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\title{36-303 Sampling, Surveys \& Society \\ Homework 01 Solutions}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  PROB1  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Question 1}
See Table~\ref{tab:question1}.\\
\begin{table}[tbp]
\begin{center}
\caption{The Health Behavior in School-Age Children Study (HBSC)}
\begin{tabular}{lp{10cm}}

\hline
Sponsor & The World Health Organization\\
Collector & collected by an international network of research teams \\
Purpose & {to gain unique insight into the health and behaviour of young people.  To study young people's health in its broadest sense -
physical, social and emotional well-being, not merely the absence of disease} \\
Year started & 1982\\
Target Population & young people attending school, aged 11,13 and 15 years.   \\
Sampling Frame & students of the age described above who attended school in the thirty-five countries of interest (Americas and Europe), listed within the article\\
Sample Design & children were selected using a clustered sampling design, where the initial sampling unit was either 
the school class or the school.  The latter was sampled when class lists were not available.\\
Sample Size & $1500 \times 3 \times 35$  \\
Use of Interviewer & There was no direct interviewer, however, respondents had to fill out a questionnaire\\
Mode of Administration & trained personnel, teachers and school nurses administered the completion of questionnaires in school
classrooms\\
Computer Assistance & not clear\\
Reporting Unit & each student\\
Time dimension & Repeated cross-sectional survey\\
Frequency & every four years\\
Interviews per Round of Survey & one\\
Levels of observation & student\\
Web Link & \url{ http://www.hbsc.org/publications/reports.html}\\
\hline
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\label{tab:question1}
\end{table}

(b)
The survey was carried out in regions of the Americas and Europe only.  There may be problems generalizing the information 
found to the entire world since the sampled regions represent mostly developed countries.  I couldn't find any information about computer assistance, although I think they probably used computer assistance
in randomizing school class. 
It is generally common to get missing data in questionnaire type of survey, I couldn't find information about how was this problem
dealt with in the survey so there might be some bias in the findings.          
   



\section{Question 2}
See Table~\ref{tab:question2}. \\

\begin{table}[tbp]
\begin{center}
\caption{Traffic Safety Culture Index}
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\hline
Sponsor &  AAA Foundation for Traffic Safety \\
Collector & Abt SRBI Inc\\
Purpose & To assess a few key indicators of the degree to which traffic safety is valued and is being pursued\\
Year started & 2008 \\
Target Population & Individuals in the United States who are sixteen years of age or older, presumably those who are allowed to drive\\
Sampling Frame & various landline and cellular telephone numbers\\
Sample Design & A list-assisted random digit dial sample of landline telephone numbers, including
both listed and unlisted numbers, and a random sample of cellular telephone numbers.\\
Sample Size & 2000 individuals\\
Use of Interviewer & yes\\
Mode of Administration & Respondents were asked questions by an interviewer who recorded the relevant 
information over a phone call\\
Computer Assistance & used to create a random number list for the stratified landline sample\\
Reporting Unit & One person age sixteen or older in a household is reported for on behalf of the interviewer.  In the case
of a household having multiple qualifying individuals, the person with the closet upcoming or past birthday was selected for the interview\\
Time dimension & two-wave panel of persons\\
Frequency & once every year\\
Interviews per Round of Survey & one\\
Levels of observation & individual\\
Web Link & \url{ http://www.aaafoundation.org/resources/index.cfm?button=research}\\
\hline
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\end{center}
\label{tab:question2}
\end{table}
(b) I found all the information needed to fill the table.  Overall, I am generally happy about the survey.  For example, response
rate and cooperation rate were adjusted for calculations.  However, It is a common problem that telephone samples 
may not actually be representative of the US population.  


\section{Question 3}

(a)The target population is US adults (18 years or older).  The population in the sample frame is a subset of all individuals using the 
five largest commercial internet service providers in the US.  \\
(b) Obviously, the sample frame over covers people who uses the five largest commercial ISP.  Samples from the target population who does not 
use emails from one of these five ISP are excluded.  Survey were sent through E-mails soliciting however, many email ISP nowadays use automatic
spam filter so the these emails may not have reached the targeted individuals.  Measurement error describes behavior that is common and 
systematic across administrations of the question.  Given that the survey is about handheld digital devices, people that actually own blackberries and PDAs are likely to respond fast.  Also, the category division is misleading because some people may consider laptops as handheld digital devices. \\
(c)the coverage error can be reduced by simply expanding E-mail soliciting to users outside of the five largest ISP.  Also, sampling frame can be extend to people that go to regular stores.  Nonresponse error arises when the values of statistics computed based only on respondent data differ
from those based on the entire sample data.  I think sample frame needs to be extended so that it covers the targeted population.  To reduce the measurement error, other sample design other than E-mails soliciting needs to be employed.  \\
(d) Cutting the sample in half increase the sampling error because sampling error is the nonobservational gap between the sampling frame and sample.  However, this wouldn't affect the coverage error because our sampling frame is still major ISPs.  

\section{Question 4}
so in section 2.3.6, the book details the non-response bias:\\
Let $\bar{y}_s = $ Mean of the entire specific sample as selected\\
$\bar{y}_r = $ Mean of the respondents within the sth sample \\
$\bar{y}_m = $ Mean of the nonrespondents within the sth sample \\
$n_s = $ Total number of sample members in the sth sample \\
$r_s = $ Total number of respondents in the sth sample \\
$m_s = $ Total number of nonrespondents in the sth sample \\
The nonresponse bias can be expressed as \\
\[ \bar{y}_r - \bar{y}_s = \frac{m_s}{n_s} (\bar{y}_r - \bar{y}_m   )\]



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