Survey of Statistical Methods

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Survey of Statistical Methods

• Monday, March 28, 2005

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Sample Problem

• A physiologist has conducted an experiment to
  evaluate the effect of 3 different concentrations
  of a hormone X on aggressive behavior. Ten rats
  were randomly assigned to one of 4 conditions.
  Rats were injected with either a low
  concentration, medium concentration, or a high
  concentration of hormone X, or with a placebo
  substance. The number of aggressive encounters
  were counted over a 20-minute period. Using
  ?.05, determine how hormone X effects aggressive
  behavior.

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Sample Data
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What Hypothesis is being tested?
X
X

• H0 M µ
• H1 M ? µ

• H0 M1 M2
• H1 M1 ? M2

• H0 M1 M2 M3 M4
• H1 at least one Mi ? Mj

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Sample Data

• H0 Mcontrol Mlow Mmedium Mhigh
• H1 at least one Mi ? Mj

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What is ANOVA?

• ANalysis Of VAriance
• A method to tests hypotheses involving more than
  two means

• Developed by Sir Ronald Fisher (1890-1962)
• "To call in the statistician after the experiment
  is done may be no more than asking him to perform
  a postmortem examination he may be able to say
  what the experiment died of." Indian Statistical
  Congress, Sankhya, ca 1938

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A little ANOVA THEORY
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Sample data file hormone_study_data.sav
If the research design is between subjects. In
order to run a One-Way ANOVA, data is entered
this way
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To run the analysisAnalyze -- Compare Means --
One-Way ANOVA
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The F-ratio is robust to violation of the
assumption of homogeneity of variance if the
sample Ns are equal.
If the sample Ns are not equal you must look at
the results here. If plt.05 you have violated the
assumption.
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Creating an ANOVA Summary Table for publication
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dfnum levels of IV - 1 3
dfden (N - 1) - dfnum 36
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Obtained F 22.77
Reject H0
Accept H0
2.84

• Evaluate the outcome
• Since the obtained F falls within the critical
  region, we reject the null hypothesis

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Steps for Analysis (cont.)

• Conclusion
• Hormone X has a significant effect on aggressive
  behavior.
• In order to determine which concentration
  produces the greatest change we need to conduct a
  post-hoc analysis.

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Post-Hoc Analyses

• A test of the statistical significance of
  differences between individual group means
  calculated after obtaining a significant F-ratio.
  
• Some typical Post-Hoc analyses include
• Fisher's LSD
• Dunnett
• Newman-Keuls
• Tukey
• Scheffe Test

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Tukey HSD Procedure

• Developed in 1953
• Called Tukey HSD(Honestly Significant
  Difference)
• Designed to compare all possible pairs of means
  while maintaining the Type I error at ?.

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Controlling Type I Error

• Multiple t-tests
• H01 MP ML
• H02 MP MM
• H03 MP MH
• H04 ML MM
• H05 ML MH
• H06 MM MH
• ?familywise6(.05).30

• Tukey HSD
• H01 MP ML
• H02 MP MM
• H03 MP MH
• H04 ML MM
• H05 ML MH
• H06 MM MH
• ?familywise.05

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• H01 MP MLaccept
• H02 MP MMreject
• H03 MP MHreject
• H04 ML MMreject
• H05 ML MHreject
• H06 MM MHreject

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Steps for Analysis (cont.)

• Conclusion
• Hormone X had a significant effect on aggressive
  behavior. Figure 1 summarizes these effects.

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Sample Problem 2

• The same course is administered by 4 different
  instructors at a University. At the end of the
  semester, each student takes the same exam. The
  question is Did the students performance differ
  between instructors?
• Data is in the file instructor.sav

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Assignment for Wednesday

• Conduct an analysis of this data and bring your
  results with you to class on Wednesday.

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