Post on 28-Dec-2015
Practice
• Odometers measure automobile mileage. Suppose 12 cars drove exactly 10 miles and the following mileage figures were recorded. Determine if, on average, the odometers were accurate (Alpha = .05).
9.8, 10.1, 10.3, 10.2, 9.9, 10.4, 10.0, 9.9, 10.3, 10.0, 10.1, 10.2
One-sample t-test
• H1 = Mean not equal to 10• H0 = Mean = 10
• t critical (11) = 2.201• t obs = 1.86
• The odometers did not record a siginficantly different distance than what was driven.
Study
You are interested in if people like Pepsi and Coke differently. To examine this you give:
20 people regular Pepsi
20 people regular Coke
You then ask them to rate how much they liked the soda
(1 = do not like at all, 5 = like a lot).
What kind of statistic could you use?
• Two-sample t-test
• An ANOVA
But what if. . . .
• In addition to brand type you were also interested in examining diet vs. regular soda.
To examine this you give:20 people regular Pepsi20 people regular Coke20 people diet Pepsi20 people diet Coke
You then ask them to rate how much they liked the soda (1 = do not like at all, 5 = like a lot).
Factorial Design
• Research design that involves 2 or more Independent Variables– Involves all combinations of at least 2 values of 2 or
more IVs
Factorial Design
Coke
Regular
Pepsi
Diet
2 X 2 Factorial Design
Diet Pepsi Diet Coke
Regular CokeRegular Pepsi
Factorial Design:Influences on Ratings of Attractiveness
Does individuals’ gender or age influence their ratings of a woman’s attractiveness?
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult2 X 2 Factorial Design
Factorial Design:Influences on Ratings of Attractiveness
Ethnicity
Gender
Male
Female
Euro-American African AmericanMexican American
Factorial Design:Influences on Ratings of Attractiveness
Ethnicity
Gender
Male
Female
Euro-American African American
2 X 3 Factorial Design
Mexican American
Factorial Design:Influences on Ratings of Attractiveness
Ethnicity
Gender
Male
Female
Euro-Amer African AmerMexican AmerAge Adults
Adolescents
Factorial Design:Influences on Ratings of Attractiveness
Ethnicity
Gender
Male
Female
Euro-Amer African Amer
2 X 2 X 3 Factorial Design
Mexican AmerAge Adults
Adolescents
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
2 X 2 Factorial Design
Factorial Design:Influences on Ratings of Attractiveness
• Rate the attractiveness of the woman in this picture on a scale from 1-10 (10 is most attractive)
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
2 X 2 Factorial Design
Average score of
8
Average score of
10
Average score of
9
Average score of
4
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
8.5 7
Average score of
8
Average score of
10
Average score of
9
Average score of
4
9
6.5
Factorial Design:Main Effects
• Main effects are the effects of one independent variable in an experiment (averaged over all levels of another independent variable)
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
8.5 7
Average score of
8
Average score of
10
Average score of
9
Average score of
4
9
6.5
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
8.5 7
Average score of
8
Average score of
10
Average score of
9
Average score of
4
9
6.5
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
8.5 7
Average score of
8
Average score of
10
Average score of
9
Average score of
4
9
6.5
Factorial Design:Interactions
• When the effect of one independent variable depends on the level of another independent variable
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
8.5 7
Average score of
8
Average score of
10
Average score of
9
Average score of
4
9
6.5
Factorial Design:Influences on Ratings of Attractiveness
Ratings of Attractiveness
0
2
4
6
8
10
12
1 2
Ag
Att
ract
iven
ess
Sco
re
Series1
Series2
Male Female
Males
Females
AgeAdolescents Adults
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
2 X 2 Factorial Design
Average score of
8
Average score of
10
Average score of
10
Average score of
8
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
9 9
Average score of
8
Average score of
10
Average score of
10
Average score of
8
9
9
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
9 9
Average score of
8
Average score of
10
Average score of
10
Average score of
8
9
9
Factorial Design:Influences on Ratings of Attractiveness
Ratings of Attractiveness
0
2
4
6
8
10
12
1 2
Ag
Att
ract
iven
ess
Sco
re
Series1
Series2
Male Female
Males
Females
AgeAdolescents Adults
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
2 X 2 Factorial Design
Average score of
8
Average score of
10
Average score of
6
Average score of
8
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
7 9
Average score of
8
Average score of
10
Average score of
6
Average score of
8
9
7
Factorial Design:Influences on Ratings of Attractiveness
Age
Gender
Male
Female
Adolescent Adult
7 9
Average score of
8
Average score of
10
Average score of
6
Average score of
8
9
7
Factorial Design:Influences on Ratings of Attractiveness
NO Interaction
Ratings of Attractiveness
0
2
4
6
8
10
12
1 2
Ag
Att
ract
iven
ess
Sco
re
Series1
Series2
Male Female
Males
Females
AgeAdolescents Adults
Factorial Design:Another Example
• A researcher is interested in studying the effects of relationship status (single, cohabitating, married) and age (30s or 40s) on individuals’ ratings of satisfaction with life
Factorial Design:Another Example
• A researcher is interested in studying the effects of relationship status (single, cohabitating, married) and age (30s or 40s) on individuals’ ratings of satisfaction with life
– What is the Dependent Variable?
– What are the Independent Variables?
– What kind of a design is this?
Factorial Design:Another Example
• A researcher is interested in studying the effects of relationship status (single, cohabitating, married) and age (30s or 40s) on individuals’ ratings of satisfaction with life
• This is the data that is collected (average scores per group with scores ranging from 1 –10, most satisfied):
Age
30s
40s
Single Cohab MarriedRelationship Status
8 9 10
9 8 7
Factorial Design:Another Example
Age
30s
40s
Single Cohab MarriedRelationship Status
8 9 10
9 8 7
8.5 8.5 8.5
9
8
Factorial Design:Another Example
Age
30s
40s
Single Cohab MarriedRelationship Status
8 9 10
9 8 7
8.5 8.5 8.5
9
8
Factorial Design:Another Example
Age
30s
40s
Single Cohab MarriedRelationship Status
8 9 10
9 8 7
8.5 8.5 8.5
9
8
Factorial Design:Another Example
• A researcher is interested in studying the effects of marital status (single, cohabitating, married) and age (30s or 40s) on individuals’ ratings of satisfaction with life
• This is the data that is collected (average scores per group with scores ranging from 1 –10, most satisfied):
Influences on Life Satisfaction
0
2
4
6
8
10
12
1 2 3
Marital Status
Sco
re o
n L
ife
Sat
isfa
ctio
n
Mea
sure
Series1
Series2
30s
40s
single cohab married
Practice
• 2 x 2 Factorial
• Determine if
• 1) there is a main effect of A
• 2) there is a main effect of B
• 3) if there is an interaction between AB
Practice
0123456789
10
B1 B2
A1
A2
A: NO
B: NO
AB: NO
Practice
0123456789
10
B1 B2
A1
A2
A: YES
B: NO
AB: NO
Practice
0123456789
10
B1 B2
A1
A2
A: NO
B: YES
AB: NO
Practice
0123456789
10
B1 B2
A1
A2
A: YES
B: YES
AB: NO
Practice
0123456789
10
B1 B2
A1
A2
A: YES
B: YES
AB: YES
Practice
0123456789
10
B1 B2
A1
A2
A: YES
B: NO
AB: YES
Practice
0123456789
10
B1 B2
A1
A2
A: NO
B: YES
AB: YES
Practice
0123456789
10
B1 B2
A1
A2
A: NO
B: NO
AB: YES