Part time MSc course Epidemiology

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The following lecture has been approved for
University Undergraduate Students This lecture
may contain information, ideas, concepts and
discursive anecdotes that may be thought
provoking and challenging It is not intended for
the content or delivery to cause offence Any
issues raised in the lecture may require the
viewer to engage in further thought, insight,
reflection or critical evaluation or reading or
watching more TV or listening to Radio 4
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Selecting Samples Deployment Allocation Group
Testing Prof Craig Jackson Head of Psychology
Division Faculty of Education Law Social
Sciences BCU
craig.jackson_at_uce.ac.uk
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Keep it simple Some people hate the very name
of statistics but.....their power of dealing with
complicated phenomena is extraordinary. They are
the only tools by which an opening can be cut
through the formidable thicket of difficulties
that bars the path of those who pursue the
science of man. Sir Francis Galton, 1889
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How Many Make a Sample?
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How Many Make a Sample? 8 out of 10 owners who
expressed a preference, said their cats preferred
it. How confident can we be about such
statistics? 8 out of 10? 80 out of 100? 800 out
of 1000? 80,000 out of 100,000?
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Multiple Measurement of small sample
25 cell clusters 22 cell clusters 24 cell
clusters 21 cell clusters Total 92
cell clusters Mean 23 cell clusters SD
1.8 cell clusters
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It all depends on the size of your needle
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Small samples spoil research
N Age IQ 1 20 100 2 20 100 3 20 100 4 20 100 5 20
100 6 20 100 7 20 100 8 20 100 9 20 100 10 20 100
Total 200 1000 Mean 20 100 SD 0 0
N Age IQ 1 18 100 2 20 110 3 22 119 4 24 101 5 26
105 6 21 113 7 19 120 8 25 119 9 20 114 10 21 101
Total 216 1102 Mean 21.6 110.2 SD 4.2 19.2
N Age IQ 1 18 100 2 20 110 3 22 119 4 24 101 5 26
105 6 21 113 7 19 120 8 25 119 9 20 114 10 45 156
Total 240 1157 Mean 24 115.7 SD 8.5 30.2
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• Background on Surveys
• Large-scale
• Quantitative
• Can be descriptive
• (2 of women think they are beautiful)
• Can be inferential
• (Significantly more single women think theyre
  beautiful than married women do)
• Done with a sample of patients, respondents,
  consumers, or professionals
• Differences between any groups assessed with
  hypothesis testing
• Important that sample size must be large enough
  to detect any such difference if it truly exists

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• Importance of Sample Size
• Forgotten in many studies
• Little consideration given
• Appropriate sample size needed to confirm /
  refute hypotheses
• Small samples far too small to detect anything
  but the grossest difference
• Non-significant results are reported as
  significant Type 2 error
• Too large a sample unnecessary waste of
  (clinical) resources
• Ethical considerations waste of patient time,
  inconvenience, discomfort
• Essential to make assessment of optimal sample
  size before starting investigation

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• Qualitative studies need to sample wisely too
• Asian GPs attitudes to ANP
• Objective
• To determine attitudes to ANP among Asian doctors
  in East Birmingham PCT
• Method
• Send invitation to 55 Asian GPs (Approx 47 of
  East Birmingham PCT)
• Intends to interview (30mins) with first 20 GPs
  who respond
• Sample would be 36 of Asian GPs and only 17
  of GPs in PCT
• Severely Biased Research (and ethically dodgy too)

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Have Some Consideration The Good 1
Pulmonary Valve Replacement on Biventricular
Function following Tetralogy of Fallot Q.
How many participants will be recruited? How many
of these participants will be in a control
group? A. Power analyses have been undertaken
based on previous data provided by Hazekamp et
al. (2001). A sample size of 18 in each group
will have 95 power to detect a difference in
right-ventricular end-diastolic volume of 78ml
(the difference between preoperative mean of
292ml and the postoperative mean of 214ml)
assuming the common standard deviation is 62ml
and using a two-group t-test with a 5 two-sided
significance level.
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Have Some Consideration The Bad 2 Survey
of knowledge and Attitudes regarding ADHD
in Adults among Specialist Adult
Psychiatrists It is a cross sectional
questionnaire survey to assess the current
knowledge and attitudes regarding ADHD in Adults
amongst ALL General and Specialist Adult
Consultants, Specialist Registrars and
Staff-grade / Associate Specialist Doctors in
Birmingham and Solihull Q. How many
participants will be recruited? How many of these
participants will be in a control group? A.
100.
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Have Some Consideration The Ugly 3 The
Sepsis Study This is a cross sectional study
which will be conducted using a postal
questionnaire with a follow-up reminder letter to
non-responders. The sample will be taken from
patients who have been admitted to the ITU
department for severe sepsis or septic shock
between Feb 1st 2004 and Aug 1st 2004. Patients
will be over the age of 18 and will have spent at
least one day on ITU. The questionnaire will be a
standard health related quality of life
questionnaire. Patients will be contacted by
letter a maximum of two times. The patients
personal details will be stored on a database
kept in hospital to maintain patient
confidentiality. Names will not be published in
the written report. The database should highlight
any patients who are deceased and obviously
questionnaires will not be sent to the addresses.

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Have Some Consideration The Ugly 3 The
Sepsis Study Q. How many participants will be
recruited? How many of these participants will be
in a control group? A. Between 30 and 60.
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Sampling a Population Process of selecting units
(e.g. people, organisations) from a population
Generalise results to the population First
question should be Who do you want to
generalize findings to ?
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Sampling a Population
A POPULATION
REPRESENTATIVE SAMPLE (theoretical)
ACCESSIBLE SAMPLE (actual)
Are this lot are REPRESENTATIVE of the POPULATION
?
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Sampling a Population
Need to do one more thing...
Develop SAMPLING FRAME (the method for selecting
subjects to include in study)
The SAMPLING FRAME acts like cross-hairs and
allows selection and exclusion of people into the
study
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Sampling Frames
Interest lies in Pig Farmers Choose Pig
Farmers from the phone book list of farmers is
the SAMPLING FRAME. Call all and see who will
take part RANDOM-DIGIT-DIALING
Criteria 1 2 3 4
A more selective sampling frame would be PIG
FARMERS WITH MORE THAN 1 FAMILY CAR WITH 50,000
TURNOVER p/a AND HAVE MORE THAN TWO CHILDREN
But how many respondents would such specificity
yield?
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Specificity versus Generality
Specific
General
pig farmers gt1 family car 50,000 gt2 children
pig farmers gt1 family car
pig farmers gt1 family car 50,000
pig farmers
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Types of Sampling
CONSCRIPTIVE sampling Ethically unsound Bias
QUOTA SAMPLING sampling Favourite of ICM and
MORI Quotas of the population Efficient Flaw
potential
RANDOM sampling Theoretically ideal
Costly Time-consuming All elements of the
population
OPPORTUNISTIC sampling Desperate measure Take
any subject available Cheap Fast Bias
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RANDOM sampling OPPORTUNISTIC
sampling CONSCRIPTIVE sampling QUOTA sampling
Distributions
N of population
56 57 58 59
510 511 6 61 62
63 64 Height

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How many makes a sample? POWER OF STUDY
CALCULATION Statistical method of calculating
the number of subjects needed in a project Based
upon.. Expected variance of subjects
scores Useful size of any differences between
groups Significance level (e.g. 5 or 1
) Power level The larger the differences you
are looking for between groups, then the fewer
subjects are needed. Looking for small
differences between groups requires larger
numbers of subjects
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Specificity and the acceptable N Jacksons
paradox As study populations become smaller,
acceptable study sample sizes reduce
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Specificity and the acceptable N Student Pop
N indepth I.D Forces yachting training
schools 300 E.M Companies using stress
counselling 150 S.M Divers and ear
barotrauma 142 N.O Solvent exposure in
Myanmar 80 V.W Routine flu vaccinations 900 A
.F Dermatitis in hairdressers 102 S.M O.H needs
of NHS staff 23 yes T.R NIHL in student
employees 14 yes I.C Blood tests in British
Army pilots 408 O.Y Upstream oil company
deaths 161 A.A Renal colic in flight deck
crew 254 A.C Hepatitis B in army regulars and
territorials 476
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Selection Bias Sampling properly is
Crucial Samples may be askew Specialist
publications attract a specialist response
group Exists a self-selection bias of those with
special interests Controversial topics, or
litigious areas
Gulf War Syndrome
AE Violence
C dif
Call Centres
Depleted Uranium Weaponry
THIS IS AN INHERENT PROBLEM WITH HEALTH RESEARCH
COMBAT IT WITH LARGE SAMPLES AND CLEVER
METHODOLOGY
Organophosphate Pesticides
Stress
Telecomms
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Sampling Methods
Company with 1000 employees Want to sample 10
How workers are listed is crucial Surname Age E
mployee id. Salary d.o.b Sex
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0
bias bias bias bias bias bias
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Sampling Methods
Non-randomly select the first 100 employees
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0
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Sampling Methods
Routinely sample 100 employees
Every 10th name is chosen until reaching criteria
of 100 employees
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0
30
Sampling Methods
Routinely Random sample 100 employees
Rolling a six sided dice. Count on x from the
last name chosen. There is a problem
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0
31
Sampling Methods
Randomly sample 100 employees
Random number generator Scratch names off the
list Blindfold pin Darts
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0
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POPULATIONS Can be mundane or
extraordinary SAMPLE Must be representative IN
TERNALY VALIDITY OF SAMPLE Sometimes validity is
more important than generalizability SELECTION
PROCEDURES Random Opportunistic Conscriptive Quota
Sampling Keywords
33
Sampling Keywords
THEORETICAL Developing, exploring, and testing
ideas
EMPIRICAL Based on observations and measurements
of reality
NOMOTHETIC Rules pertaining to the general case
(nomos - Greek)
PROBABILISTIC Based on probabilities
CAUSAL How causes (treatments) effect the outcomes
34
Errors in hypothesis testing Type 1 errors
False positive Occurs if null-hypothesis
rejected when it should be accepted e.g. a
significant result obtained when null
hypothesis is in fact true Probability of
making Type 1 error denoted as a
Type 2 errors False negativeOccurs if
null-hypothesis accepted when it should be
rejectede.g. a non-significant result obtained
when null hypothesis is in fact not
trueProbability of making Type 2 error denoted
as ß
35
Factors affecting Sample Size Dependent upon 4
inter-related factors 1. Possible to calculate
each one if the other three are known
N ?
36
1. Power Probability that study of given size
would detect a real statistically significant
difference Usually between 80 to
90 .80 .85 .90 Higher power higher chance
of detecting a genuine significant difference and
low chance of making a type 2 error With high
power, can be reasonably sure any non-significant
result is genuine e.g. ok to accept
null-hypothesis
37

• 2. Minimal Important Size of difference to be
  detected
• If difference between treatments is large, small
  samples can produce significant results
• If difference between treatments is small,
  larger samples are needed
• Important to know if any differences are
  expected to be small
• Determine the min. difference between treatments
  considered clinically relevant
• Given large enough sample, any difference can be
  made statistically significant
• Experience Judgement needed in deciding minimal
  treatment effect that is of any value to
  justify effort, time and finance involved

38
2. Minimum Important Difference to be detected
(MID) Bronchodilator Chronic Bronchitis
Example New bronchodilator causes a real
increase in tidal volume in patients (10ml
average) Standard deviation (natural
variation) in tidal volume in this clinical
population is more than 10ml Given huge sample
a significant tidal volume increase in users
could be proved (but this is due to natural
variation) Expensive Pointless Such a small
(but stat. significant) increase - the drug is of
little clinical use
39

3. Standard Deviation Variability Larger the
SD of 2 groups, relative to CID, then the larger
the sample needed Smaller the SD, the smaller
the sample required Ratio of MID to SD is the
standardized difference used in calculating
sample sizes Estimated SD Estimate of SD may
not be available 1. Pilot study 2. Begin trial
and estimate SD from initial patients 3. Use SD
found in previous trials 4. Use SD found in
similar patients / circumstances in other
literature
40
P

• 4. Significance Level
• Significance level (a) important bearing on
  sample size required
• Relationship between significance level (a) and
  the chance of making type 2 error (ß)
• Smaller significance level (e.g. P0.01 rather
  than P0.05) requires larger sample size to avoid
  type 2 error
• As nominated significance level gets smaller,
  so does chance of type 2 error
• Significance level of P0.05 implies a type 2
  error will occur in every 20 trials
• 5 out of 100 studies will make type 2 errors - -
  purely by chance. Acceptable
• Prob. of type 2 error should be approx. 4 times
  sig. level chosen e.g.
• a 5 then power 80 a 1 then power 95

41
Calculating Sample Size Sample size calculations
available for all study designs, trials, and data
types e.g. categorical data, continuous data,
means, proportions, multiple groups, paired
samples, unpaired samples, equal / unequal sized
groups Calculations are complex but easily done
with a PC and www Statistician helpful (if s/he
can communicate clearly!)
Two approaches for us non-statisticians 1.
Altmans Normogram 2. Internet
42
10000 6000 4000 3000 2000 1400 1000 8000 600 500
400 300 240 200 160 140 120 100 80 70 60 50 40 30
24 20 16 14 12 10 8
Altmans Normogram
Power
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.0 1.1 1.2
0.995 0.99 0.98 0.97 0.96 0.95 0.90 0.85 0.8
0 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.3
0 0.25 0.20 0.15 0.10 0.05
N
Standardized difference Min. important
difference Standard deviation
43
Example Calculation Effects of Pesticide
Study IQ survey, concerning workers exposed to
pesticides What we already know Mean IQ score
is 100 points SD is 10 points e.g. Normal
IQ 90-110 What we need to do. a) Decide on
CID. A difference of 11 IQ points seems
clinically important to me b) Calculate
Standardized Difference Min Important
Difference 11 1
Standard Deviation 10 c) Use Altmans
Normogram to observe N
44
10000 6000 4000 3000 2000 1400 1000 8000 600 500
400 300 240 200 160 140 120 100 80 70 60 50 40 30
24 20 16 14 12 10 8
Altmans Normogram - Effects of Pesticide Study
Power
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.0 1.1 1.2
0.995 0.99 0.98 0.97 0.96 0.95 0.90 0.85
0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35
0.30 0.25 0.20 0.15 0.10 0.05
N
Standardized difference Min. important
difference Standard deviation 1.1 11
10
45
2. Electronic Calculation of Sample Size Not
covered in most stats packages e.g. SPSS,
Statistica Many sites available Real time
calculation Hyperstat by David M Lane
www.davidmlane.com Other additional
software e.g. Xlstat.com
46
Summary of Sample Size Power Correct sample
size helps avoid type I type II errors A
correct study has balance of four factors Power
(no less than .80) Bigger Better study Min.
clinical difference (effective difference) Bigger
Better study Standard deviation (variability)
Smaller Better study Significance level
(0.05) Smaller Better study Looking for
big differences much easier than smaller
differences
fixed
fixed
47
Deploying Participants Deployment is crucial
(as important as sampling correctly) Deployment
is only really an issue in natural experiments
e.g lab work or clinical trials
Independent Subjects Matched Subjects Repeated
Subjects
Determined by subject matter, environment,
economics, organization
48
Deploying Participants INDEPENDENT
SUBJECTS Subjects in x groups, who are measured
in some way Group means compared between the x
groups MATCHED SUBJECTS (Similar to INDEPENDENT
SUBJECTS) Subjects are in x groups Each
individual subject is matched with a subject in
another group on the basis of one or more matched
variables e.g age, sex, ability REPEATED
SUBJECTS / MEASURES Use one group only Subjects
are measured more than once (e.g. start, during
and after) Any Differences / changes within
themselves are looked at
49
Independent Design Subjects in x
groups Measured in some way and compared with
another of the x groups Comparing 2 groups is
easiest But can compare more than 2 groups e.g
comparing a high exposure group with a low
exposure group
50
Matched Design Similar to INDEPENDENT
SUBJECTS Subjects are in x groups, and each
individual subject is matched with a subject in
another group Matched on the basis of one or
more matched variables e.g age, sex, ability,
IQ, health status Interested in controlling for
prognostic factors
51
Repeated Design Uses one group only Subjects
are measured more than once on different
occasions The differences between individuals
themselves in time are compared Comparison is
still based on the group means not individual
scores Looking at differences in people over a
set time period e.g. time 1 and time 2
mean ?
mean ?
52
Example 1 - Independent Design
Workers exposed to pesticide versus controls (not
exposed to pesticide)
Independent T test
53
Example 2 - Matched Design Workers exposed to
pesticide versus controls not exposed to pesticide
Paired Samples T test
54
Example 3 - Repeated Design Workers before and
after exposure to pesticide
Independent T test
N numbers doubled from independent
methods Repeated subjects is efficient
55
Sampling Deployment RANDOM SAMPLING Selecting
a sample from the POPULATION Related to the
EXTERNAL VALIDITY of the research, Related to
the GENERALIZABILITY of the findings to the
POPULATION RANDOM ASSIGNMENT How to assign the
sample into different treatments or
groups Related to the INTERNAL VALIDITY of the
research Ensures groups are similar (EQUIVALENT)
to each other prior to TREATMENT Both RANDOM
SAMPLING and RANDOM ASSIGNMENT can be used
together, or singularly, or not all Waste of
time randomly sampling but not randomly
allocating Having a choice in this matter is a
luxury
56
Restrictions on Methods Study may involve
clinical interventions No controls may be
available for a comparison e.g all workers are
exposed e.g all participants male e.g. all
participants need treatment Data may be
retrospective Data collection may be made by
other parties
57
Power Hierarchy of Study Designs Best - Repeated
Subjects / Repeated Measures comparing like with
like each subject stays the same in other
factors reduces the need for covariate adjustment
in analyses doubles the number of
subjects Middle - Matched subjects important
factors are matched between groups unmatched
covariates still need to be adjusted for not
comparing like with like in all respects Weakest
- Independent subjects comparing groups which may
be vastly different covariate adjustment is
needed need to use strict exclusion criteria in
order to maintain comparability
58
Final Points Bias Avoiding bias is a good aim
to have Not necessarily everything in
research Existence of some bias in a sample
does not ruin a project entirely Spector et al,
(2000) shows the inflating effect of
self-report bias may not be so prominent Mostly
leads to underestimation rather than
overestimation of any main effects Spector PE,
Chen PY, OConnell BJ. A longitudinal study of
relations between job stressors and job strains
while controlling for prior negative affectivity
and strains. Journal of Applied Psychology 2000
85 211-218.
59
Final Points Generalizability In epidemiological
investigation Basic principles Internal
validity is always more important than its
generalizability Never appropriate to
generalise an invalid finding Mant et al.
(1996) Mant J, Dawes M, Graham-Jones S.
Internal validity of trials is more important
than generalizability. British Medical Journal
1996 312 779.