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Experimental Design - Statistical Analysis - Practice Exam | STAT 401, Exams of Statistics

University of Idaho (U of I)Statistics
Prof. Brian C. Dennis

Material Type: Exam; Professor: Dennis; Class: Statistical Analysis; Subject: Statistics; University: University of Idaho; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

koofers-user-hcs
koofers-user-hcs 🇺🇸

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Experimental design
Randomization: assigning experimental units to
treatments at random
• Eliminates conscious or unconscious bias in
assigning units to treatments
• Spreads variability
Random sample: each of items is equally likely toR
appear in a sample of size 8
• Observational study: permits valid inferences about
population parameters
• Experimental study: that (above), plus serves as a
method of randomization (assign units to83
treatment )3
pf3
pf4
pf5

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Experimental design

Randomization: assigning experimental units to treatments at random

ï Eliminates conscious or unconscious bias in assigning units to treatments

ï Spreads variability

Random sample: each of R items is equally likely to appear in a sample of size 8

ï Observational study: permits valid inferences about population parameters

ï Experimental study: that (above), plus serves as a method of randomization (assign 83 units to treatment 3 )

Randomization algorithms

A. Shuffling method

  1. Label the units 1 to R
  2. Generate R uniform 0, 1a brandom variables and associate each one with the unit labels 1? (^) " 2? (^) # 3? (^) $ ã R? (^) R
  3. Sort the observations by the uniform variable
  4. Pick the first 8 observations in the sorted data

B. Fast method (one pass through the data)

  1. Read the next unit label and make it current
  2. Generate Y μ uniform 0, 1a b
  3. Test if R Y + 8. If yes, go to step 6
    1. Include current label in sample
    2. Set R œ R - 1 and 8 œ 8 - 1
    3. If 8 +0 go to step 1; otherwise terminate
  4. Skip over current label
    1. Set R œ R -1 and go to step 1

(Vitter, J. S. 1984. Faster methods for random sampling. Communications of the ACM 27:703-718)

ex. Estimating : in a binomial a8 : , bsample

s : „ D

:s - :s !Î# 8

Ê

a 1 b

Guess : (or take : œ "# as worst case)

I œ D (^) !Î# :^8 -: Ê pick 8 œ I

D : -: É a^ b^ 1 !Î## a^1 b

Hypothesis tests: typically in the form

H :! ) œ)! ( ) a parameter)

H :a ) Á )!

Test statistic W : reject H (^)! ifW -

Under H , has a etc. depending on

t distribution F distribution chi-square dist

! W

Ú

Û

Ü

application. But what is the distribution of W if Ha is true?

has a

noncentral t distribution noncentral F distribution noncentral chi-square dist

W

Ú

Û

Ü

Noncentral distributions depend on:

sample size

k ) - )!k, the effect size

Design strategy: fix the effect size one wants to be able to detect, and fix 1 - " (the power of the test); solve for the sample size that ìmakes it soî.

In SAS: inverse distribution functions (for calculating critical values) and noncentral distributions are library functions

TINV( :< .0, , - ) PROBT( ,B .0 , - ) FINV( :< .0, (^) " , .0 (^) # , - ) PROBF( ,B .0 (^) " , .0#, - ) CINV( :< .0, , - ) PROBCHI( ,B .0 , - )

Here, - is the ìnoncentrality parameterî which is related to the effect size (formula for - varies between applications).