EPI-546 Block I
Lecture 2 – Descriptive Statistics
Michael Brown MD, MSc
Professor Epidemiology and Emergency
Medicine
Credit to Michael P. Collins, MD, MS
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
1
Objectives - Concepts
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Classification of data
Distributions of variables
Measures of central tendency and dispersion
Criteria for abnormality
Sampling
Regression to the mean
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
2
Objectives - Skills
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Distinguish and apply the forms of data
types.
Define mean, median, and mode and locate
on a skewed distribution chart.
Apply the concept of the standard deviation
to specific circumstances.
Explain why a strategy for sampling is
needed.
Recognize the phenomenon of regression to
the mean when it occurs or is described.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
3
Clinical Measurement –
2 kinds of data
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Categorical
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Interval
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
4
Distinction Interval = “the interval between
successive values is equal, throughout
the scale”
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
5
Clinical Measurement –
subtypes of data
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Categorical
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Nominal
Ordinal
Interval
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Discrete
Continuous
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
6
Nominal data: no order
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Alive vs. dead
Male vs. female
Rabies vs. no rabies
Blood group O, A, B, AB
Resident of Michigan, Ohio, Indiana…
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
7
Ordinal scale: natural order,
but not interval
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1st vs. 2nd vs. 3rd degree burns
Pain scale for migraine headache:
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None, mild, moderate, severe
Glasgow Coma Score (3-15)
Stage of cancer spread – 0 through 4
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
8
Clinical Measurement –
2 kinds of data
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Categorical
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Nominal
Ordinal
Interval
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Discrete
Continuous
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
9
Discrete Interval variables:
on a “number line”
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Number of live births
Number of sexual partners
Diarrheal stools per day
Vision – 20/?
1 2 3
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
10
Continuous variables:
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Blood pressure
Weight, or Body Mass Index
Random blood sugar
IQ
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
11
Interval: Continuous vs. Discrete
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No variable is perfectly continuous – e.g. you
never see a BP of 152.47 mmHg
It’s a matter of degree – lots of possible values
within the range clinically possible = continuous
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
12
Recording data 
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Sometimes the variable is intrinsically one type
or another – but, frequently it is the observer
who decides how a variable will be measured
and reported
Consider cigarette smoking:
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
13
Continuous variable
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Underlying (nearly) continuous variable –
cigarettes/day
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32, 63, 2,…
However, this level of detail may not be
necessary or desirable.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
14
Discrete interval variable
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Packs per day (probably rounded off to the
nearest whole number)
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2, 1, 0
Cruder - but maybe good enough and more
reliably reported
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
15
Ordinal categorical variable
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Non-smoker vs. light smoker vs. heavy smoker.
May further collapse the pack/day variable.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
16
Nominal categorical variable
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Non-smoker vs. former smoker vs. current
smoker.
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No obvious order here, just named categories
Ever-smoker vs. never-smoker.
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Dichotomous outcome
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
17
So, the form of the variable is often decided by
the investigator, not by nature
In fact, the normal vs. abnormal
distinction is generally a matter of
taking a much richer measure and
making it dichotomous.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
18
Quick Quiz Slide
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What kind of a variable is religion? – Protestant,
Catholic, Islamic, Judaism. . .
What kind is Body Mass Index (weight divided
by height2)?
What is alcohol intake if classed as none,
< 2 drinks/day, and > 2 drinks/day?
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
19
First question when meeting with statistician:
1.
Define the type of data (continuous, ordinal,
categorical, etc.)
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
20
A Few Examples of Statistical Tests
Test
Comparison
Principal Assumptions
Student's
t test
Means of
two groups
Continuous variable,
normally distributed,
equal variance
Wilcoxon
rank sum
Medians of
two groups
Continuous variable
Chi-square
Proportions
Categorical variable,
more than 5 patients in
any particular "cell"
Fisher's
exact
Proportions
Categorical variable
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
21
Objectives - Concepts






Classification of data
Distributions of variables
Measures of central tendency and dispersion
Criteria for abnormality
Sampling
Regression to the mean
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
22
Distributions of continuous variables
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A way to display the individual – to – individual
variation in some clinical measure.
Consider the example in Fletcher using PSA
levels:
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
23
Clinical Epidemiology: The Essentials, 3rd Ed, by Fletcher RH, Fletcher SW, 2005.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
24
F
r
e
q
u
e
n
c
y
x Variable
www.msu.edu/user/sw/statrev/images/normal01.gif
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
25
Clinical Epidemiology: The Essentials, 3rd Ed, by Fletcher RH, Fletcher SW, 2005.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
26
The “nicest” distribution
Is the normal, or Gaussian, distribution
– the “bell-shaped curve”.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
27
If we want to summarize a frequency
distribution, there are two major aspects to
include:
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Central tendency
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Dispersion
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
28
Principles of Epidemiology, 2nd edition. CDC.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
29
Principles of Epidemiology, 2nd edition. CDC.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
30
Measures of Central Tendency:
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Mean
Median
Mode
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
31
Consider this data: Parity (how many
babies have you had?) among 19
women:
0,2,0,0,1,3,1,4,1,8,2,2,0,1,3,5,1,7,2
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
32
Mean (Arithmetic)
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Add up all the values and divide by N
43 / 19 = 2.26
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
33
Median
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The middle value
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Must first sort the data and put in order:
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0,0,0,0,1,1,1,1,1,2,2,2,2,3,3,4,5,7,8
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
34
Mode
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The most common value
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0,0,0,0,1,1,1,1,1,2,2,2,2,3,3,4,5,7,8
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
35
In a normal distribution, all three are
equal
Parametric statistical methods assume
a distribution with known shape
(i.e. normal or Gaussian distribution)
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
36
F
r
e
q
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c
y
x Variable
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
37
Quick Quiz Slide
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If the mode is “100” and the mean is “80” –
what can you tell me about the median?
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
38
mean
mode
F
r
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q
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c
y
x Variable
80
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
100
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Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
40
Dispersion
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Standard Deviation - most common measure
used for normal or near normal distributions.
Defined by a statistical formula, but remember
that:
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The mean +/- one SD contains about 2/3 of the
observations.
the mean +/- 2 SD’s includes about 95% of the
observations.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
41
Clinical Epidemiology: The Essentials, 3rd Ed, by Fletcher RH, Fletcher SW, 2005.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
42
M J Campbell, Statistics at Square One, 9th Ed, 1997.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
43
So, how about this definition of “abnormal” for total
serum cholesterol: A value higher than the mean + 1
S.D.?
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How many people would fall beyond that cutoff?
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
44
Rose, G: The Strategy of Preventive Medicine; Oxford Press, 1998.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
45
So what’s the “best” definition of
abnormality?
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Fletcher lists three:
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Being unusual
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Sick
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Greater than 2 SD from mean
Observation regularly associated with disease
Treatable
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Consider abnormal only if treatment of the condition
represented by the measurement leads to improved
outcome
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
46
Miura et al, Archives Int Med 2001; 161:1504.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
47
If you were to design a study to define an
abnormal DBP for adult females in the US,
how would you do it?
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Measure DBP in every adult female in the US?
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Then define abnormal as above 2 SD from mean?
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
48
Sampling
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Impossible to measure the BP of everyone, so
must take measurements of a representative
sample of subjects.
Random sample
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May miss important subgroup (ethnicity for example)
May need to obtain a larger sample from these
important subgroups and select subjects at random
within subgroup
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
49
Clinical Epidemiology: The Essentials, 3rd Ed, by Fletcher RH, Fletcher SW, 2005.
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
50
Hanna C, Greenes D. How Much Tachycardia in Infants
Can Be Attributed to Fever? Ann Emerg Med June 2004
Dr. Michael Brown
© Epidemiology Dept., Michigan State Univ.
51