Stat 401 Lab October 10, 2005

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Stat 401 LabOctober 10, 2005

• James D. Abbey
• Iowa State University

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Contact Information

• James Abbey
• Email jdabbey_at_iastate.edu
• Website www.public.iastate.edu/jdabbey
• Office and Office Hours
• 306 Snedecor Hall
• M and F 1000-1030
• Th 200-300

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Homework

• Schedule for today
• Homework 6
• Brief Review for Homework 5
• Questions? Ask away!

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Homework 6

• HW6 Concepts
• ANOVA. Yes, you will learn to love ANOVA (or at
  least learn how to use ANOVA).
• When do you need ANOVA?
• Hand calculations ? until you get to use SAS or
  JMP, you had best keep your calculator batteries
  charged
• Calculating the pooled standard error is the same
  as before only expanded.
• The pooled standard error is also called the MSE
  or MSW

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Homework 6

• When do you need ANOVA?
• When you are comparing more than two
  treatments/groups. How would you do a t-test on
  the treatments A, B, C, , Z?
• Pairwise t-tests? That would be r-choose-2
  tests! For the above example, you would need 325
  comparisons! Look ahead What is our error rate
  for each test? Need corrections such as
  Tukey-Kramer.
• Even with adjustment, you would lose information
  ANOVA can provide.
• Still have the assumptions of normality, equal
  variance and independence. Outliers are
  dangerous to the first two assumptions.

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Homework 6

• Note Dr. Carageas Handouts
• The One-Way Analysis of Variance (ANOVA) Table
• http//www.public.iastate.edu/pcaragea/S401F05/Ha
  ndouts/wanova.pdf
• My notation will primarily be based off of this
  handout
• The F-Test as a Comparison of Full and Reduced
  Models
• http//www.public.iastate.edu/pcaragea/S401F05/Ha
  ndouts/FullvsRed.pdf

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Homework 6

• How do you fill in an ANOVA table?
• First, fill in the degrees of freedom
• I-1 d.f. for the treatments, where I is the
  number of treatments
• n-I d.f. for the error, where n is the number of
  sample units
• n-1 d.f. for the total
• Second, if no other information is provided, you
  will have to hand calculate the SS. Use the
  formulas provided on The One-Way Analysis of
  Variance (ANOVA) Table (link on prior page)

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Homework 6

• How do you fill in an ANOVA table?
• Second step alternatives
• Back out SS/MS by playing with the equations.
• Note that SSTotal SSBetween SSWithin
• Alternatively, SSTotal SSModel SSError
• Note that you need only calculate two of the
  values to get the third
• If you have the MSError or MSWithin and d.f.
  error or d.f. within
• SSE MSE d.f. error or SSW MSW d.f. within
• Note the mathematical relationships!
• SSB and MSB (SSB MSB d.f. between)
• SSE and MSE or SSB and SSE (above)

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Homework 6

• How do you fill in an ANOVA table?
• The F-Test
• F MSB/MSW or FMSModel/MSError
• Ho All treatment means equal
• Ha at least one treatment mean different from
  the others
• Note that with the F-Distribution, we do not
  double the p-value. The F-statistic is a ratio
  of chi-squares. Hence, find F comparison value
  from the table using the numerator (treatment
  d.f.) and denominator (error d.f.).

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Homework 6

• Summary of the ANOVA Table
• Note the d.f. between I-1 and d.f. within
  n-I
• is the grand mean or mean of all observed
  means.

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Homework 6

• The MSE Sp2
• See your text page 121 for a nice expansion of
  the MSE Sp2 formula
• The same formula in a compact form
• Hint On question 2, your Sp should be pooled
  for ALL the treatments in the study even for the
  two-sample t-tests. Your SE for each test will
  be based on each tests sample sizes.

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Homework 6 Summary

• Steps in ANOVA 1) d.f. 2) SS 3) MS 4) F-Stat
  5) p-value
• If you are given an MS value, you can back out
  information without hand calculation. Remember
  the relationships!
• MSE Sp2 (see page 121 of your text)
• Again, note the relationships between SS, MS and
  their d.f.!

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Homework 6 Hints

• Question 1
• You do not need to calculate all of the values
  using the summation formulas! You have SSB.
  Find the d.f. between. Next, get MSB. Remember,
  SSTotal SSB SSW.
• Question 2
• Remember, Sp2 is the same for all the tests,
  including the t-tests. Your SE for the pairwise
  comparisons will vary.
• Question 3
• Get that calculator going!

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Homework 5 Review

• Summary
• T-tests are not always feasible even when you
  have two samples or pre-differenced data check
  the assumptions
• Signed Rank tests are for single samples tests
  (e.g., pre-differenced pairs)
• Rank Sum is a two-sample test (e.g., Treatment A
  and Treatment B not on the same unit)
• The Sign Test (page 99)
• Works for two-sample (e.g., question 1 on HW5) or
  pre-differenced data
• Lower power than the other tests