Transcript
In Lab This Week…
• links to feedback on assignment #3
• overview of CRF design
• summary of interpreting results
• example analysis
• assignment #5
Feedback: Assignment #3
A complete list of commonly made errors can be found on the lab blog: http://uwo3800g.tumblr.com/post/77297554105/assignment-3-commonly-made-errors
A refresher on formatting figures according to APA requirements has also been posted on the blog: http://uwo3800g.tumblr.com/post/77297442346/refresher-apa-formatting-for-figures
OVERVIEW OF THE DESIGN q
(1) two or more independent variables (IVs) or factors
(2) two or more levels per factor
(3) each participant randomly assigned to only one condition
(4) measuring all individuals on one dependent variable (DV)
…extension of the single-factor analysis of variance (ANOVA)
adding at least one extra factor to create a factorial design
Features of the Design
Example Problem
Do alcohol consumption and gender have an effect on academic performance?
Research Question
independent variables (i.e. factors)
(A) alcohol consumption 4 levels: 5 oz., 10 oz., 15 oz., 20 oz. (B) gender 2 levels: males, females
dependent variable
academic performance test out of 10 marks
Variables of Interest
Gender Level of alcohol consumption
5 oz. 10 oz. 15 oz. 20 oz.
Male
Female
2 (gender) x 4 (alcohol) factorial design
Example Problem
€
x 5oz =6 + 7 + 6 + 8 + 5 + 7 + 7 + 6 + 8 + 7
10= 6.70
€
x male, 5oz =6 + 7 + 6 + 8 + 5
5= 6.40
€
x female, 5oz =7 + 7 + 6 + 8 + 7
5= 7.00
6 7
6 8 5
7 7
6 8 7
Gender Level of alcohol consumption
5 oz. 10 oz. 15 oz. 20 oz.
Male 6.40 8.40 7.00 6.00
Female 7.00 9.00 9.60 2.20
Example Problem
6.70 8.70 7.00 3.50
6.95
6.95
Can use the scores to calculate condition means (within the table) or overall means for the various factor levels (blue boxes):
no longer interested in comparing means following introduction of only one treatment/IV (as in a one-way ANOVA)
more elaborate analyses possible
• can compare males versus females on academic performance • can compare consumption of 5 oz., 10 oz., 15 oz., or 20 oz. of alcohol on academic performance • can look at the combined effect of gender and alcohol consumption on academic performance
Moral of the story: allows us to explore interactions between variables (combined effect of two or more IVs on one DV)
Uses of Factorial Design
(1) main effect of factor A (gender) Does gender affect academic performance (ignoring alcohol consumption)?
(2) main effect for factor B (alcohol consumption) Does alcohol consumption affect academic performance (ignoring gender)?
(3) interaction between factor A and factor B Does gender change (increase/decrease) the effect of alcohol consumption on academic performance?
or Does alcohol consumption change (increase/decrease) the effect of gender on academic performance?
Uses of Factorial Design
INTERPRETING THE RESULTS q
main effects: testing whether at least two means (levels) differ significantly for a given factor (think one-way ANOVA)
• when a factor has 2 levels, we will know whether or not the two means differ significantly with the omnibus test (only have two means)
• when a factor has 3+ levels, omnibus test cannot tell us where the differences are found
need to follow up with post hoc analyses of the level means
Main Effects
Gender Level of alcohol consumption
5 oz. 10 oz. 15 oz. 20 oz.
Male 6.40 8.40 7.00 6.00
Female 7.00 9.00 9.60 2.20
6.95
6.95
if these two means differ significantly, we have a main effect for gender (post hoc tests not needed)
Main Effects
Main Effect for Factor A (Gender)
Gender Level of alcohol consumption
5 oz. 10 oz. 15 oz. 20 oz.
Male 6.40 8.40 7.00 6.00
Female 7.00 9.00 9.60 2.20
Main Effects
Main Effect for Factor B (Alcohol Consumption)
6.70 8.70
if these four means differ significantly, we have a main effect for alcohol consumption (post hoc tests needed to pinpoint where differences exist)
7.00 3.50
interaction: -combined effect of IVs (factors) on the measured DV -effect of one variable is not consistent across all levels of the other variables (as suggested by main effects) -factors are interacting to produce unique result
• if significant interaction found, we need to investigate effect of one variable at varying levels of other variable to make sense of it
this is basically an investigation of cell means called “simple main effects” (SME)
multiple approaches possible
Interaction
• looking at the effect of gender at each level of alcohol consumption
• consider sex differences for each alcohol intake level: how does gender affect academic performance at 5 oz. of alcohol? how does gender affect academic performance at 10 oz. of alcohol? how does gender affect academic performance at 15 oz. of alcohol? how does gender affect academic performance at 20 oz. of alcohol?
Gender Level of alcohol consumption 5 oz. 10 oz. 15 oz. 20 oz.
Male 6.40 8.40 7.00 6.00
Female 7.00 9.00 9.60 2.20
Interaction: Simple Main Effects Option #1: Simple Main Effects of Gender on Alcohol Consumption
vs. vs. vs. vs.
0
2
4
6
8
10
5 oz. 10 oz. 15 oz. 20 oz.
Mea
n Te
st S
core
Alcohol Consumption Level
Male Female
Comparing male vs. female means at each alcohol level:
At 5 oz. of alcohol: males vs. females
At 10 oz. of alcohol: males vs. females
At 15 oz. of alcohol: males vs. females
At 20 oz. of alcohol: males vs. females
Interaction: Simple Main Effects Option #1: Simple Main Effects of Gender on Alcohol Consumption
total of 4 comparison to be made
• looking at the effect of various levels of alcohol consumption for each gender
• consider the four alcohol levels among males, and then again among females: how does alcohol consumption affect academic performance amongst males? how does alcohol consumption affect academic performance amongst females?
Interaction: Simple Main Effects Option #2: Simple Main Effects of Alcohol Consumption on Gender
Gender Level of alcohol consumption 5 oz. 10 oz. 15 oz. 20 oz.
Male 6.40 8.40 7.00 6.00
Female 7.00 9.00 9.60 2.20 vs. vs. vs.
vs. vs. vs.
0
2
4
6
8
10
Male Female
Mea
n Te
st S
core
Gender
5 oz. 10 oz. 15 oz. 20 oz.
Comparing alcohol intake at each gender level:
For males: 5 oz. vs. 10 oz. 5 oz. vs. 15 oz. 5 oz. vs. 20 oz. 10 oz. vs. 15 oz. 10 oz. vs. 20 oz. 15 oz. vs. 20 oz.
For females: 5 oz. vs. 10 oz. 5 oz. vs. 15 oz. 5 oz. vs. 20 oz. 10 oz. vs. 15 oz. 10 oz. vs. 20 oz. 15 oz. vs. 20 oz.
Interaction: Simple Main Effects Option #2: Simple Main Effects of Alcohol Consumption on Gender
total of 12 comparison to be made
• do not look at the data BOTH ways when interpreting interactions that would be redundant
• pick approach that makes most sense it may make equal sense both ways, so in that case, pick the one you can explain more easily
IMPORTANT! If you find a significant interaction, interpret main effects cautiously and in light of the interaction.
Interaction: A Cautionary Tale
Gender Level of alcohol consumption
5 oz. 10 oz. 15 oz. 20 oz.
Male 6.40 8.40 7.00 6.00
Female 7.00 9.00 9.60 2.20
6.95
6.95
Investigation of main effects here could suggest that men and women perform equally well on the academic test…
0
2
4
6
8
10
5 oz. 10 oz. 15 oz. 20 oz.
Mea
n Te
st S
core
Alcohol Consumption Level
Male
Female
…but the interaction reveals that that there are clear differences between the two groups at different levels of alcohol intake.
Further tests are needed to determine which differences are statistically significant, but it is evident that the main effect does not tell us the whole story.
Interaction: A Cautionary Tale
EXAMPLE ANALYSIS q
Factor A: participant gender
1 = male 2 = female
Factor B: alcohol intake
1 = 5 oz. 2 = 10 oz. 3 = 15 oz. 4 = 20 oz.
DV: academic test score (out of 10)
The Data
Analyze General Linear Model Univariate
Running CRF Design in SPSS
dependent variable
all factors (IVs) under investigation (in this case, two factors)
Options Menu
Running CRF Design in SPSS
request post hoc tests (Tukey) for all factors in the analysis…
Post Hoc Menu
Running CRF Design in SPSS
plotting simple main effects of alcohol consumption on gender…
Running CRF Design in SPSS
Plots Menu
plotting simple main effects of gender on alcohol consumption…
Running CRF Design in SPSS
Plots Menu
Click “OK” in main window to obtain output in separate window…
Running CRF Design in SPSS
Means provided for all levels and conditions, but standard error needs to be calculated:
Example: Males (total)
(M = 6.95, SE = 0.31)
€
SE =sxn
=1.39520
= 0.31
Example: Females, 10 oz.
(M = 9.00, SE = 0.63)
€
SE =sxn
=1.4145
= 0.63
€
SE =sxn
=standard deviation
number of observations
Output: Descriptive Statistics
Levene F(7, 32) = 1.56, ns
• results of Levene’s test are not significant • can conclude that all condition variances are approximately equal
Output: Levene’s Test
Output: Main Effect for Gender
F(1, 32) = 0.00, ns, η2 = .00, power = .05
• no significant main effect for gender • males do not differ significant from females in terms of their academic performance
Output: Main Effect for Alcohol Consumption
F(3, 32) = 38.30, p < .001, η2 = .78, power = 1.00
• significant main effect for alcohol consumption • at least two alcohol level means differ significantly • follow up with post hoc tests to determine where differences exist
• significant info provided, but qobtained values still need to be calculated for the alcohol consumption comparisons
• as in the one-way ANOVA unit, some of these comparisons are redundant, so select and report only the unique comparisons (6 in total for our example problem)
Output: Post Hoc Tests for Main Effects
Post Hoc Comparisons for Alcohol Consumption
Output: Post Hoc Tests for Main Effects
Post Hoc Comparisons for Alcohol Consumption
To determine the qobtained values, enter the alcohol consumption means into the POSTHOC program (no pooled error term)
Example:
5 oz. vs. 10 oz.: q(4, 32) = 5.93, p < .01
q(df1, df2) = qobtained, significance
# of levels in factor (4) df value for error (32)
Output: Post Hoc Tests for Main Effects
Post Hoc Comparisons for Gender
In our example, these follow-up comparisons are not necessary because the overall assessment of the main effects was not significant. Had it been significant:
As stated earlier: for a factor with only two levels, post hoc tests are not needed (we already know which two means differ significantly).
Output: Interaction
F(3, 32) = 16.06, p < .001, η2 = .60, power = 1.00
• significant interaction exists between gender and alcohol consumption • one factor changes the effect of the other factor on academic performance • proceed with tests of simple main effects to dissect the interaction
Inspect the plots to get a sense of which approach to interpreting the interaction you would like to take (either option is fine… but one is much easier).
Output: Interaction
Output: Simple Main Effects for Interaction Option #1: Simple Main Effects of Gender on Alcohol Consumption
DV is “academic”
File New Syntax
Factor A is “gender” (levels coded 1-2)
Factor B is “alcohol” (levels coded 1-4)
• in line 3, we specify that we are assessing gender at each level of alcohol consumption (comparing gender levels with each alcohol level)
• to run the syntax, we highlight the text and click:
Output: Simple Main Effects for Interaction Option #1: Simple Main Effects of Gender on Alcohol Consumption
e.g., males vs. females after 5 oz. of alcohol: F(1, 32) = 0.79, ns
Therefore, males and females do not differ significant in terms of their academic performance after consuming 5 oz. of alcohol.
Output: Simple Main Effects for Interaction Option #1: Simple Main Effects of Gender on Alcohol Consumption
0
2
4
6
8
10
5 oz. 10 oz. 15 oz. 20 oz.
Mea
n Te
st S
core
Alcohol Consumption Level
Male Female
F(1, 32) = 0.79, ns F(1, 32) = 0.79, ns F(1, 32) = 14.86, p < .01
F(1, 32) = 31.74, p < .001
Option #2: Simple Main Effects of Alcohol Consumption on Gender
Output: Simple Main Effects for Interaction
Output: Simple Main Effects for Interaction
0
2
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8
10
Male Female
Mea
n Te
st S
core
Gender
5 oz. 10 oz. 15 oz. 20 oz.
Option #2: Simple Main Effects of Alcohol Consumption on Gender
F(3, 32) = 4.85, p < .01 F(3, 32) = 49.51, p < .001
Note: even with the results of MANOVA, we still don’t know exactly which means differ (just know that differences exist for both males and females) follow up with analyses in POSTHOC to pinpoint which specific means differ
ASSIGNMENT q
• APA-style results section (2-page maximum)
• all SPSS and POSTHOC output
• figure depicting the interaction approach: muscle relaxant drugs at each level of anti-inflammatory drugs computer generated and adhering to APA standards
• any hand calculations that you have done
• Note: You have been given the syntax file to run the SMEs
Assignment #5
• intro sentences (IVs, DV, levels, design)
• Levene’s test (statistic, interpretation, implications)
• interaction effect • graph the interaction (figure separate from written results) • report simple main effects if applicable (MANOVA)
• main effect 1 + post hoc if applicable • main effect 2 + post hoc if applicable
• overall conclusion
• don’t forget to include your descriptive values, observed power values, effect sizes, and concluding sentences
even with significant interaction
Parts of the Assignment
• Assignment #5 due: Thursday, March 6, 2013 at start of lab
• Unit 6 introduced: split plot factorial design o brings together what we know about the one-way ANOVA and the repeated ANOVA o can be challenging (and work-intensive) so please review all basics pertaining to ANOVA that have been taught to date
Next Week
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