You have more than two groups

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MORE COMPARISONS OF MEANS

• You have more than two groups
• and a mean (average) for each
• e.g., young 4.0,
• middle aged 5.0,
• older 4.5
• How do you determine the strength of the
  covariation?

2
Hypothesis Tests Related to Differences
Black Box
sig. tests p. value .001
H0 µ1 µ2 µ3
3
Hypothesis Tests Related to Differences
.001
1.0
Disagree
Agree
Conditional probability P (Sample Data Null is
True) Level of agreement between Null and sample
data
sig. tests p. value .001
H0 µ1 µ2 µ3
4
Hypothesis Tests Related to Differences
Looking at the averages for each box size (u1,
u2, u3), do we believe that these 3 types sell
the same?
Hmmm, is there anything else that we might like
to know about each group of sales data?
Consider the potential sales volume of three
different sizes of the same Cheerios cereal.
Okay, so is the same (or lack of) difference
occurring in the next set of comparison?
What about the variance? Lets look and see.
With the variance in sales (across stores), are
the three different comparisons the same? Why or
why not?
Lets get rid of the Black Box
What about this third set of comparisons?
sig. tests p. value .001
H0 µ1 µ2 µ3
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ANOVA

• Decomposes variance into
• treatment effects
• other factors
• unexplained factors
• Compares data to group means
• Subtracts each data point from group mean
• Squares it
• Keeps a running total of Sum of Squares

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ANOVA

• The Sums of Squares are then
• Divided by the number of groups
• (To get an estimate per group)
• Mean Squares
• MSSr SSr / df
• (variance per group)
• MSSr / MSSu F
• Total variance explainable
• F compared to F crit dfn, dfd
• if F gt F crit, difference in population

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ANOVA (continued)

• One way ANOVA investigates
• Main effects
• factor has an across-the-board effect
• e.g., age
• or involvement

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Example

• Study of movie profits
• Dependent variable
• Gross revenue in dollars continuous
• Independent variables
• Sex categorical
• Violence
• Examine predictors of profitability
• Sex, violence, interaction (sex violence)

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Example
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Main effect Sex
VIOLENCE LEVEL
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Example
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Main effect Violence
VIOLENCE LEVEL
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ANOVA

• A TWO-WAY ANOVA investigates
• INTERACTIONS
• effect of one factor depends on another factor
• e.g., larger advertising effects for those with
  no experience
• importance of price depends on income level and
  involvement with the product

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Example
15
Interaction Sex by Violence
VIOLENCE LEVEL
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Example

• Study of movie profits
• Dependent variable
• Gross revenue in dollars continuous
• Independent variables
• Sex categorical
• Violence
• Examine predictors of profitability
• Sex, violence, interaction (sex violence)

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SPSS Output

• Interpret the results

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The End