Análisis de anova

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Chapter 17: Two-way ANOVA

In the lecture on one-way ANOVA, we discussed the following experiment:
• Observe an emergency alone
• Observe an emergency w/ 1 other
• Observe an emergency w/ 2 others

|P + 2 people |P + 1 person |P + 0 people |
|[pic]2= 9 |[pic]1= 8|[pic]0= 3 |

In this experiment, we have ONE IV: the # of bystanders present

What if we wanted to look at other IVs too?

EX: Would the amount of time people wait to help be affected by the gender of the person in need of help?
Let’s do an experiment where we stage an emergency situation:

IV1: The victim of the emergency is either male OR female

IV2: The Pwitnesses the emergency alone, w/ 1 other, OR 2 others

These two IVs are “crossed,” meaning that each level of one IV is paired with all levels of the other IV

Put another way, we have all possible combinations of the IVs

| |P + 2 people |P + 1 person |P + 0 people |
|Male victim|[pic]= 9 |[pic]= 8 |[pic]= 3 |
|Female victim |[pic]= 4 |[pic]= 4 |[pic]= 2 |

Vocabulary

Factor = Independent variable

Two-factor ANOVA / Two-way ANOVA: an experiment with 2 independent variables

Levels:number of treatment conditions (groups) for a specific IV

Notation

3 X 2 factorial = experiment w/ 2 IVs: one w/ 3 levels, one w/ 2
levels

2 X 2 factorial = experiment w/ 2 IVs: both w/ 2 levels

3 X 2 X 2 = ????

Why do a two-factor (two-way) ANOVA?

1. Greater generalizability of results

--EX: If experiment is only done with a male victim, we don’t know if theresults are also true for female victims

2. Allows one to look for interactions

--The effect of one IV depends on the level of the other IV

--EX: Sample of patients who have an infection:
¼ get antibiotics and are not allergic
¼ don’t get antibiotics and are not allergic
¼ get antibiotics and are allergic
¼ don’t get antibiotics and are allergic--Measure how well the patients feel the next day
[pic]

This illustrates an interaction
[pic]

If there were no interaction, then the graph would have looked like this
Let’s return to our bystander intervention experiment:

| |P + 2 people |P + 1 person |P + 0 people|
|Male victim |[pic]= 9 |[pic]= 8 |[pic]= 3 |
|Female victim |[pic]= 4 |[pic]= 4 |[pic]= 2 |

When we do a two-way ANOVA, we will obtain three different statistical tests:

1. Maineffect of IV1: Gender of Victim
2. Main effect of IV2: # of Bystanders Present
3. Interaction b/n the two IVs (gender & # of bystanders)

Each is a hypothesis test:

Gender Main Effect:
H0: all levels of gender have the same mean
H1: all levels of gender do not have the same mean

Bystander Main Effect:
H0: all levels of bystander have the same mean
H1: alllevels of bystander do not have the same mean

Interaction:
H0: there is no interaction between the factors
H1: there is an interaction between the factors

Main Effects

Defined: The effect of ONE IV on the DV averaged across the levels of the other IV

In our example:

--Main effect of gender: Is there a difference in response time for male versus female victims,...
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