Analysis of Variance (ANOVA)Chapters 11 - 13.docx

Analysis of Variance (ANOVA)
Chapters 11 - 13
ANOVA:
statistical analysis of experiments with more than 2 groups
requires a more complex technique
Most frequently used technique among social and behavioral
scientists
Based on assigning the variability of data to different sources

One-Way ANOVA:
Chapter 11
Used to find out if there are any differences among three or
more population means (Recall t-test measured two)
Null hypothesis is again that two or more population means in
an independent samples design are equal. That is,
Used when treatment levels are independent of each other
NHST with ANOVA:
Populations you are comparing (different treatment groups) may
be exactly the same OR one or more of them may have a
different mean. These are your null and alternative hypotheses
in that order.
At the beginning, we assume that the null hypothesis is true.
That is, we believe that the groups have the same mean and any
variation is due to chance.
Choose a sampling distribution that shows the probability of
various differences among sample means when the null
hypothesis is true. For more than 2 sample means, we use the F

distribution.
Obtain the data from your populations and do calculations until
you have an F value.
NHST with ANOVA:
Compare the F value to the critical value of F in the F
distribution Chart in back of book.
Come to a conclusion about null hypothesis. If your F value is
less than the number in the chart, you fail to reject the null
hypothesis which means that either the null or alternative
hypothesis could be true. If your F value is greater than or
equal to the value in the chart, we reject the null hypothesis and
can state that there is reason to believe there are measurable
differences in the means and further investigation may explain
these differences (i.e. the differences are not due to chance or
randomness)
Tell the story of what the data shows. Rejecting the null
hypothesis warrant further study and analysis or discussion.
Failing to reject the null hypothesis gives no strong conclusion,
but the data is not invalid.

The value F:
For ANOVA, we will be using a new statistic that is called the
F value that corresponds to the F-distribution and the chart in
the back of the book.
When the null hypothesis is true, this value is close to 1. When
it is false, we get a number greater than 1.
Add Data Analysis Pack to Excel
Calculate ANOVA using Excel

Repeated Measures ANOVA
Statistical technique for designs with repeated measures of
subjects or groups of matched subjects
Null hypothesis is same as before
CASE 31 :: JOHNSON & JOHNSON C233
On January 20, 2015, Johnson & Johnson CEO Alex
Gorsky proudly announced that his firm had sales of
$74.3 billion during the previous year, representing an
increase of 4.2 percent over 2013. Most of this growth
came from the firm’s pharmaceutical division, which
Gorsky pointed out was clearly generating the largest
revenues and was the fastest-growing such division in the
drug industry in the United States. The results of this divi-
sion compensated the relatively modest increases in reve-
nue from the firm’s medical devices and consumer health
divisions, both of which were recovering from lawsuits

and recalls.
Several years earlier, Johnson & Johnson (J&J) had
settled with an estimated 8,000 patients over problems
with its flawed all-metal artificial hip. The device had a
design flaw that caused it to shed large quantities of metal-
lic debris after implantation. It was finally recalled by the
firm in 2010, after Johnson & Johnson had covered up the
problems for almost five years after they began to surface.
The settlement cost the firm as much as $3 billion to com-
pensate patients who had to have the artificial hip replaced.
The problems with this device would classify it as one of
the largest medical failures in recent history.
The problems with the medical devices unit were com-
pounded by serious issues that arose with the consumer
products unit, leading it to recall many of its products—
including the biggest children’s drug recall of all time—that
were potentially contaminated with dark particles. The Food
and Drug Administration also slapped a plant at one of its
business units, McNeil Consumer Healthcare, with a scald-
ing inspection report, causing the company to close down
the factory to bring it up to federal standards. The publicity
that arose from these problems tarnished the name of one of
the nation’s most trusted firms.
Much of the blame for Johnson & Johnson’s stumbles fell
on William C. Weldon, who stepped down as CEO in April
2012 after presiding over one of the most tumultuous decades
in the firm’s history (see Exhibits 1 and 2). Critics said the
company’s once-vaunted attention to quality had slipped
under his watch. Weldon, who had started out as a sales repre-
sentative at the firm, was believed to have been obsessed with
meeting tough performance targets, even by cutting costs that
might affect quality. Erik Gordon, who teaches business at

the University of Michigan, elaborated on this philosophy:
“We will make our numbers for the analysts, period.”1
Weldon was replaced by Alex Gorsky, who had
headed the medical devices and diagnostics unit. Like
his predecessor, Gorsky had worked his way up by meet-
ing tough performance targets as a sales representative,
and his appointment as CEO continued the firm’s 126-
year tradition of hiring leaders from within. “The future
of Johnson & Johnson is in very capable hands,” said
Weldon.2 However, the decision to hire another insider
raised concerns that the firm was not very serious about
changing the corporate culture that had created so many
of its recent problems. “As somebody steeped in J.&J.
culture, I would be very surprised to see big changes,”
said Les Funtleyder, a portfolio manager at a firm that
owned J&J stock.3
CASES
CASE 31
JOHNSON & JOHNSON*
* Case prepared by Jamal Shamsie, Michigan State University,
with the
assistance of Professor Alan B. Eisner, Pace University.
Material has been
drawn from published sources to be used for purposes of class
discussion.
Copyright © 2015 Jamal Shamsie and Alan B. Eisner.
Year Ending December
2010 2011 2012 2013 2014
Revenue 61,587 65,030 67,224 71,312 74,331

Gross profit 42,795 44,670 45,566 48,970 51,585
Operating income 16,527 16,153 15,869 18,377 20,959
Income before taxes 16,947 12,361 13,775 15,471 20,563
Net income 13,334 9,672 10,853 13,831 16,323
Source: Johnson & Johnson.
EXHIBIT 1 Income Statement ($ millions)
des78212_case31_233-238.indd 233 7/9/15 2:40 PM
Final PDF to printer
C234 CASE 31 :: JOHNSON & JOHNSON
fostered an entrepreneurial attitude that kept J&J intensely
competitive as others around it faltered. The relative auton-
omy that was accorded to the business units also provided
the firm with the ability to respond swiftly to emerging
opportunities.
Johnson & Johnson was actually quite proud of the
considerable freedom that it gave to its different subsid-
iaries to develop and execute their own strategies. Besides
developing their strategies, these units were also allowed
to work with their own resources. Many of them even
had their own finance and human resources departments.
While this degree of decentralization had led to relatively
high overhead costs, none of the executives who ran J&J,
Weldon included, had ever thought that this was too high

a price to pay. “J&J is a huge company, but you didn’t feel
like you were in a big company,” recalled a scientist who
used to work there.4
Pushing for More Collaboration
The entrepreneurial culture that Johnson & Johnson devel-
oped over the years clearly allowed the firm to show a
consistent level of high performance. Indeed, Johnson &
Johnson had top-notch products in each of the areas in
which it operated. It had been spending heavily on research
and development for many years, taking its position among
the world’s top spenders (see Exhibit 4). In 2014, it spent
about 12 percent of its sales on about 9,000 scientists
working in research laboratories around the world. This
allowed each of the three divisions to continually introduce
promising new products.
In spite of the benefits that Johnson & Johnson derived
from giving its various enterprises considerable auton-
omy, there were growing concerns that these units could
no longer be allowed to operate in near isolation. Shortly
after Weldon had taken charge of the firm, he realized that
J&J was in a strong position to exploit new opportunities
by drawing on the diverse skills of its various subsidiar-
ies across the three divisions. In particular, he was aware
that his firm might be able to derive more benefits from
the combination of its knowledge in drugs, devices, and
Cultivating Entrepreneurship
Johnson & Johnson relied heavily upon acquisitions to enter
into and expand into a wide range of businesses that fell
broadly under the category of health care. It purchased more
than 70 different firms over the past decade. Among Johnson
& Johnson’s recent moves was the $20 billion purchase of
Synthes, a leading player in trauma surgery. In November
2014, J&J completed its $1.75 billion acquisition of Alios

BioPharma, which produced therapeutics for viral infections.
As it grew, Johnson & Johnson developed into an
astonishingly complex enterprise, made up of over 250
different subsidiaries that were divided among three dif-
ferent divisions. The most widely known of these was the
division that made consumer products such as Johnson &
Johnson baby care products, Band-Aid adhesive strips,
and Visine eyedrops. The division grew substantially after
J&J acquired the consumer health unit of Pfizer in 2006
for $16.6 billion, the biggest acquisition in its 120-year
history. The acquisition allowed J&J to add well-known
products to its lineup, such as Listerine mouthwash and
Benadryl cough syrup.
But Johnson & Johnson reaped far more sales and prof-
its from its other two divisions. Its pharmaceuticals divi-
sion sold several blockbuster drugs, such as anemia drug
Procrit and schizophrenia drug Risperdal. A new drug,
named Zytiga, prescribed to treat prostate cancer, was
selling well. The medical devices division was respon-
sible for best-selling products such as DePuy orthopedic
joint replacements and Cypher coronary stents. These two
divisions generated operating profit margins of around
30 percent, almost double those generated by the consumer
business.
To a large extent, however, Johnson & Johnson’s suc-
cess across its three divisions and many different busi-
nesses hinged on its unique structure and culture. Most
of its far-flung subsidiaries were acquired because of the
potential demonstrated by some promising new products
in their pipelines. Each of these units was therefore granted
near-total autonomy to develop and expand upon its
best-selling products (see Exhibit 3). That independence

Year Ending December
2010 2011 2012 2013 2014
Total current assets 47,307 54,316 46,116 56,407 59,311
Total assets 102,908 113,644 121,347 132,683 131,119
Total current liabilities 23,072 22,811 24,262 25,675 25,085
Total liabilities 46,329 56,564 56,521 58,630 61,367
Total stockholders’ equity 56,579 57,080 64,826 74,053 69,752
EXHIBIT 2 Balance Sheet ($ millions)
des78212_case31_233-238.indd 234 7/9/15 2:40 PM
would get business units to work together on promising
new opportunities. “It’s a recognition that there’s a way to
treat disease that’s not in silos,” Weldon stated, referring to
the need for collaboration between J&J’s largely indepen-
dent businesses.6
For the most part, however, Weldon confined himself
to taking steps to foster better communication and more
frequent collaboration among Johnson & Johnson’s dis-
parate operations. He was convinced that such a push for

communication and coordination would allow the firm to
diagnostics, since few companies were able to match its
reach and strength in these basic areas.
This led Weldon to find ways to make J&J’s fiercely
independent units work together. In his own words: “There
is a convergence that will allow us to do things we haven’t
done before.”5 Through pushing the various far-flung units
of the firm to pool their resources, Weldon believed that
the firm could become one of the few that was actually
able to attain that often-promised, rarely delivered idea of
synergy. To pursue this, he created a corporate office that
Johnson & Johnson was made up of over 250 different
companies, many of which it had acquired over the years.
These individual companies were assigned to three different
divisions.
Segments of Business and Geographic Areas
Sales to Customers
Dollars in Millions 2014 2013 2012
Consumer —
United States $ 5,096 5,162 5,046
International 9,400 9,535 9,401
Total 14,496 14,697 14,447
Pharmaceutical —
United States 17,432 13,948 12,421

International 14,881 14,177 12,930
Total 32,313 28,125 25,351
Medical Devices —
United States 12,254 12,800 12,363
International 15,268 15,690 15,063
Total 27,522 28,490 27,426
Worldwide total $74,331 71,312 67,224
Segment Pretax Profit
Percent of Segment Sales
(Dollars in Millions) 2014 2013 2014 2013
Consumer $ 1,941 1,973 13.4% 13.4
Pharmaceutical 11,696 9,178 36.2 32.6
Medical Devices 7,953 5,261 28.9 18.5
Total 21,590 16,412 29.0 23.0
Less: Expenses not allocated to segments 1,027 941
Earnings before provision for taxes on income $20,563 15,471
27.7% 21.7

EXHIBIT 3 Segment Information ($ millions)
des78212_case31_233-238.indd 235 7/9/15 2:40 PM
Year Expenditure
2014 $8,494
2013 8,183
2012 7,665
2011 7,548
2010 6,864
2009 6,986
2008 7,577
2007 7,680
2006 7,125
2005 6,462
EXHIBIT 4 Research Expenditures ($ millions)

Antiseptic Surgery (1888)
Three brothers start up a firm based on antiseptics designed for
modern surgical practices.
Band-Aids (1921)
Debuts the first commercial bandages that can be applied at
home without oversight by a professional.
No More Tears (1954)
Introduces a soap-free shampoo that was gentle enough to clean
babies’ hair without irritating their eyes.
Acuvue Contact Lenses (1987)
Offers the first-ever disposable lenses that can be worn for up to
a
week and then thrown away.
Sirturo (2012)
Gets approval to launch a much-needed treatment for drug-
resistant tuberculosis, the first new medication to fight this
disease in more than 40 years.
Source: Fast Company, March 2014.
EXHIBIT 5 Significant Innovations
develop the synergy that he was seeking. But Weldon was
also aware that any effort to get the different business units
to collaborate must not quash the entrepreneurial spirit that
had spearheaded most of the growth of the firm to date.
Jerry Cacciotti, managing director of consulting firm Stra-
tegic Decisions Group, emphasized that cultivating those
alliances “would be challenging in any organization, but
particularly in an organization that has been so successful
because of its decentralized culture.”7

These collaborative efforts did lead to the introduction
of some highly successful products (see Exhibit 5). Even
the company’s fabled consumer brands started to show
growth as a result of increased collaboration between the
consumer products and pharmaceutical divisions. The
firm’s new liquid Band-Aid was based on a material used
in a wound-closing product sold by one of J&J’s hospital-
supply businesses. And J&J used its prescription antifun-
gal treatment, Nizoral, to develop a dandruff shampoo. In
fact, products that were developed in large part out of such
cross-fertilization allowed the firm’s consumer business to
experience considerable internal growth.
Confronting Quality Issues
Even as Johnson & Johnson was trying to get more
involved with the efforts of its business units, it ran into
quality control problems with several over-the-counter
drugs made by McNeil Consumer Healthcare. Since
2008, FDA inspectors had found significant violations of
manufacturing standards at two McNeil plants, leading
to the temporary closure of one of them. These problems
had forced the firm to make several recalls of some of its
best-selling products. Weldon did admit that problems
had surfaced, but he insisted that they were confined to
McNeil. He responded to them in an interview: “This is
one of the most difficult situations I’ve ever had to per-
sonally deal with. It hits at the core of who J&J is. Our
first responsibility is to the people who use our products.
We’ve let them down.”8
Quality problems had arisen before, but they were usu-
ally fixed on a regular basis. Analysts suggested that the
problems at McNeil might have exacerbated in 2006 when
J&J decided to combine McNeil with the newly acquired
consumer health care unit from Pfizer. Johnson & Johnson

believed that it could achieve $500 million to $600 million
in annual savings by merging the two units. After the
merger, McNeil was transferred from the heavily regulated
pharmaceutical division to the marketing-driven consumer
products division, headed by Colleen Goggins. Because
the consumer executives lacked pharmaceutical experi-
ence, they began to demand several changes at McNeil that
led to a reduced emphasis on quality control.
Weldon realized the significance of the threat faced by
Johnson & Johnson as a result of its problems with quality.
He was especially concerned about the FDA’s allegation
that the firm had initially tried to hide the problems that it
found with Motrin in 2009, hiring a contractor to quietly go
from store to store buying all of the packets on the shelves.
McNeil’s conduct surrounding the recalls led to an inquiry
by both the House Committee on Oversight and Investiga-
tions and the FDA’s Office of Criminal Investigations.
Various changes were subsequently made at McNeil
to resolve these quality issues. Goggins was pushed out
of her post as senior executive in charge of all consumer
businesses. Weldon allocated more than $100 million to
upgrade McNeil’s plants and equipment, appoint new
manufacturing executives, and hire a third-party consulting
firm to improve procedures and systems. Bonnie Jacobs, a
McNeil spokeswoman, wrote in a recent email: “We will
des78212_case31_233-238.indd 236 7/9/15 2:40 PM

invest the necessary resources and make whatever changes
are needed to do so, and we will take the time to do it
right.”9
The problems at McNeil, coupled with growing prob-
lems with J&J’s artificial hips and contact lenses, also
led Johnson & Johnson to make changes to its corporate
oversight of its supply chain and manufacturing. In August
2010, the firm appointed Ajit Shetty, a longtime execu-
tive, to oversee a new system of companywide quality
control that involved a single framework for quality across
all of the operating units and a new reporting system. The
need for these changes was highlighted by Erik Gordon,
a professor at the Ross School of Business at the Univer-
sity of Michigan: “Nothing is more valuable to Johnson &
Johnson than the brand bond of trust with consumers.”10
Passing the Baton
In April 2012, Johnson & Johnson appointed Gorsky to
lead the health care conglomerate out of the difficulties
that it had faced over the previous few years. He had been
with the firm since 1988, holding positions in its pharma-
ceutical businesses across Europe, Africa, and the Middle
East before leaving for a few years to work in Novartis.
Shortly after his return to Johnson & Johnson in 2008, he
took over its medical device and diagnostic group. Because
of his extensive background with the firm, and with the
division that was being investigated about its faulty hip
replacements, Gorsky might have been regarded as the
ideal person to take over the job.
When he took over, DePuy, the firm’s orthopedic unit,
was already running into trouble with its newest artifi-
cial hip. The firm finally recalled the artificial hip, amid
growing concerns about its failure among those who had
received the implant. Until then, however, executives from

the firm had repeatedly insisted that the device was safe.
Andrew Ekdahl, the current president of DePuy, recently
reiterated that position. “This was purely a business deci-
sion,” he said.11 In the trial in Los Angeles Superior Court
regarding the defective hip replacement, however, Michael
A. Kelly, the lawyer making the case against Johnson &
Johnson, suggested that company executives might have
concealed information out of concern for firm profits.
In spite of all these issues, Johnson & Johnson did not
attempt to clarify what information Gorsky might have had
about the problems associated with the artificial hip. Under
the circumstances, his promotion to lead the firm surprised
Dr. Robert Hauser, a cardiologist and an advocate for
improved safety of medical devices. “He’s been oversee-
ing one of the major J&J quality issues and the board of
J&J sees fit to name him the new C.E.O.,” he questioned.12
These issues raised concerns about the ability of the firm
to effectively deal with the quality concerns and to take
steps to prevent them from recurring in the future.
Gorksy’s first job as Johnson & Johnson’s chief execu-
tive was, in fact, to reassure shareholders that the firm would
move quickly to overcome its problems with manufacturing
defects, product recalls, and lawsuits. “We’ve got to adapt
faster than ever before, be more agile than ever before,” he
stated at the firm’s annual meeting after taking over.13 He
acknowledged that some of the problems could partly be
attributed to the firm’s attempt to continue to meet Wall
Street’s increasingly short-term demands. Gorsky announced
that moving forward, J&J was committed to managing for
the long term, actively soliciting feedback from all quarters
and adhering to the mission that made customers the first
priority.

Gorsky’s biggest challenge, however, came from a pro-
posal that Johnson & Johnson might be better off if it was
broken into smaller companies, perhaps along the lines
of its different divisions. There were growing concerns
about the ability of the conglomerate to provide sufficient
supervision to all of its worldwide subsidiaries. Gorsky
dismissed the proposal, claiming that J&J drew substantial
benefits from the diversified nature of its businesses. He
did concede, however, that the firm would have to be more
selective, careful, and decisive about the products that it
would pursue.
Is There a Cure Ahead?
Under Gorksy, Johnson & Johnson began to divest some
of its lower-growth businesses and reduce annual costs
by $1 billion. In 2014, the firm sold off its blood-testing
unit, called Ortho-Clinical Diagnostics, for $4.15 billion
to the private equity firm Carlyle Group. It was actively
seeking a buyer for Cordis, which made medical devices
such as stents and catheters. Johnson & Johnson, which
had helped to develop the roughly $5 billion global market
for cardiac stents, announced that it was shifting its focus
to other medical technologies that showed more potential
for growth.
To repair the damage to its reputation from the many
recalls across two of its divisions, Johnson & Johnson
recently announced that it would remove a host of poten-
tially harmful chemicals, like formaldehyde, from its line
of consumer products by the end of 2015. It was the first
major consumer products company to make such a wide-
spread commitment. “We’ve never really seen a major
personal care product company take the kind of move that
they are taking with this,” said Kenneth A. Cook, president
of the Environmental Working Group.14

As he tried to plot a course for the future of Johnson &
Johnson, Gorsky realized that he had to deal with a variety
of issues. He was aware that much of the firm’s success
to date resulted from the relative autonomy that it granted
to each of its businesses. At the same time, he realized
that he had to provide more direction for the businesses
to collaborate with each other in order to pursue emerg-
ing opportunities. He also understood that it was critical
for J&J to develop sufficient controls that could minimize
future problems with quality control.
In overall terms, it was clear that the health care
giant had to rethink the process by which it managed its
des78212_case31_233-238.indd 237 7/9/15 2:40 PM
diversified portfolio of companies in order to ensure that it
could keep growing without creating issues that could pose
further threats to its reputation. “This is a company that was
purer than Caesar’s wife, this was the gold standard, and all
of a sudden it just seems like things are breaking down,”
said William Trombetta, a professor of pharmaceutical
marketing at Saint Joseph’s University in Philadephia.15
ENDNOTES
1. Katie Thomas. J.&J.’s next chief is steeped in sales culture.
New York
Times, February 24, 2012, p. B6.
2. Katie Thomas & Reed Abelson. J.&J. chief to resign one

role. New
York Times, February 22, 2012, p. B8.
3. Thomas, op.cit., p. B1.
4. Peter Loftus & Shirley S. Wang. J&J sales show health care
feels the
pinch. Wall Street Journal, January 21, 2009, p. B1.
5. Avery Johnson. J&J’s consumer play paces growth. Wall
Street
Journal, January 24, 2007, p. A3.
6. Holly Hubbard Preston. Drug giant provides a model of
consistency.
Herald Tribune, March 12–13, 2005, p. 12.
7. Amy Barrett. Staying on top. Business Week, May 5, 2003,
p. 62.
8. Ibid.
9. Natasha Singer & Reed Abelson. Can Johnson & Johnson
get its act
together? New York Times, January 16, 2011, p. B4.
10. Ibid., p. B4.
11. Thomas & Abelson, op. cit.
12. Michael L. Diamond. J&J’s CEO calls for fast action.
Ashbury Park
Press, April 27, 2012, p. 13.
13. Thomas, op. cit.
14. Katie Thomas. Johnson & Johnson to remove questionable
chemicals
in products. New York Times, August 16, 2012, p. B1.
15. Natasha Singer. Hip implants are recalled by J&J unit. New

York
Times, August 27, 2010, p. B1.
des78212_case31_233-238.indd 238 7/9/15 2:40 PM
Nonparametric Tests
Chapter 15
Errors
TYPE I
-rejecting a true null hypothesis
TYPE II
-failing to reject a false hypothesis

Chi-Square is an important nonparametric test to be able to
perform
Chapter 15 has more information than you may use in your
program
You should read through Chapter 15 for exposure, but
concentrate on Spearman’s Correlation of Ranked Data
Understand that we are covering information in a nontraditional
order to highlight the purpose of the information and its
importance to you
If you are completely lost and words are being used that you
never heard, a short read may help
Sampling & Distribution of Samples – read over Chapter 8
Standard deviation – Chapter 4
Normally Distributed – Chapter 7 talks about distributions
Where are we??
Spearman’s rs
A descriptive “statistic”

Mathematical expression of degree to which two sets of ranked
data are related
Referred to as a correlation coefficient but is specifically for
two sets of ranked data
Most often used when the number of pairs is less than 20
Special case of the correlation coefficient we will work with in
Chapter 6
Calculating Spearman’s rs
D is the difference in ranks of a pair of scores
N is the number of pairs of scores
means find the sum

Example
In the Gunther High School athletic department, does a person’s
track performance give any indication to their academic
performance?NameTrack RankingClass StandingClass
RankJoe1473Amy2805Nick3764Susan482Andrea531Jacob6856
Example
RankDifferenceJoe1233Amy2805Nick3764Susan482Andrea531J
acob6856

Example
RankDifferenceJoe1233-
2Amy2805Nick3764Susan482Andrea531Jacob6856
Example
RankDifferenceJoe1233-2Amy2805-
3Nick3764Susan482Andrea531Jacob6856
Example

RankDifferenceJoe1233-2Amy2805-3Nick3764-
1Susan482Andrea531Jacob6856
Example
Example

Example
Example

ExampleNameTrack RankingClass StandingClass
ExampleNameTrack RankingClass StandingClass

Example
Using Table L in Appendix C, we look to the row for 6
subject:Number of PairsTwo-Tailed .01Two-Tailed
0.0561.000.886
We first ranked track performance, so a positive indicates that
track performance could indicate a better academic
performance…HOWEVER,
After looking at the table, our statistic is not greater than or
equal to either value, so our assumed correlation is not
reasonable.
At this point, you would do one of the following:
Gather more data
Change your hypothesis (or test)

Move on to other problems
Next Steps:
Read Chapter 15 if you have not already
Read places you need to refresh in memory
Correlation & Regression
Chapter 6

Correlation
Two sets of data have a correlation if they seem to depend on
one another or if they share the same highs and lows
The correlation factor is a number between -1 and 1
The closer the correlation factor is to 1, the more correlated
Correlation Example:
Do the following sets of numbers seem to be correlated?
3 4 5 7
9 7 1 13

-we can use Excel Again
Can crickets determine the temperature?
Regression:
A technique to use correlated data to predict the second variable
when provided the first variable.
Regression Line:

What temperature is it if we detect the cricket chirps 14 times
per second?
= 80.04 – (3.291 * 16.65) = 25.23
1. Last year, on one quarterly proficiency exam 15% of the
students scored above average, 60% scored average, and 25%
scored needs improvement. The results from the first quarter
test are below. Does this exam fit the same model?
Above Average
161
Average
700

Needs Improvement
139
TOTAL
1000
1. The Rathus Assertiveness Schedule is a 30-item
questionnaire. It was given to ten teachers that received the
following scores:
16
35
0
50
18
-10
48
27
20
4
Suppose that the school offered personal development and a
conducted a six-week course in assertiveness. At the end of the
course, the following scores were obtained from the 10 who
completed the course. Write a conclusion about the
assertiveness course.
20
36
0
44
16
-6
50
28

24
8
1. In an elementary school, it was claimed that Mrs. Smith’s
students did substantially better than the rest of the school on a
particular exam. The school had an average exam score of
79.23 while Mrs. Smith’s 23 students had an average score of
82.6 with a sample standard deviation of 3. Was the higher
average due to chance?
1. The same exam was given to all the students in the sixth
grade, but they were divided into 4 classrooms. Each classroom
had a different distraction taking place except for Room 1 that
was the control group and free of noise. Using the scores
ranging from 0 to 60 of the students below, state a conclusion
about the nature of testing practices used.
Control
60 degrees
Classical Music
Next to Cafeteria
31
53
27
29
16
39
36
18
11
41
32

16
19
39
14
20
43
54
40
7
49
41
60
12
4
9
47
20
11
17
2
45
34
13
27
33
39
8
5
53
60
32
55
23
40
29
53

24
57
35
27
18
59
45
4
49
43
42
50
29
Grade
Classes Missed
75
2
90
4
45
8
47
4
90
1
100
0
93
1
85
0
77
5
94

6
42
6
40
7
73
4
64
5
1. School leadership teams would like to know if there is any
correlation between an athlete’s grade and the number of days
missed for events. Use the chart below to give your conclusion.

Analysis of Variance (ANOVA)Chapters 11 - 13.docx

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Analysis of Variance (ANOVA)Chapters 11 - 13.docx