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Hadley Wickham

Stat310Fin

Saturday, 24 April 2010

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!


1. Eat!

2. Final & help sessions

3. Finish off hypothesis testing

4. Other statistics opportunities

5. Feedback (TA & me)


Final


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.


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

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


http://goo.gl/mod/joIx

http://goo.gl/mod/joIx

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.


Hypothesis testing


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?


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)


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


Say is guilty

Say is innocent

Is guilty

Is innocent

CorrectFalse

acquittal

False conviction

Correct


Your turn

Which type of error is more expensive/more costly/worse in the criminal justice system?


Reject HO Accept HO

HO false

HO true

CorrectType II error

Type I error

Correct


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


α↑ β↓α↓ β↑


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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20 40 60 80 100

μx=80, μy=85


Difference

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μx=80, μy=85


|Difference|

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μx=80, μy=85


z−score

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μx=80, μy=85


p−value

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20 40 60 80 100

μx=80, μy=85

Correctly reject null 39% of the time


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μx=μy=80


difference

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20 40 60 80 100

μx=μy=80


z−score

0.0

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μx=μy=80


|difference|

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20 40 60 80 100

μx=μy=80


p−value

0.0

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20 40 60 80 100

μx=μy=80

Incorrectly reject null 6% of the time


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?


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.


Statistics


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


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


Stat410

Introduction to linear models

Powerful and general statistical tool.

Theory and data.

Offered in Fall.


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.




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)


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


Documents

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