis and obscure the effects of
other variables. If a psychologist is inter-
ested in gender-related differences in
problem-solving ability but does not control
for age differences, differences in gender
may be confounded by differences that are
actually age-related.
dependent-groups designs Statistical
procedures in which the groups are related,
either because multiple measures are taken
of the same participants, or because each
participant in a particular group is matched
on characteristics relevant to the analysis to
a participant in the other groups with the

same characteristics. Dependent-groups
designs minimize error variance because
they reduce score variation due to factors
unrelated to the independent variable.
matched-pairs t test A dependent-groups
application of the t test in which each par-
ticipant in the second group is paired to a
participant in the first group with the same
characteristics, so as to limit the error vari-
ance that would otherwise stem from using
dissimilar groups.
within-subjects F The dependent-groups
equivalent of the one-way ANOVA. In this
procedure, either participants in each group
are paired on the relevant characteristics
with participants in the other groups, or one
group is measured repeatedly after differ-
ent levels of the independent variable are
introduced.
Key Terms
Review Questions
Answers to the odd-numbered questions are provided in
Appendix A.
1. A group of clients is being treated for a compulsive behavior
disorder. The number of
times in an hour that each one manifests the compulsivity is
gauged before and after
a mild sedative is administered. The data are as follows:
Client Before After

1 5 4
2 6 4
3 4 3
4 9 5
5 5 6
6 7 3
7 4 2
8 5 5
a. What is the standard deviation of the difference scores?
tan82773_07_ch07_191-226.indd 221 3/3/16 12:26 PM
b. What is the standard error of the mean for the difference
scores?
c. What is the calculated value of t?
d. Are the differences statistically significant?
2. A researcher is examining the impact that a political ad has
on potential donors’
willingness to contribute. The data indicate the amount (in

dollars) each is willing to
donate before viewing that advertisement and after viewing the
advertisement.
Potential donor Before After
1 0 10
2 20 20
3 10 0
4 25 50
5 0 0
6 50 75
7 10 20
8 0 20
9 50 60
10 25 35
a. Do the amounts represent significant differences?
b. What is the value of t if this study is an independent t test?
c. Explain the difference between before/after and independent t
tests.
3. Participants attend three consecutive sessions in a business
seminar. The first has
no reinforcement when participants respond to the session
moderator’s questions.
In the second, those who respond are provided with verbal

reinforcers. In the third
session, responders receive pieces of candy as reinforcers. The
dependent variable is
the number of times the participants respond in each session.
Participant None Verbal Token
1 2 4 5
2 3 5 6
3 3 4 7
4 4 6 7
5 6 6 8
6 2 4 5
7 1 3 4
8 2 5 7
tan82773_07_ch07_191-226.indd 222 3/3/16 12:26 PM
a. Are the column-to-column differences significant? If so,
which groups are signifi-
cantly different from which?

b. Of what data scale is the dependent variable?
c. Calculate and explain the effect size.
4. In the calculations for Question 3, what step is taken to
minimize error variance?
a. What is the source of that error variance?
b. If Question 3 had been a one-way ANOVA, what would have
been the degrees of
freedom for the error term?
c. How does the change in degrees of freedom for the error term
in the within-
subjects F affect the value of the test statistic?
5. Because SScol in the within-subjects F contains the treatment
effect and measure-
ment error, if there is no treatment effect, what will be the value
of F?
6. Why is matching uncommon in within-subjects F analyses?
7. A group of nursing students is approaching the licensing test.
Their level of anxiety
is measured at 8 weeks prior to the test, then 4 weeks, 2 weeks,
and 1 week before
the test. Assuming that anxiety is measured on an interval scale,
are there significant
differences?
Student 8 weeks 4 weeks 2 weeks 1 week
1 5 8 9 9
2 4 7 8 10

3 4 4 4 5
4 2 3 5 5
5 4 6 6 8
6 3 5 7 9
7 4 5 5 4
8 2 3 6 7
a. Is anxiety related to the time interval?
b. Which groups are significantly different from which?
c. How much of anxiety is a function of test proximity?
tan82773_07_ch07_191-226.indd 223 3/3/16 12:26 PM
8. A psychology department sponsors a study of the relationship
between participation
in a particular internship opportunity and students’ final grades.
Eight students in
their second year of graduate study are matched to eight
students in the same year
by grade. Those in the first group participate in the internship.
The study compares
students’ grades after the second year.

Student Internship No Internship
1 3.6 3.2
2 2.8 3.0
3 3.3 3.0
4 3.8 3.2
5 3.2 2.9
6 3.3 3.1
7 2.9 2.9
8 3.1 3.4
a. Are the differences statistically significant?
b. The study should be completed as a dependent-samples t test.
Since two separate
groups are involved, why?
9. A team of researchers associated with an accrediting body
studies the amount of
time professors devote to their scholarship before and after they
receive tenure.
Scores represent hours per week.
Professor Before tenure After tenure
1 12 5
2 10 3

3 5 6
4 8 5
5 6 5
6 12 10
7 9 8
8 7 7
a. Are the differences statistically significant?
b. What is t if the groups had been independent?
c. What is the primary reason for the difference in the two t
values?
tan82773_07_ch07_191-226.indd 224 3/3/16 12:26 PM
10. A supervisor is monitoring the number of sick days
employees take by month.
For 7 people, these numbers are as follows:
Employee Oct Nov Dec
1 2 4 3
2 0 0 0

3 1 5 4
4 2 5 3
5 2 7 7
6 1 3 4
7 2 3 2
a. Are the month-to-month differences significant?
b. What is the scale of the independent variable in this analysis?
c. How much of the variance does the month explain?
11. If the people in each month of the Question 10 data were
different, the study would
have been a one-way ANOVA.
a. Would the result have been significant?
b. Because total variance (SStot) is the same in either 10 or 11,
and the SScol (10) is
the same as SSbet (11), why are the F values different?
Answers to Try It! Questions
1. Small samples tend to be platykurtic because the data in
small samples are often
highly variable, which translates into relatively large standard
deviations and large
error terms.
2. If groups are created by random sampling, they will differ
from the population from
which they were drawn only by chance. That means that error
can occur with ran-

dom sampling, but its potential to affect research results
diminishes as the sample
size grows.
3. The before/after t and the matched-pairs t differ only in that
the before/after test
uses the same group twice, while the matched-pairs test matches
each subject in the
first group with one in the second group who has similar
characteristics. The calcu-
lation and interpretation of the t value are the same in both
procedures.
4. The within-subjects test will detect a significant difference
more readily than
an independent t test. Power in statistical testing is the
likelihood of detecting
significance.
tan82773_07_ch07_191-226.indd 225 3/3/16 12:26 PM
5. Because the same subjects are involved in each set of
measures, the within-subjects
test allows us to calculate the amount of score variability due to
individual differ-
ences in the group and eliminate it because it is the same for
each group. This source
of error variance is eliminated from the analysis, leaving a
smaller error term.

6. The eta squared value would be the same in either problem.
Note that in a one-way
ANOVA, eta squared is the ratio of SSbet to SStot. In the
within-subjects F, it is SScol to
SStot. Because SSbet and SScol both measure the same
variance, and the SStot values
will be the same in either case, the eta squared values will
likewise be the same.
What changes is the error term. Ordinarily, SSresid will be
much smaller than SSwith,
but those values show up in the F ratio by virtue of their
respective MS values, not in
eta squared.
tan82773_07_ch07_191-226.indd 226 3/3/16 12:26 PM
Digital Economy creates a new relationship between Business,
the State and the Consumers.
Assignment 3
Title:

Student Number & Name:
19722115 Mohammad Taifur Rahman
Unit Name:
The Digital Economy
Email Address:
[email protected]
Date Submitted:
21 February 2019
Word Count:
2330
URL (if applicable):
I declare that I have retained a copy of this assignment. I have
read and understood Curtin University policies on Plagiarism
and Copyright and declare that this assignment complies with
these policies. I declare that this assignment is my own work
and has not been submitted previously in any form for
assessment.
______________MOHAMMAD TAIFUR
21/02/2019_____________
(Date/Signature)
(Typing your name in the space provided is sufficient when
submitting online via FLECS-Blackboard.)

2
the State and the Consumer
19722115 Mohammad Taifur Rahman
Table of Contents
Introduction 3
Analysis 3
The relationship between the state, business and consumers as
influenced by digital economy 3
Influence of digital economy to business, State and Consumers
5
Digital buying and selling 6
Conclusion 7
References 8
Introduction
Digital economy can be defined as an economy based on
the digital computing technologies, which is sometimes
perceived as the conducting of the business through the market
based on the internet. The business is also an organization
where people work together towards achieving certain economic
goal. A business can generate a profit or a loss. In a business,
people buy and sell products and services. Consumers are the
people who use economic services or activities.
When looking at the way the world is rapidly changing due to
introduction of technology, it is clear to say that this digital
period has transformed everything more especially the product
and the market nature and how they operate through production,
delivery and payment of the capital scale in order to operate

around the world and the requirements of human capital. The
period has also boosted productivity, technologies, exposure of
the companies to the new ideas, business models and improved
management and creation of the access of the new market
channels. It is possible therefore to predict that, in the near
future, the firms will adopt the digital ways of doing things by
increasingly relying on artificial intelligence when handling
basic routines and the more sophisticated tasks. For the current
digital technology to affect economic development there must
be appropriate policies to be put in place so as to remove the
possible obstacles that prevents the emergence of the economy
from engaging fully in the digital economy and benefit
optimisation, while risk minimisation not left behind.
The article will examine the relationship between the business,
the state and consumers that is created by digital economy. It
will also discuss the relationship between the digital economy
and the economic development and try to explore the challenges
that arise from the emerging economies. The article will explore
the benefits of digital world to business, state and consumer
relations. It is through exploring of the benefits that will enable
us to understand the relationship that has been created by digital
economy to the current global business.Analysis
The relationship between the state, business and consumers as
influenced by digital economy
The digital economy has brought a new perception and total
transformation of the ways the businesses are located when
compared with the past. In the old economy for instance, the
business location mattered a lot. The companies were located
near transportation and raw materials and the needed labour so
as to meet the consumer’s demands and also make a lot of
profit. The places which were viewed to be expensive in terms
of location of the new business were considered to be unfit.
Nowadays due to digital economy, such believes are foregone
tales. Digital economy is concerned with how the firms interact
and consumers obtain the required services, how information is

passed and how goods are being delivered. The new digital
economy has taken a great role on taking the shape on how the
business should be structured. The violent use of data has
contributed to transformation of business models, facilitation of
new products and services and also has helped in accompanying
in the new management culture.
The digital economy has also contributed to the changing of the
paradigm regarding on how the business should be structured as
well as the required resources to help increases business
productivity. It has also changed the importance of the
partnerships and structure and also industry collaboration both
within and across the country. The marketing and goods and
service distributions are made to meet consumer demands and
also digital economy. The notable transformation recently is
the news site from digital economy, the largest company of the
world; 'Uber' has no vehicles to help it carry out its services.
The popular Facebook owner creates no content to the business.
Also, Alibaba, the most known retailer, has no inventories and
finally Airbnb, the largest provider of accommodation in the
world, has no real estate.
All economic sectors have adopted the enhancement of ICT
productivity, reduction of operation costs and also enlargement
of the market reach across the economy. The ICT adoption is
revealed through the spread of the business broadband
connectivity, which almost every country is universal for the
large enterprises or the smaller businesses. The wide spread of
ICT adoption, and the faster decline and increased on the
technology performances, has led to the development of new
activities in both private and public sector. The technologies
have also enabled new products and services development,
together with the developed market reach and the costs of goods
have been lowered. Through these technologies, the production
and delivery of products and services have changed as well as
the business models that are used in the companies that range
from multinational enterprises to the start-ups. ICT activities
also support individuals and the consumers and they are led to

the formation of new payment mechanisms which is consisted of
the new forms of digital currencies. The introduction of the
internet brought many changes to entertainment, advertisements,
news and in the retail industries. In the retail industries, the
common digital players started initially form the traditional
business models which were later adopted and were made the
end-user equipment and increased extensive internet
connections.
For instance, online retailers first adapted the model of business
by selling traditional physical goods like the books digitally.
Furthermore, many online intermediaries whom were
responsible in managing specific sales began to evolve and
developed the capability of creating digital online services. This
included the auctioning of vehicles and properties which paved
a way for other inspiring traders, hence, kick starting the
beginning of a new generation of traditional online services
such as insurance brokers and many more (Schmid, 2011). The
retailers later adapted the selling of the digital products and
services online like the movies, downloadable music and games
among others. Online advertisement was later developed
through advertising business models, which increased the
potential digital technology in the industries. The new online
services that enables sharing and providing economic services
have developed allowing people rent out their vehicles, homes
and skills to their third parties.
The advancement of ICT has led to fall of prices which have
proven to be the general-purpose technology is the central if the
business models of the companies operating around the
economy. The business across the sectors are now in a position
to design and built operating models which revolves around
technological capacity so as to improve flexibility and be able
to reach out their global markets. The businesses have changed
across all the sectors in the manner in which they are conducted
by taking advantage of communication and data processing
ability advancements to lower costs of production and
transactions and extension of their market reach. The

advancements together with trade policy liberalisations and
reduction in the costs of transport, have expanded the business
ability in all economic sectors to take the value of chains
advantage in which geographical disbursed areas top enjoy the
advantage of their services globally.
Influence of digital economy to business, State and Consumers
Digital economy despite playing a great role in changes of
business models and cultures, it has also developed a diverse
logistical education and also keeps changing it due to
widespread of ICT. Looking at the retails, the digital economy
has enabled the retailers to be able to place orders online which
makes it easier for the retailers to gather and analysis customer
data and also provision of personal set services and
advertisements. Digital economy has also enabled the retailers
to be in a position of managing logistics and supply stores with
the products which has brought a positive impact to retail
productivity and profits.
On the same note, transport logistics sector has also been
transformed by digital economy. This is by enabling the
tracking of cargo and the vehicles across the world, providing
customers with information and facilitation of development of
the new processes of operation like timely delivery of goods in
the manufacturing sector. Keeping records of the vehicles helps
in maximising efficiency of fuels and also ensuring efficient use
of maintenance activities of the support fleet and transport
networks as a whole. The information that has been collected by
the fleets may be useful in creating the commercial value
datasets.
Digital economy has played a great role in financial services.
Under this, the insurance providers, banks and companies of
different types, where non-traditional providers are included,
has enabled the customers increasingly to be able to manage
their contact transactions, finance and new line of products. The
digital economy has made it easier for the companies and the
country to be able to track indices and investment portfolio

management and specialist expenditure in high trading
frequency.
The digital economy has also influenced agriculture and
manufacturing by enhancing design and development. It is
through digital technology that it has enabled the ability of
monitoring the process of production in the factories and the
control robots which has contributed to the greater design
precision and development together with refinement of the
ongoing products. The products that are produced has a high
knowledge intensive (Valenduc, & Vendramin, 2016). In the
automobile industry for instance, it is estimated that the new car
features as an important software component. On the farms, the
produced systems can be used to monitor animals and crops, and
soil quality. Precisely, agricultural processes and routine
equipment’s can be controlled through the automated systems.
Digital economy not only has influence on business, it also has
a great influence in education. This is because, the spread of
digital economy is accompanied with the increase of the tutor
services, universities implementing online learning and many
other education services, which helps the state to have informed
and educated citizens. This online education services offered
are able to provide remote courses without the need of face to
face interaction through the influence of technology like online
collaboration portals and video conferencing which has enabled
the universities to trap into leverage demands and global brands
in the way which previously seemed to be difficult. This enables
the State to address the tax challenges on the digital economy
and also business modelling around the States.
Digital buying and selling
While worldwide trade in the goods and flow of finance seem to
be in the peak in terms of the share they hold in GDP, the flow
of data is exponentially growing. According to (Araya & Peters
2016), they clearly state that, between 2005 and 2014 global
data flow grew from 45 and it is predicted to grow further by
nine in the next five years. On the same note, the flow of data

added $3.2 trillion directly to global GDP and $2.8 trillion were
added indirectly. Expanding of the connectivity, network
effects, and sensor costs. infrastructure, open software
architectures and introduction of the digital markets have
accelerated the adoption and technological use as a whole. It
therefore seems reasonable to assume that, the effect of
adopting the new digital technology on the competitive flows
when the firms in an industry are given access to the new
technology, the competitiveness rapidly increases as illustrated
in the figure below.
Fig 1: Relationship between online buying and selling and
competitiveness
Conclusion
The gains of the digital economy to the country cannot be
underrated for in the emerging countries, the benefits are
gradually large. This is because, it provides a significant
competitiveness and productivity. This is done by boosting the
related opportunities to access to the digital products and
services that help in optimization of the production processes
and reduction of production costs and the supply chains. The
digital economy on the same note has declined the costs of
information and communication technology that encourages
developments of investments and providing the firm with
competitive prices. All this is meant to enable the firms to
participate the value of chains globally and enhancement of the
direct access to customers in the foreign markets for the
advanced economies.
The benefits to the consumers are that, the consumers have
access to wider range of goods and services at low prices. The
digital economy also offers the consumers with the new
opportunities for job creation and entrepreneur developments.
The government also benefits from the digital economy in that,
the country has access to technologies that enables it to deliver
more and better public services, evaluating the policies and
overall delivery of the better results.
References

Araya, D., & Peters, M. A. (Eds.). (2016). Education in the
creative economy: Knowledge and learning in the age of
innovation. Peter Lang.
Degen, M., Melhuish, C., & Rose, G. (2017). Producing place
atmospheres digitally: Architecture, digital visualisation
practices and the experience economy. Journal of Consumer
Culture, 17(1), 3-24.
Quah, D. (2003). Digital goods and the new economy.Schmid,
B. F. (2011). What is new about the digital
economy? Electronic Markets, 11(1), 44-51.
Valenduc, G., & Vendramin, P. (2016). Work in the digital
economy: sorting the old from the new (No. UCL-Université
Catholique de Louvain). Brussels: European Trade Union
Institute.
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The Digital Economy - Assignment 3
By Mohammad Taifur Rahman

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Yam San Chee. "Games-To-Teach or Games-To-Learn",
Springer Nature America, Inc, 2016
1% match (student papers from 05-Nov-2018)
1% match (student papers from 26-Oct-2017)
Submitted to University of Queensland on 2017-10-26
< 1% match (student papers from 05-Nov-2018)
< 1% match (student papers from 11-Dec-2018)
Submitted to Carnegie Mellon University on 2018-12-11
< 1% match (Internet from 15-May-2018)

http://shura.shu.ac.uk/19642/1/10694523.pdf
< 1% match (student papers from 03-Nov-2018)
< 1% match (publications)
Tai-Yoo Kim, Eungdo Kim, Jihyoun Park, Junseok Hwang.
"Chapter 5 The Faster-Accelerating Digital Economy", Springer
Nature America, Inc, 2014
Assignment 3 Title: Digital Economy creates a new relationship
between Business, the State and the Consumers. Student
Number& 19722115 Mohammad Taifur Rahman Name: Unit
Name: The Digital Economy Email
Address:[email protected].com Date Submitted: 21 February
2019 Word Count: 2330 URL (if applicable): I declare that I
have retained a copy of this assignment. I have read and
understood Curtin University policies on Plagiarism and
Copyright and declare that this assignment complies with these
policies. I declare that this assignment is my own work and has
not been submitted previously in any form for assessment.
______________MOHAMMAD TAIFUR 21
/02/2019_____________ (Date/Signature) (Typing your name in
the space provided is sufficient when submitting online via
FLECS-Blackboard.) Digital Economy creates a new
relationship between Business, the State and the Consumer
19722115 Mohammad Taifur Rahman Table of Contents
Introduction
...............................................................................................
............................................. 3 Analysis
...............................................................................................
.................................................... 3 The relationship between
the state, business and consumers as influenced by digital
economy. 3 Influence of digital economy to business, State and
Consumers ................................................... 5 Digital buying
and selling
...............................................................................................
................. 6 Conclusion
...............................................................................................

................................................ 7 References
...............................................................................................
............................................... 9 Introduction Digital economy
can be defined as an economy based on the digital computing
technologies, which is sometimes perceived as the conducting
of the business through the market based on the internet. The
business is also an organization where people work together
towards achieving certain economic goal. A business can
generate a profit or a loss. In a business, people buy and sell
products and services. Consumers are the people who use
economic services or activities. When looking at the way the
world is rapidly changing due to introduction of technology, it
is clear to say that this digital period has transformed
everything more especially the product and the market nature
and how they operate through production, delivery and payment
of the capital scale in order to operate around the world and the
requirements of human capital. The period has also boosted
productivity, technologies, exposure of the companies to the
new ideas, business models and improved management and
creation of the access of the new market channels. It is possible
therefore to predict that, in the near future, the firms will adopt
the digital ways of doing things by increasingly relying on
artificial intelligence when handling basic routines and the more
sophisticated tasks. For the current digital technology to affect
economic development there must be appropriate policies to be
put in place so as to remove the possible obstacles that prevents
the emergence of the economy from engaging fully in the digital
economy and benefit optimisation, while risk minimisation not
left behind. The article will examine the relationship between
the business, the state and consumers that is created by digital
economy. It will also discuss the relationship between the
digital economy and the economic development and try to
explore the challenges that arise from the emerging economies.
The article will explore the benefits of digital world to
business, state and consumer relations. It is through exploring
of the benefits that will enable us to understand the relationship

that has been created by digital economy to the current global
business. Analysis The relationship between the state, business
and consumers as influenced by digital economy The digital
economy has brought a new perception and total transformation
of the ways the businesses are located when compared with the
past. In the old economy for instance, the business location
mattered a lot. The companies were located near transportation
and raw materials and the needed labour so as to meet the
consumer’s demands and also make a lot of profit. The places
which were viewed to be expensive in terms of location of the
new business were considered to be unfit. Nowadays due to
digital economy, such believes are foregone tales. Digital
economy is concerned with how the firms interact and
consumers obtain the required services, how information is
passed and how goods are being delivered. The new digital
economy has taken a great role on taking the shape on how the
business should be structured. The violent use of data has
contributed to transformation of business models, facilitation of
new products and services and also has helped in accompanying
in the new management culture. The digital economy has also
contributed to the changing of the paradigm regarding on how
the business should be structured as well as the required
resources to help increases business productivity. It has also
changed the importance of the partnerships and structure and
also industry collaboration both within and across the country.
The marketing and goods and service distributions are made to
meet consumer demands and also digital economy. The notable
transformation recently is the news site from digital economy,
the largest company of the world; 'Uber' has no vehicles to help
it carry out its services. The popular Facebook owner creates no
content to the business. Also, Alibaba, the most known retailer,
has no inventories and finally Airbnb, the largest provider of
accommodation in the world, has no real estate. All economic
sectors have adopted the enhancement of ICT productivity,
reduction of operation costs and also enlargement of the market
reach across the economy. The ICT adoption is revealed through

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