Stats for Medical Students

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Statistics
Or How to make the numbers say whatever you want.
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Announcements
Free Pizza Lunch with Faculty Jordan Hall 4th
floor lounge Congrats to the four individuals
who were successful in the syllabus challenge
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Manipulating Numbers
There are lies, damned lies, and statistics --
Disraeli
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Why use statistics?
Anecdotal evidence is unreliable
Why does the phone always ring when youre in the
shower?
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Why use statistics?
Determining the difference between chance and
real effects
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Signal and Noise
Data Signal Noise Signal What were trying
to measure Noise Error in our measurement
If noise is random, then as the sample size
increases, noise tends to cancel, leaving only
signal.
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The elusive 'average'
Mean arithmetic average ?x/n Median the
halfway point Mode the most common answer
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The elusive 'average'
1
3
3
2
2
2
Mean 4.8 Median 3 Mode 2
4
4
27
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The elusive 'average'
0
5
4
3
2
1
Mean 7.5 Median 4 Mode 27
6
27
27
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The elusive 'average'
1
23
2
2
1
1
Mean 10.7 Median 2 Mode 1
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26
27
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Variability
Range Overall difference between the highest
and lowest scores. Variance Average difference
from the mean.
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Variability
Identical Range
1 9 9 9 9 9 11 11 11 11 11 19
1 1 1 1 1 1 19 19 19 19 19 19
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Variability
Identical Variance
1 9 9 9 9 9 11 11 11 11 11 19
6 6 6 6 6 7 13 14 14 14 14 14
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Distributions
The Normal Curve
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Distributions
Central Limit Theorem
Any time you have a measure which is created by
summing several individual trials of data (Signal
Noise) you will end up with a normal curve
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Signal and Noise
Regression to the mean
On any given free throw, Bob has an 80 chance of
making it.
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Distributions
Bimodal Distributions
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Distributions
Skewed Distributions
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Distributions
Uniform distributions
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The P value
P value -- The probability that a particular set
of data was gained by chance alone. Statistical
Significance Any P value of less than .05
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The Correlation
Correlation measures the strength of a
relationship between two variables.
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The Correlation
Positive Correlation 0 lt R lt 1
No Correlation R 0
Negative Correlation -1 lt R lt 0
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The Correlation
Correlation does not imply causation
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The Correlation
Correlations can be misleading!!!
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The Right Statistic
A person wearing red is 129 times more likely to
be gored by a charging bull!
But what is the base rate?
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The Right Statistic
Mean 275 minutes
Mean 53 minutes
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The Right Statistic
98 of Americans have internet access available.
The average temperature in Oklahoma City over the
past 100 years is 63.4 degrees. (and each year
has been within 1 degree of that average)
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The Right Statistic
Consumer spending on prescription drugs has
doubled since 1980.
85 of all car accidents occur within 10 miles of
the home.
10 times as many people die each year by plane
crashes than train crashes.
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The Right Statistic
During the Spanish-American war, the death rate
for soldiers was 9 per 1000. The death rate for
civilians in New York City was 16 per 1000.
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Funny Graphs
Fluffy Os Cereal Gives a body Energy!!
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??
5
1 minute 2 minutes
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Funny Graphs
Earnings
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Funny Graphs
Earnings
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Funny Graphs
Even when the scale is fine, graphs can still be
deceptive
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Funny Graphs
Even when the scale is fine, graphs can still be
deceptive
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Funny Graphs
As you can see, Bob earns substantially more than
Joe
Joes income
Bobs Income
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Funny Graphs
Is it really a two to one ratio thats being
displayed?
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Funny Graphs
Percent of US income going to federal taxes
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Funny Graphs
Percent of US income going to federal taxes
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Where's the control?
Tylenol is used by 90 doctors for their own
aches and pains!
So are Asprin, Ibuprofen, and Bayer!
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Semi-attached Numbers
When Dewey was elected Governor in 1942, the
minimum teachers salary in some districts was as
low as 900 per year. Upon Governor Deweys
recommendation the Legislature in 1947
appropriated 32,000,000 out of state surplus to
provide an increase in teachers salaries. As a
result, the minimum salaries of teachers in New
York City range from 2500 to 5325.
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Semi-attached Numbers
1) Stanford is the 1 program in psychology 2) I
am the only (and therefore 1) student at
Stanford studying Decision Errors Therefore I
am the top student studying Decision Errors in
the country.
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What drives the data
Group A I II III IV V 6.2 6.4 7.6 6.1 6.2 Group
BI II III IV V 6.1 6.3 2.2 6.0 6.2
Is Group A superior to Group B?
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Over Precise Numbers
The average American sleeps 8 hours a night The
average American sleeps 8.2 hours a night The
average American sleeps 8.2339 hours a night
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Interactions
Main Effects Effect of one independent variable
on the dependent variable Interactions When
the effectiveness of independent variable X is
influenced by another independent variable Y
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Interactions
Curing the Hiccups
Cure 1 Standing on Tiptoes Cure 2 Holding
Breath Dependent Measure Number of Hiccups
before relief
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Interactions
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Interactions
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Interactions
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Interactions
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Interactions
Real effect
No effect
False Positive (Type 1)
Find effect
Correct Hit
False Negative (Type II)
Correct Miss
Dont find effect
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Assignment 1
Critical Analysis of psychology in the popular
press 2-3 pages (double spaced, normal
font/margins) 4 articles to choose from You may
discuss the articles with classmates, but under
the honor code you must write your own analysis.
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Conclusions

• Statistics are useful for figuring out random
  noise from real effects
• 2) Numbers are not absolute, and they can be
  easily manipulated
• 3) Always scrutinize data closely, and draw your
  own conclusions.
• 4) 85 of all statistics are made up on the spot
  the rest are all wrong