ANOVA

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ANOVA
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Independent ANOVA

• Scores vary why?
• Total variability can be divided up into 2 parts
• 1) Between treatments
• 2) Within treatments

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Between design
Total variability
Within treatments Individual differences Experim
ental error
Between treatments Treatment effect Individual
differences Experimental error
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• F variance between treatments
• variance within
• F treatment indiv diffs error
• indiv diffs error

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INDEPENDENT ANOVA assumptions

• the observations within each sample must be
  independent
• 2) the populations from which the samples were
  selected must be normal
• 3) the populations from which the samples are
  selected must have equal variances (homogeneity
  of variance)
• Same assumptions for t test

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• F measures variance which is standard deviation
  squared
• F (differences between sample)2
• (differences expected by chance)2
• F t2

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Figure 1 Mean calories in hotdogs
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Post hoc test
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• Information about the purpose of the experiment.
• The number of participants.
• Descriptive Statistics (effect size more later)
• Analysis result
• Post hoc differences

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• The difference in calories between beef,
  (n20), meat (n17) and poultry (n17) hotdogs
  was tested. Mean calorie level was determined for
  each hotdog type, beef 156.85 (22.64), meat
  158.71 (25.24) and poultry 118.76 (22.55).
  Confidence intervals for the means in each group
  are shown in figure 1.The calorie level varied
  between the hotdog types F(2,51) 16.07, plt.05.
  MS 8846. Post hoc test show poultry had fewer
  calories than both meat (LSD -38 plt.05) and beef
  (LSD -39.9 plt.05).

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APA To examine the effects of memory training on
retention of words, 20 college students were
randomly assigned to four training conditions
(n5) defined by the instructions to
participants story method, imagery method thyme
method, and control (no specific instructions).
Mean recall out of a possible 20 words (and the
sample standard deviation) were for each of the
conditions story 13.2(1.3), imagery 14.4 (1.8),
rhyme 13.4 (1.3) and control 10.0 (1.6).
Confidence intervals for the means in each group
are shown in figure 1. Mean recall differed
significantly among the four instruction
conditions, F(3,16) 7.8, plt.05. MS Post
hoc test show.
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Repeated Measures ANOVA
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Total variability
Between treatment variability Treatment
effect Experimental error
Within treatment variability Individual
differences Experimental error
Error variability Experimental error
Between subject variability Individual differences
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• F treatment effect experimental error
• experimental error

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Figure 1 Mean Anxiety by Trial Number
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F(3,33) 127.56
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assumptions