Bennett - Homework 5
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This case study is based on an investigation by Philip Landrigan, EIS ‘70. The investigation
is described in:
Landrigan PJ. Epidemic measles in a divided city. JAMA 1972; 221: 567-570.
This case study was original developed by Philip Landrigan, Lyle Conrad and John Witte in 1971. The current version was updated by Richard Dicker in 2001 and 2003.
CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 1
Rachel Bennett
5 March 2024
Centers for Disease Control and Prevention Epidemiology Program Office Case Studies in Applied Epidemiology
No. 711-903
Texarkana — Epidemic Measles in a Divided City
Student's Guide
Learning
Objectives
After completing this case study, the participant should be able to:
-
Discuss the advantages and disadvantages of using a sensitive and/or specific case definition in an epidemic investigation;
-
Calculate vaccine efficacy and discuss its interpretation; and
-
Discuss the advantages and limitations of selecting a specific age as the recommended target date for administering vaccinations.
CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 2
PART
I
On Tuesday, November 3, 1970, the Center for Disease Control (CDC) in Atlanta received the weekly telegram of surveillance data from the Texas State Health Department. The telegram reported 319 cases of measles in the state during the previous week
. In contrast, Texas had reported an average of 26 cases per week during the previous four weeks
. In follow-up telephone calls, CDC learned from State health officials that 295 cases of measles had been diagnosed in the city of Texarkana, including 25 in children reported to have been previously immunized.
An invitation to investigate the situation was extended to the CDC on November 4, 1970. An EIS officer departed for Texarkana early on November.
Texarkana is a city of roughly 50,000 that straddles the Texas- Arkansas state line
. Texarkana, Texas (Bowie County), had a population of 29,393 in the 1960 census; the population had been stable during the 1960s
. Texarkana, Arkansas (Miller County), had a 1960 population of 21,088. Although Texarkana is divided by the state line, it is a single town economically and socially. Persons of all ages on both sides of town have frequent contact
. Churches, physicians, offices, movie theatres, and stores draw people from both the Arkansas and Texas sides of town. People cross the state line to attend social functions such as football games and school dances. Many families have friends and relatives who visit back and forth on both sides of town. Private nurseries and kindergartens receive children
from both sides of town. The two sides of Texarkana, however, do have separate public-school systems and separate public health departments.
Question
1
: (3 pts) List the reasons to investigate a suspected outbreak. Which reasons may have prompted an investigation of this
outbreak?
There are several reasons to investigate a suspected outbreak. These reasons include understanding the source of outbreak, preventing further spread, and protecting public health. Identifying the source of the pathogen
allows for targeted interventions to prevent further cases and identifying and isolating affected individuals helps prevent the spread of the pathogen to others, reducing the overall impact of the outbreak. Investigating outbreaks is essential for protecting the health of the public, as it allows for the implementation of control measures to minimize the impact of the outbreak. These control measures are guided by surveillance during and after outbreaks to allow earlier detection and response and polices used for preventing and controlling infectious diseases.
A reason to investigate this measles outbreak is the fact that this outbreak is occurring in Texarkana is the fact that there is an increase in cases reported from the Texas State Health Department, but not from the Arkansas State Health Department. Since Texarkana is a town that
CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 3
straddles the Texas-Arkansas state line, and many people cross the state line frequently there would likely be reports from Arkansas too. Since each side has its own separate public-school systems there is some limitation between the children in town but there are private nurseries and daycares receive children from both sides increasing the interaction likelihood. Making the fact that only Texas is reporting increased cases concerning.
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CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 4
PART
II
The Investigation
The investigators obtained names of cases from the health departments, physicians, school and nursery records
. They conducted a door-to-door survey. They also asked families of cases for names of other cases. They used the same methods of case-finding and epidemiologic investigation on both the Arkansas and Texas sides of town.
Clinical Picture
The illness was clinically compatible with measles. Typically, the patients had a 4- to
5-day prodrome with high fever, coryza (runny nose), cough, and conjunctivitis (red, irritated eyes) followed by the appearance of a bright maculopapular (red spots and areas) rash. The temperature usually returned to normal 2 to 3 days after appearance of the rash, while the rash persisted for 5 to 7 days.
Question
2
: (2 pts) How might you define a case for purposes of this investigation?
For the purpose of the investigation a case definition should use the information regarding the clinical picture and the knowledge regarding the epidemiological investigation. Suspected Case/Probable Case
Any individual who has experienced high fever, coryza (runny nose), cough, and conjunctivitis (red, irritated eyes) for 4-to-5 days followed by the appearance of a bright maculopapular (red spots and areas) rash.
Confirmed Case
Any suspected case with laboratory confirmation of a pathogen, through nucleic acid testing, culture, or other diagnostic method.
Question
3
: (4 pts) Describe the difference between a sensitive case definition and a specific case definition. What are the advantages and disadvantages of each?
A sensitive case definition is one that encompasses all possible cases of a disease, this involves keeping criteria broad with symptoms and signs of the
illness. This will include both true positives and false positives as sensitive case definitions are designed to minimize the likelihood of missing any actual cases, ensuring that the surveillance system is highly sensitive to detecting the disease. Some advantages of sensitive case definition are the reduced likelihood of missing actual cases ensuring effective surveillance to
detect outbreaks and is especially helpful in the early stages of an outbreak when it is important to identify and contain cases quickly.
Some disadvantages of sensitive case definition is the increased likelihood of false positives which results in unnecessary investigations into secondary
exposure, allocation of resource stop non-cases, and make it more challenging to interpret surveillance data, as the number of reported cases
CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 5
may be higher than the actual number of true cases.
A specific case definition is more ridged with the criteria, so it only includes
cases that are highly likely to be true positive, even it excludes borderline cases of the disease. This aims to reduce the number of false positives, which can help improve the accuracy of the surveillance data. Some advantages of specific case definition are the reduced number of false positives which ensures accuracy of surveillance data and analysis. Also allows for focused allocation of resources to the true positives. Some disadvantages of specific case definition are the likelihood of missing cases that do not fit the exact definition, particularly in the early stages when the disease may not yet be well recognized and when symptom presentation is atypical fashion. Making it more difficult to detect outbreaks as fewer cases meet the case definition. The Outbreak
Between June 1970 and January 1971, 633 cases of measles were reported from Texarkana
. Dates of onset were accurately determined for 535 cases. The epidemic curve is shown below.
Question 4: (2 pts) Discuss the key features of the epidemic that you can derive from the epidemic curve. In particular, does this look like
a propagated outbreak or point source outbreak? Also, what likely was responsible for ending the outbreak?
The epidemic curve shows around August 23
rd
, it association with the opening of schools there is a small spike in cases. Then a month later
CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 6
around September 20
th
there is a increasing number of cases being reported
where it reaches a pea and remains fairly high or a couple of weeks before decreasing through November and it returned to “normal” levels around the
start of January. The first spike was mostly in preschool children as shown by the dark grey color, while at the height of the outbreak a majority of the cases were school age children. Based on the knowledge that Texas had many cases reported and that the Texas and Arkansas sides of Texarkana have separate public-school systems suggests that since a majority of the children at the peak of the outbreak were school age children measles was not passed between the towns as would be expected due to the social interactions that typically occur. The epidemic curve appears to show that this outbreak was due to a point source. Based on the spike at school starting and the infectious period of measles the most likely period of exposure was the school opening. This indicated that the interaction in school setting played a large role in the outbreak of measles in Texarkana, there was a significant decrease after
the vaccination campaign in preschoolers and school age children, around November 15
th
. However, another spike occurred towards the end of November among people not in an unknown range, which may suggest an ongoing measles epidemic in the community of persons not in day care or schools. Though infants, adolescents, and adults were involved in the epidemic, the
majority of cases occurred in children 1 to 9 years of age
. Measles cases
were not evenly distributed within the two counties. Table 1 displays the
number of measles cases and population by age group for Bowie County,
Texas and in Miller County, Arkansas.
Table 1. Number of measles cases and population (1960 census) by
age group and county, Texarkana outbreak, 1970
Residence Urban/Rural
Age
Group
#
Cases Populatio
n
Rate (per
1,000)
Bowie
Co., Texas
Rural
1-4 yr
47
2,452
19.1
5-9
178
3,242
54.9
1-9
225
5,694
39.5
Urban
1-4 yr
195
2,481
78.6
5-9
73
3,010
24.3
1-9
268
5,491
48.8
Total
1-4 yr
242
4,933
49.1
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CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 7
5-9
251
6,252
40.1
1-9
493
11,185
44.1
Miller
Co.,
Arkansas
Total
1-4 yr
19
2,671
7.1
5-9
6
3,345
1.8
1-9
25
6,016
4.2
Question 5: (7.5 pts) Calculate the totals and attack rates indicated in Table 1. Fill in all of the squares that are highlighted.
Question 6: (6 pts) Discuss the differences in attack rates for the Texas and Arkansas counties, for rural versus urban children, and for preschool versus school-age children
.
Bowie County, Texas, has a much higher attack rate than Miller County, Arkansas. The Bowie County final total rate per 1,000 was 44.1, whereas the Miller County final total rate per 1,000 was 4.2. This is a very large difference, 39.9, between the two county that are very close together. For the rural children and urban children there is not a very large difference between the two. The total rate per 1,000 for rural children was 39.5, while the total rate per 1,000 for urban children was 48.8. This is a difference of 9.3 which does not seem to be significantly different. For children age 1-4 (preschool age) and children age 5-9 (school-age) there
is not a very large difference between the two. The total rate per 1,000 for preschool children was 49.1, while the total rate per 1,000 for school-age children was 40.1. This is a difference of 9 which does not seem to be significantly different. Urban children age 1-4 have a higher attack rate than rural children of the same age. While, rural children age 5-9 have attack rate twice as high as urban children of the same age. This may suggest the modes of transmission may be more efficient in pre-school setting in urban areas like day care programs while in rural areas transmission seem to be efficient in a school setting.
CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 8
Part
III
Measles in Previously Vaccinated Children
Before this outbreak, the proportion of children vaccinated against measles on the Arkansas side was substantially higher than the proportion vaccinated on the Texas side
. The Texas side had never had a community or
school vaccination campaign for measles. In contrast, the Arkansas side had
held mass community programs against measles for school and pre-school children in 1968 and 1969. Based on health department and physician records
, investigators estimated that over 99% of children aged 1-9 years in
Miller County, Arkansas had received measles vaccine prior to the outbreak. The overall vaccination level in Bowie County, Texas, was estimated to be 57%. In this outbreak, 27 of the measles cases in Bowie County and all 25 of the measles cases in Miller County gave a history of prior vaccination with live attenuated measles-virus vaccine. Parental history of vaccination was corroborated for all the cases by clinic or physician records. Local health authorities in both counties were very concerned that children who had previously received measles vaccine got the disease.
Question 7: (4 pts) Calculate the attack rates among the vaccinated populations in both counties and comment on your findings. Present the attack rates per 1,000 people. You will need to calculate the percent vaccinated and as a first step to do these calculations. Here is an example of the setup of the calculations needed to determine the attack rate among those vaccinated:
Texas vaccinated population = (total population)*(percent vaccinated)
= (11,185)*(0.57) = 6,375.45
Arkansas vaccinated population = (total population)*(percent vaccinated)
= (6,016)*(0.99) = 5,955.84
Texan Attack Rate = [number ill/number vaccinated]*1000
=[27/6,375.45]*1000 = [0.00423]*1000 = 4.23 cases with vaccination history
Arkansas Attack Rate = [number ill/number vaccinated]*1000
= [25/5,955.84]*1000 = [0.00419]*1000 = 4.19 cases with vaccination history
CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 9
Although there were more 1–9-year-old children overall who got measles in Bowie County, Texas than in Miller County, Arkansas, the attack rate among the vaccinated children in both counties were about same. It is therefore likely that the high attack rate among all children in Bowie County was probably due to low vaccination coverage.
Table 2. Hypothetical populations with vaccine coverage of 0%, 20%,
60%, and 100%
Population
A
B
C
D
a. Number of persons in population
100
100
100
100
b. Vaccine efficacy (VE)
90%
90%
90%
90%
c. Percent population vaccinated (PPV)
0%
20%
60%
100%
d. Number vaccinated (a x c)
100*0.0=
0
100*0.2=
20
100*0.6=
60
100*1.0=
100
e. Number unvaccinated (a - d)
100-0=
100
100-20=
80
100-60=
40
100-100=
0
f. Number protected (d x b)
0*0.9=
0
20*0.9=
18
60*0.9=
54
100*0.9=
90
g. Number vaccinated but ill (d - f)
0-0=
0
20-18=
2
60-54=
6
100-90=
10
h. Total number ill (e + g)
100+0=
100
80+2=
82
40+6=
46
0+10=
10
i. Percent cases vaccinated (PCV) (g/h)
0/100=
0%
2/82=
2.4%
6/46=
13.04%
10/10=
100%
Consider the use of a vaccine with 90% efficacy in four different hypothetical populations of 100 people each, with vaccine coverage of 0%,20%, 60%, and 100%, respectively.
Assume that every unvaccinated person will be exposed to, and will develop, measles.
Question 8: (4.5 pts) Complete Table 2.
Question 9: (4 pts) What do you conclude about the relationship between coverage and number of cases vaccinated? What might your
public health message be for these data?
The relationship between vaccine coverage and the number of cases vaccinated is inversely proportional. As vaccine coverage increases, the number of cases vaccinated decreases. This relationship is expected, as higher vaccination coverage generally leads to greater herd immunity, which reduces the likelihood of transmission and thus the number of cases.
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CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 10
The public health message for these data would emphasize the importance of high vaccine coverage to prevent disease outbreaks. It would highlight the role of vaccines in not only protecting individuals but also in protecting the community by reducing the overall number of cases. Achieving high vaccine coverage rates can help prevent outbreaks and protect vulnerable populations.
Vaccine Efficacy
The ability of a vaccine to prevent disease depends on its potency and proper administration to an individual capable of responding. The success of vaccination performed under field conditions may be assessed by measuring protection against clinical disease. Such field assessments can be very useful, particularly when doubt is cast on the efficacy of the vaccine
because of the occurrence of disease among vaccinated persons.
Vaccine efficacy is measured by calculating the incidence (attack rates) of disease among vaccinated and unvaccinated persons and determining the percentage reduction in incidence of disease among vaccinated persons relative to unvaccinated persons. The greater the percentage reduction of illness in the vaccinated group, the greater the vaccine efficacy. The basic formula is written as:
Question
10
: (5 pts) Using the basic formula, calculate vaccine efficacy for Bowie County, Texas
.
ARU: attack rate in unvaccinated population ARU = [(493-27)/ (11,185*0.43)] = 0.0969
ARV: attack rake in vaccinated population
ARV = [(27)/ (11,185*0.57)] = 0.00423
VE = [(ARU – ARV)/ARU]*100
VE = [(0.0969-0.00423)/0.0969]*100 = [0.09267/0.0969]*100 = 95.63%
Question
11:
(2 pts) Was inadequate vaccine efficacy primarily responsible for this outbreak? If not, what is your alternative explanation?
CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 11
The vaccine efficacy is high, which means that the vaccine reduces the risk of developing the disease by 95.63% among vaccinated individuals compared to unvaccinated individuals under ideal, controlled conditions. Inadequate vaccine efficacy does not seem be primarily responsible for the outbreak, the high vaccine efficiency indicates it is highly effective at preventing the disease. An alternative explanation could be low vaccination coverage in the population. Even with a highly effective vaccine, if a large proportion of the population is not vaccinated, there may not be enough herd immunity to prevent the spread of the disease. This can allow outbreaks to occur, particularly if the disease is highly contagious.
CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 12
Part
IV
In previously vaccinated children aged 1-9 years in Bowie County, the measles attack rate in this outbreak was 4.2 per 1000; the comparable rate in unvaccinated children was 96.9 per 1000. From these data, a vaccine efficacy of 95.7 percent was calculated. This is a minimum figure since it has been assumed that all 27 children were correctly vaccinated and that all
of the cases therefore represent vaccine failure.
In actuality some of these patients did not receive vaccine under ideal conditions. Eight of the 27 previously vaccinated patients had been vaccinated by nurses from the Texarkana/Bowie County Health Unit at a day nursery. The vaccine for these eight children had been carried back and
forth to the nursery from the Health Unit in a cooler in a car on three separate days in June and July 1970
. Although a lapse in technique which allowed warming of the vaccine cannot be documented here, it is a possible explanation. An additional seven patients had been vaccinated under the age of 1 year. These children were vaccinated in the years 1963-67 when it was recommended that measles vaccine be given at age 9 months. It has since been learned that a vaccine failure rate as high as 15% may accompany vaccination at 9 months in the United States.
Question 12
: (4 pts) What is the WHO recommended age for measles
vaccination in developing countries? Why is the recommended age for vaccination different in the United States? This might require some additional research that is not presented in this case report.
The difference in recommended ages for vaccination between developing countries and the United States is influenced by factors such as healthcare infrastructure, access to vaccines, and the prevalence of measles in the population. According to WHO, children in developing countries should be given two doses of measles vaccine to ensure proper immunity. The first dose of measles containing vaccine should be given around nine months of age. The second dose should be administered at 15-18 months of age. The vaccine should be given whether the child is HIV infected or not and to any children above the WHO recommended age who are unvaccinated. This schedule is designed to ensure that children in high-risk areas receive protection against measles as early as possible, as they may be more vulnerable to the disease due to factors such as malnutrition and limited access to healthcare.
In contrast, the recommended age for measles vaccination in the United States is slightly different. The CDC recommends the first dose of the measles, mumps, and rubella (MMR) vaccine at 12-15 months of age, with a second dose at 4-6 years of age. This schedule is based on the epidemiology of measles in the United States, where the disease is less common and the risk of exposure is lower compared to developing countries. The later age for vaccination in the U.S. allows for greater immune response to the
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CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 13
vaccine and longer-lasting protection.
Centers for Disease Control and Prevention. (2021, January 26). Measles, Mumps, and Rubella (MMR) Vaccination
. Centers for Disease Control and Prevention. https://www.cdc.gov/vaccines/vpd/mmr/public/index.html#:~:text=CDC%20recommends%20all
%20children%20get,days%20after%20the%20first%20dose
.
World Health Organization. (2023, August 9). Measles
. World Health Organization. https://www.who.int/news-room/fact-sheets/detail/measles#:~:text=Children%20should
%20receive%20two%20doses,usually%20at%2015%E2%80%9318%20months
.
CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 14
PART
V
-
CONCLUSION
Prior to the development of a vaccine, about 500,000 people developed measles in the United States annually
; 50% of persons contracted the disease by age 6 years and 90% by age 15 year
s. In 1963 both a killed measles vaccine (KMV) and a live, attenuated vaccine were licensed. Since 1969 only live attenuated vaccine has been used in this country.
At the time of original licensure in 1963, the recommended age of vaccination in the United States was 9 months. The recommended age was raised to 12 months in 1965 and to 15 months in 1976
. Compared with the pre-vaccination era, the occurrence of measles in the U.S. declined by more than 99% by the late 1980s
. However, measles cases increased in 1989-
1991, and a two- dose strategy was adopted
. After the adoption of the two-
dose strategy and a substantial increase in immunization program resources, measles cases again declined. Since 1997, fewer than 140 cases of measles have been reported each year in the United Sates, almost all of which could be traced to imported cases. The provisional total for 2002 was
a record low of 37 cases.
REFERENCES
1.
Landrigan PJ. Epidemic measles in a divided city. JAMA 1972; 221: 567-
570.
2.
CDC. Case definitions for infectious conditions under public health surveillance. MMWR 1997;46(No. RR-10):23-24.
3.
WHO. Core information for the development of immunization policy: 2002 update. Geneva: World Health Organization, 2003.
ADDITIONAL READING
1.
Orenstein WA, Bernier RH, Hinman AR. Assessing vaccine efficacy in the
field: further observations. Epidemiologic Reviews 1988; 10: 212- 241.
CDC-EIS, 2003: Texarkana: Measles in a Divided City (711-903) – Student’s Guide
Page 15
2.
CDC. Measles, mumps, and rubella – vaccine use and strategies for elimination of measles, rubella and congenital rubella syndrome and control of mumps: recommendations of the Advisory Committee on Immunization Practices (ACIP). MMWR 1998; 47 (No. RR-8): 1-57.
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The following table summarizes the results of the study, giving the number of observations and the sample mean and variance of the subjects’ weight loss in each program.…
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A certain virus affects 0.4% of the population. A test used to detect the virus in a person is positive 90% of the time if the person has the virus (true positive) and 10% of the time if the person does not have the virus (false positive). Fill out the remainder of the following table and use it to answer the two questions below based on a total sample of 100,000 people.
Virus
No Virus
Total
Positive Test
Negative Test
Total
100,000
a) Find the probability that a person has the virus given that they have tested positive. Round your answer to the nearest hundredth of a percent and do not include a percent sign. %
b) Find the probability that a person does not have the virus given that they test negative. Round your answer to the nearest hundredth of a percent and do not include a percent sign. %
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In a study entitled "Hello from the Other Side", Yael Schneider studied the frequency, conditions of, and content of attempted electronic communications with a former significant other in the month immediately following a breakup. Yael looked at messages sent via social media, text, and email of 32 individuals who had recently broken up with their significant other. Her findings can be found in the Almanac of Questionable Statistics, Vol 16 (1242). What is the population in this study?
Question 13 options:
1)
Social media, mobile phone, and internet providers
2)
The 32 individuals whose electronic communications were studied
3)
Researchers of social and behavioral science
4)
All individuals who have recently broken up with a significant other
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Give 5 examples of situations using this:
1. Retrospective Study
2. Observational Study
3. Designed Experiment
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In a study entitled "Hello from the Other Side", Yael Schneider studied the frequency, conditions of, and content of attempted electronic communications with a former significant other in the month immediately following a breakup. Yael looked at messages sent via social media, text, and email of 32 individuals who had recently broken up with their significant other. Her findings can be found in the Almanac of Questionable Statistics, Vol 16 (1242). What is the population in this study?
Social media, mobile phone, and internet providers
2)
The 32 individuals whose electronic communications were studied
3)
Researchers of social and behavioral science
4)
All individuals who have recently broken up with a significant other
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. A study of cell phones and the associated risk of brain cancer looked at a group of 519 people who have brain cancer. The investigators matched each cancer patient with a person of
the same sex, age, and race who did not have brain cancer, then asked about their use of cell phones. This kind of study is known as
eBook
O prospective
retrospective
O observational
O double-blind
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In a study entitled "Hello from the Other Side", Yael Schneider studied the frequency, conditions of, and content of attempted electronic communications with a former significant other in the month immediately following a breakup. Yael looked at messages sent via social media, text, and email of 32 individuals who had recently broken up with their significant other. Her findings can be found in the Almanac of Questionable Statistics, Vol 16 (1242). What is the population in this study?
Question 1 options:
1)
The 32 individuals whose electronic communications were studied
2)
Social media, mobile phone, and internet providers
3)
Researchers of social and behavioral science
4)
All individuals who have recently broken up with a significant other
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This question is from the below book, Chapter 15 (Comparing means of more than two groups) , AP 27
Book-Analysis of biological data
2nd Edition
Michael C. Whitlock, Dolph Schluter
Publisher: W. H. Freeman
ISBN: 978193622148
Does adding math to a scientific paper make readers think that it has more value? Erikkson (2012) sent two abstracts of scientific papers to 200 people with postgraduate degrees. For each participant, one of the abstracts was randomly chosen and had a meaningless sentence inserted describing an unrelated. mathematics model, while the other had no mathematical addition. The sentence had no conceptual connection to the subject matter of the abstract; it was just meaningless mathematics in that context. Participants were asked to rate the quality of the research in each abstract on a scale from 1 to 100 and the differences between the scores of their two abstracts -score of the abstract with math minus score of abstract without math-were recorded. Participants were…
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Based on these tables, would you accept or reject the hypothesis that individuals in bad neighborhoods commit more crime?
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