STAT 3843A Fall 2013
Assignment 2
Due: October 11 on paper in class
1. For any sampling scheme, i is the probability that unit i is selected.
The HorvitzThompson estimator of the population total t is t =
iS yi /i .
(a) Show that the SRS estimate t = N y
SS 3843a Final Exam
Name:
ID:
1
Department of Statistical and Actuarial Sciences
SS 3843a Fall 2012
Instructor: D. Murdoch
Final Exam December 15, 710 PM
Instructions
A basic calculator is allowed; no other aids are allowed. Cell phones, pagers and othe
Intro to study design lecture 21 31/oct
the completely randomized design
t treatments
r replicates of each treatment
rt units assigned at random
simple model
Research question
Does the treatment affect
? i.e are all the
To address this, fit the model wit
Intro to study design lecture 16
Administrative data data that were collected for a non statistical purpose.
Guidelines from statcan continued:

Look particularly at items you prepare to use
Questions like occupation might be recorded too coarsely
Admini
Intro to study design lecture 13
Should you stratify?
Some reasons?
Total data
May be able to optimize costs
It might reduce the variance of
When does it do this?
Assume
This leads to proportional allocation
We want to compare
to
Think as though were usin
Lecture 12
Allocating
When
values
are all the same, allocate
(nearest integer value)
We had
If all
To choose
values to minimize this, minimize
A more realistic model of sampling
varies from stratum to stratum. Treat these as known (maybe coming from a pil
Lecture 15 (15oct)
Administrative data
Data collected in the course of some nonstatistical program used for statistical purposes.
Hospital records
Driver licensing
Tax returns
Property tax assessments
Customs declarations
Births, deaths, marriages
Intro to study design lecture 18
Designed experiments
Studies can be observational e.g surveys
Or experimental the experimenter takes an active part is they control the conditions the subjects
are exposed to.
In observational studies, we researchers sele
Lecture 10 intro to study design
Confidence interval
We could repeat
Wed like to make a probability statement. i.e a confidence interval. The 95% CI for
The probability that
is in this interval is 95% only before observing the sample
If we assume that the
Lecture 11 intro to study design
Stratified sampling
Sample
Take SRS of size
in stratum h
Sample quantities
We estimate
Estimate
by
Estimate this by plugging in for
What about confidence intervals?
Want a
for
use
Some use
, and we get an unbiased estimat
Clinical trials (intro to study design) lesson (1)
Need a reliable source of data to understand Canada
Fellegi, former Chief Statistician of Canada
No consultation with the public
Voluntary response, the responders are not representative of the population
Intro to study design lecture 19
Experiment Design
Experimenters play an active role. Subjects of experimental units

The individuals being studied
The experimenters can control the treatment of each subject separately
Factors: explanatory variables (som
Study on Toronto sun: men prefer bigger women
Internal validity
randomized
Construct validity
measure stress?
Induce stress through certain methods
 measure attraction?
External
How were the participants selected?
81 heterosexual undergraduates
briti
Intro to study design lecture 7
Probability sampling (Loh chapter 2)
Convenience samples tend to be biased. Probablity samples are an alternative
Simple random samples (SRS)

Randomly choose in units out of the sampling frame (or population) of N units
E
Topics covered in SS 3843a, Fall 2013.
1. Long form census controversy
Arguments for a mandatory census: less selection bias, more ecient than many small surveys, needed as a reference.
Arguments for optional survey: questions are intrusive, shouldnt
co
Intro to study design lecture 23 5th nov
Factorial design
Treatments are made up of factors.
Example: drug test
Factor1: drug A vs drug B
Factor2: pill vs injection
Factor3: frequency: one dose/day vs two dose/day
With 3 factors, each at 2 levels, there a
Validity of statistical studies (week 2, Wednesday lecture 3)
Experiment 1
Hydrogen
and oxygen
in two test tubes.
s/he applies heat to one of them
the heated tube gives a pop & forms water vapour
Conclusion
Is the heat caused the water to form
Seems like
Clinical trails
Planned experiments to access the most appropriate medical treatment for future patients
Treatments: drug, surgical procedure, other therapy
Outcomes:
Labs test results
qualify of life measure
Survival on other major outcome
Nowadays, clin
Intro to study design lecture 28
3 factor interaction is a tetrahedron
Shouldnt use factorial model when you have a outlier ( e.g mistake in your data recording)
*exam will give you a picture and ask you what is it measuring (cube)
only looking at high le
Topics covered in SS 3843a, Fall 2013, up to midterm.
1. Long form census controversy
Arguments for a mandatory census: less selection bias, more ecient than many small surveys, needed as a reference.
Arguments for optional survey: questions are intrusi
Intro to study design lecture 31
Unusual informed consent procedure
Randomized patients to ECMO or CMT 1st
Only ECMO patients (then patients) wre asked for consent

Better to ask CMT patients for consent too and let htem know hte possible outcome for eac
Intro to study design lecture 32
We calculated 28 pvalues (from uniform (0,1)
Smallest was
Distribution of smallest pvalue is not uniform, there is about a 70% chance of being a significant
one.
Bongerroni correction:
Do all tests at 0.05/28 level, so o
Intro to study design lecture 8
Suppose n=1, * box sometimes this is called the population variance. We say
SRS (simple random survey without replacement)
Define sample mean:
However, this is hard to calculate, so nice trick. Define
Then,
Therefore,
as
is
Intro to study design lecture 6
Requirements for a good sample
Observation unit
Target population
Sample
Sampled population
Sampling unit
Sampling frame
Selection bias
Measurement bias

Bias in the observation on an observation unit
o A miscalibrated sca
Intro to study design lecture 5
Sample survey
Measure only a sample from a population.
What is a good sample to choose?
o You want it to be representative
i.e characteristics of the sample matches the population
types of samples
o voluntary response samp
Intro to study design lecture 30/11
Bayesian interim analysis
Simple model
treatment difference.
good
bad
Prior idea for ,
Model
Posterior distribution
Now
(likelihood data density) since i.i.d, and
Now,
is our prior density
doesnt depend on , you can tr
1
COURSE INFORMATION
SepDec 2013
Department of Statistical and Actuarial Sciences
Statistical Sciences 3843A: Introduction to Study
Design
Course Description The calendar description for this course is:
A case study approach to how data are collected in
Lecture 9 intro to study design
We could imagine
is the population, is the population is itself a sample
Under reasonable assumptions, about how the population was selected
This
Its
 (for both formulas) increases as N increases but not very much and it g
Intro to study design lecture 30
ECMO treatment

Maybe has 80% success compared to 20% for conventional treatment (CMT)
Worry that it may have longterm bad effects (brain damage,etc)
1st study at Michigan a play the winner design
Put one white and one b