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Hadley Wickham
Stat310Fin
Saturday, 24 April 2010
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To those of you who bought your textbooks from my amazon link.
To the textbook publishers who generously sent me free copies of books.
To Kensey for suggesting chik-fil-a
Thank you!
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1. Eat!
2. Final & help sessions
3. Finish off hypothesis testing
4. Other statistics opportunities
5. Feedback (TA & me)
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Final
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FinalTake home. Two hours long. Three (double-sided) pages of notes.
Available Wednesday April 28 9am.Due Wednesday May 5, 5pm, under my door.
Ten small questions of approximately equal weight. Similar to questions from the homework/book.
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Common themes
Probability of an event.
Independence & conditioning.
Distributions: pdf/pmf, cdf, mgf, named.
Transformations.
Sampling distribution of mean and variance.
Estimation and testing.
Philosophy of gradingSaturday, 24 April 2010
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Mon, Tue, Wed, Thurs, Fri, Sat, Sun?
Morning or afternoon?
One-on-one help, plus brief revision of topics of particular interest. Suggest and vote at http://goo.gl/mod/joIx
Help sessions
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Honour code
Remember to pledge your exam, and note the time at which you started and ended.
You may refer only to your note sheets, not to the text book or old homeworks etc.
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Hypothesis testing
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Course grades
Assume I took a random sample of 20 students from each years, and that course grades are normally distributed by variance 80.
What is the distribution of difference of the two group means?
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Your turn
The average grade from 2009 was 85 and the average grade from 2010 was 90.
What is the p-value? (The probability that you’d see a difference this large or large if there really was no difference in the population means)
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1. Write down Ho and Ha (positions of defence and prosecution)
2. Figure out good test statistic (what numeric summary?)
3. Work out null distribution (distribution of innocents)
4. Calculate p-value by comparing actual value to null distribution (what proportion of true innocents look more guilty than the suspect)
5. Reject Ho if p-value smaller than cutoff
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Say is guilty
Say is innocent
Is guilty
Is innocent
CorrectFalse
acquittal
False conviction
Correct
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Your turn
Which type of error is more expensive/more costly/worse in the criminal justice system?
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Reject HO Accept HO
HO false
HO true
CorrectType II error
Type I error
Correct
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For a given test,
P(false conviction) = α = significance level
P(false acquittal) = 1 - ββ = power
What do think happens to β if you try to make α smaller?
Rates
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α↑ β↓α↓ β↑
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Cut off
Choose cut-off based on rate of false convictions.
If you want a 5% rate of false convictions, reject Ho if the p-value is less than 0.05. (This is the industry standard rate)
Can work out power.
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76
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20 40 60 80 100
μx=80, μy=85
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Difference
−2
0
2
4
6
8
10
20 40 60 80 100
μx=80, μy=85
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|Difference|
0
2
4
6
8
10
20 40 60 80 100
μx=80, μy=85
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z−score
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
20 40 60 80 100
μx=80, μy=85
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p−value
0.0
0.2
0.4
0.6
0.8
20 40 60 80 100
μx=80, μy=85
Correctly reject null 39% of the time
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76
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20 40 60 80 100
μx=μy=80
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difference
−5
0
5
20 40 60 80 100
μx=μy=80
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z−score
0.0
0.5
1.0
1.5
2.0
2.5
3.0
20 40 60 80 100
μx=μy=80
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|difference|
0
2
4
6
8
20 40 60 80 100
μx=μy=80
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p−value
0.0
0.2
0.4
0.6
0.8
20 40 60 80 100
μx=μy=80
Incorrectly reject null 6% of the time
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Your turn
The average grade from 2009 was 85 and the average grade from 2010 was 90. Would you reject the null hypothesis that the average grade was the same?
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Connection to confidence intervals
If you construct a 90% confidence interval, and it doesn’t include the parameter until the null, then the p-value must be > 1 - 0.9 = 0.1.
If the p-value is 0.08, then a 92% or greater confidence interval would include the null parameter, and a smaller confidence interval would not.
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Statistics
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Majoring3 required stat classes (Stat310, Stat405, Stat410) + 6 stat electives + calc, linear algebra, computing+ design project
Makes for a great double major. Particularly useful if you’re thinking about grad school. (Appealing to employers too)
http://statistics.rice.edu/ShowInterior.aspx?id=58
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Minoring
From next year
Three required:Track A: stat310, stat405, stat400/410Track B: stat100, stat280, stat385
Three elective:300 level+, one outside stat if it has strong statistical component
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Stat410
Introduction to linear models
Powerful and general statistical tool.
Theory and data.
Offered in Fall.
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Stat405
Project based introduction to data analysis. Lots of computing and hardly any maths.
http://had.co.nz/stat405
Offered in Fall, and next year in Spring.
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ElectivesSOCI 436 (Houston area survey), 313 (demography)
ECON 340/440 (game theory), 400 (econometrics), 475 (optimisation), 477 (math of economics), 479 (modelling)
STAT 385, 431 (more theory), 420 (process control), 421 (time series), 422 (Bayesian data analysis), 423 (bioinformatics), 453 (biostatistics), 485 (environmental)
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One form for me.
One form Xin Zhao, who most of you never met but was the TA in charge of your grading.
No form for Garrett.
Feedback
Saturday, 24 April 2010