Statistic for the day: Chances that a doctor practicing in the US today has a foreign medical degree: 1 in 6

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Statistic for the dayChances that a doctor
practicing in the US today has a foreign medical
degree 1 in 6
Source Education Council for Foreign Graduates

• Read Chapter 10 again
• Exercises pp172-175 2, 4, 6, 9, 11, 12, 13

These slides were created by Tom Hettmansperger
and in some cases modified by David Hunter
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Thought question 2, p157
Suppose you were to make a scatter plot of adult
sons heights versus fathers heights by
collecting data from several of your male
friends. You would like to predict how tall
your nephew will be when he grows up, based on
his fathers height. Could you use your scatter
plot to help you make the prediction?
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Deterministic relationship
Value of response is exactly determined by
explanatory variable.
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Statistical relationship
Value of response only partly determined by
explanatory variable
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Another statistical relationship
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Correlation (r) Strength of linear association
r0.910
r-0.191
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Facts about Correlation

• 1 means perfect increasing linear relationship
• -1 means perfect decreasing linear relationship
• 0 means no linear relationship
• means increasing together
• - means one increases and the other decreases

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Correlation .1
9
Correlation .23
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Correlation .37
11
Correlation .58
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Correlation .7
13
Correlation .8
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Correlation .92
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Correlation .97
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Strength is not the same asstatistical
significance

• Strength of linear relationship is measured by
  correlation coefficient, r.
• Statistical significance is measured as follows

Assume that the truth is NO linear relationship.
What proportion of randomly generated
scatterplots would have a stronger linear
relationship than the one observed?
ANSWER p-value
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Strength vs. statistical significance

• Even a weak relationship can be statistically
  significant (if it is based on a large sample)
• Even a strong relationship can be statistically
  insignificant (if it is based on a small sample)

Common rule of thumb If p-value is smaller than
0.05 (five percent), then the result is
considered statistically significant.
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Correlation (r) Strength of linear association
r0.910
r-0.191
p-value 0.0896
p-value 0.0036
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Ave number of words a child knows at various ages
Imagine a scatter plot of the average number Of
words a child knows for ages about 1.5 to 6
. Relationship is nearly linear and quite strong.
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Note the problem of extrapolation here. At age 1,
ave 3, but predicted is 251!! Extrapolation
occurs when you try to predict beyond the range
of the explanatory variable
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PA Election Fraud
Special election to fill state senate seat in
1993. William Stinson (D) received 19,127
machine counted votes Bruce Marks (R) received
19,691 machine votes Stinson got 1,391 absentee
votes Marks got 366 Stinson wins by 461
votes Question Is this an unusual number of
absentee votes?
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Dem minus Rep vote counts (positive means D ahead
etc.) For absentee versus machine
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R wins machine D wins absentee