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Biostatistics in Practice
Session 2:
Quantitative and Inferential Issues II
Youngju Pak
Biostatistician
http://research.LABioMed.org/Biostat
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What we have learned in Session 1?
 Basic Study Design
 Parallel vs., Cross-over Designs?
 Categorical vs., Quantitative Data? Why
important?
 Summarizing the data with graphs:
Contingency Tables, Box Plots, Histogram,
etc.
 How to run MYSTAT
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Today’s topics
 Article : McCann, et al., Lancet 2007 Nov
3;370(9598):1560-7
 Descritive Statistics vs. Inferential Statistics
 Normal Distributions
 Confidence Intervals & P-values
 Correlations
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McCann, et al., Lancet 2007 Nov 3;370(9598):1560-7
 Food additives and hyperactive behaviour in 3-yearold and 8/9-year-old children in the community: a
randomised, double-blinded, placebo-controlled trial.
 Target population: 3-4, 8-9 years old children
 Study design: randomized, double-blinded, controlled,
crossover trial
 Sample size: 153 (3 years), 144(8-9 years) in
Southampton UK
 Objective: test whether intake of artificial food color
and additive (AFCA) affects childhood behavior
McCann, et al., Lancet 2007 Nov 3;370(9598):1560-7
 Sampling: Stratified sampling based on SES in Southampton, UK
 Baseline measure: 24h recall by the parent of the child’s pretrial diet
 Group: Three groups, for 3 years old
– mix A : 20 mg of food colorings + 45 mg sodium benzoate, which is a widely used
food preservative
– mix B : 30mg of food coloring + 45 mg sodium benzoate(current average daily
consumption)
– Placebo
– For 8/9 years old: multiply these by 1.25
 Cross-over Design
Typical Diet
T0 (baseline)
Week 1
Randomize
Week 2
Washout
Week 3
Randomize
Week 4
Washout
Week 5
Randomize
Week 6
 A participants receive one of 6 possible random sequences. In a separate study with
N=20, no significant difference in looks and taste of drinks among three groups was
found even though people ask about which diet type they got when they received
placebo (65%) > mix B (52%) > mix A (40%)
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McCann, et al., Lancet 2007 Nov 3;370(9598):1560-7
 Outcomes: Global Hyper Activity(GHA) Score
 Attention-Deficit Hyperactivity Disorder(ADHD)
rating scale IV by teachers, scaled 1 – 5, higher number
means more hyperactive
 Weiss-Werry-Peters(WWP) hyperactivity scale by
parents,
 Classroom observation code,
 Conners continuous performance test II (CPTII)
 GHA to be aggregated from these four scores
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Non-Completing or Non-Adhering Subjects
Non-response bias?
Societal effect vs. Scientific effect ?
Efficacy vs. Effectiveness ?
Describing the sample
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Describing the findings w/ descriptive statistics
GHA= (post –pre)/standard deviation (SD) for pre-scores
What was your research question ?
Did you get answer for that that research questions from
this table? Why or Why not?
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Describing the findings w/ inferential statistics
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Describing the findings w/ Graphs
using confidence intervals
The Life Cycle of a Research Study
With Statistical Applications
Population parameter
Population
Sampling mechanism:
random sample or
convenience sample
Sample
Confidence
Interval
for
population
parameter
Sample
estimate of
population
parameter
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So why use a sample?
 Often the population is too large to obtain data
 Saves time and money
 All members of the population may be difficult to contact
Parameter vs. Statistic
 A parameter is a numerical description of a
population characteristics
e.g., μ (called as”mu:”): population mean,
σ2 (called as “sigma square”): population
variance
 A statistic is a numerical description of a sample
characteristics
e.g., m: sample mean, S2 : sample variance
Branches of Statistics
•
Descriptive statistics involves the organization,
summarization, and presentation of the sample.
e.g., sample means, sample standard
deviations, histograms, box plots, etc.
•
Inferential statistics involves using a sample to draw
conclusions about a population.
e.g., confidence intervals, p-values, etc.
3 questions
that statisticians attempt to answer
• How should I collect my data ?
- Study design, sample size, statistical power.
• How should I analyze and summarize the data
that I’ve collected ?
- displaying the data, descriptive statistics,
statistical tests
• How accurate are my data summaries ?
-Inferences: confidence intervals, p-values
Mean vs. Median
(measure the central tendency)
• Mean
– What most people think
of as “average”
– Easy to calculate
– Easily distorted
– Be cautious with
SKEWED data
– Calculate:
sum of data / number of
data points
• Median
– Relatively easy to obtain
– Not affected by extreme
values so it is considered
a “ROBUST” statistic
– Calculate:
• Sort data
• If odd number points,
the middle is the
median
• Otherwise, the
median is the average
of the middle two
numbers
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Standard Deviation (SD) &Inter-Quartile Range(IRQ)
(measuring the variability of the data )
•
Inter-Quartile Range (IQR)=
75th percentile (Q3) - 25th percentile(Q1)
, where 25% of the data <Q1 , 75% of the data < Q3
•
SD is usually used for the normally distributed data
(bellshape, symmetric around the mean)
IQR is usually used when the data distribution is skewed.
Range = Max -Min
•
•
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Checking for the normality
• Symmetric.
• One peak.
• Roughly bell-shaped.
• No outliers.
Many statistical tests assume outcome
variable follow the normal distribution
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Other properties of the normal
distribution
For bell-shaped distributions of data
(“normally” distributed):
• ~ 68% of values are within mean ±1 SD
• ~ 95% of values are within mean ±2 SD
“(Normal) Reference Range”
• ~ 99.7% of values are within mean ±3 SD
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Histograms: Not OK for Typical Analyses
Skewed
Multi-Peak
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Frequency
20
100
50
0
10
0
0
1
2
3
4
5
6
7
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Intensity
Need to transform
intensity to another scale,
e.g. Log(intensity)
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70
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Tumor Volume
Need to summarize
with percentiles, not
mean.
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Summary Statistics:
Two quantitative Variables
(Correlation)
• Always look at scatter plot.
• Correlation, r, ranges from -1 (perfect inverse
relation) to +1 (perfect direct), Zero=no
relation.
• Specific to the ranges of the two variables.
• Typically, cannot extrapolate to populations
with other ranges.
• Measures association, not causation.
.
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Correlation Depends on Range of Data
A
B
Graph B contains only the points from graph A that are in
the ellipse.
Correlation is reduced in graph B.
Thus: correlation between two quantities may be quite
different in different study populations.
 Do not extrapolate
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Confidence Interval (CI)
• How well your sample mean(m) reflects the
true( or population) mean  How
confident?  95%?
• A confidence interval (CI) is one of
inferential statistics that estimate the true
unknown parameter using interval scales.
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Confidence Interval for Population Mean
95% Reference range or “Normal Range”, is
sample mean ± 2(SD)
_____________________________________
95% Confidence interval (CI) for the (true, but
unknown) mean for the entire population is
sample mean ± 2(SD/√N)
SD/√N is called “Std Error of the Mean” (SEM)
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Confidence Interval: Case Study
Table 2
Confidence Interval:
Adjusted
CI
0.13
-0.12
-0.37
-0.14 ± 1.99(1.04/√73) =
-0.14 ± 0.24 → -0.38 to 0.10
close to
Normal Range:
-0.14 ± 1.99(1.04) =
-0.14 ± 2.07 → -2.21 to 1.93
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P-values !
• Used the evidence of contradiction to your
null hypothesis (H0)
– e.g., H0 : no difference in mean GHA scores
among three different diet.
• Based on the statistical test
– Eg., T test statistics = Signal / Noise
– if Signal >> Noise  statistically significant
• Usually p < 0.05 called as “statistically
significant” in favor of Ha
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Units and Independence
Experiments may be designed such that each
measurement does not give additional independent
information.
Many basic statistical methods require that
measurements are “independent” for the analysis
to be valid.
In mathematics, two events are independent if and
only if the occurrence of one event makes it
neither more nor less probable that the other
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occurs.
Experimental Units in Case Study
What is the experimental unit in this study?
1. School
2. Child
3. Parent
4. GHA score (results from three diets)
Are all GHA scores(eg. 153 x 3 groups=459 GHA
scores for 3-4 years old children) independent?
The analysis MUST incorporate this possible
correlation (clustering) if there exists.  eg.,
Mixed Model allowing for clustering due to
schools.
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Announcements
• Keys for HW1 and HW 2 will be posted on
class website by Wednesday.
• Next session will be held in Oct 15 at RB-1
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