lecture 10: one way anova between subjects: practice! laura mcavinue school of psychology trinity...
Post on 20-Dec-2015
219 views
TRANSCRIPT
![Page 1: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/1.jpg)
Lecture 10:One Way ANOVA
Between Subjects: Practice!
Laura McAvinue School of PsychologyTrinity College Dublin
![Page 2: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/2.jpg)
Example 1: ANOVA by hand
• Our research interest is the treatment of social anxiety
• We would like to evaluate different therapies for social anxiety
• We took a sample of 15 people suffering from social anxiety & randomly assigned them to three groups– Placebo– Cognitive Behavioural Therapy (CBT)– Gestalt Therapy
• Did any of the treatments significantly improve social anxiety?
• Are any of the means significantly different?
![Page 3: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/3.jpg)
StepsGroup A Group B Group C
Placebo CBT Gestalt
0 4 1
1 3 2
3 6 2
1 3 0
0 4 0
Mean 1 4 1
1. Sum of Squares
2. Degrees of Freedom
3. Mean Square
4. F Ratio
5. P ValueWhat is the grand mean of these observations?
2
![Page 4: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/4.jpg)
SSTotal
(0-2)2 + (1-2) 2 + (3-2) 2 + (1-2) 2 + (0-2) 2
4 1 1 1 4+ (4-2) 2 + (3-2) 2 + (6-2) 2 + (3-2) 2 + (4-2) 2
4 1 16 1 4+ (1-2) 2 + (2-2) 2 + (2-2) 2 + (0-2) 2 + (0-2) 2
1 0 0 4 4
= 46
∑ (Xij – Grand mean)2
![Page 5: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/5.jpg)
SSBetween
= 30
n∑ (Group mean – Grand mean)2
5 ∑ (1-2) 2 + (4-2) 2 + (1-2) 2
5 ( 1 + 4 + 1)5 (6)
![Page 6: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/6.jpg)
SSwithin
= 16
∑ (Xij – Group meanj)2
SSplacebo (0-1) 2 + (1-1) 2 + (3-1) 2 + (1-1) 2 +(0-1) 2
1 0 4 0 1 = 6SSCBT (4-4) 2 + (3-4) 2 + (6-4) 2 + (3-4) 2 + (4-4) 2
0 1 4 1 0 = 6SSgestalt (1-1) 2 + (2-1) 2 + (2-1) 2 + (0-1) 2 + (0-1) 2
0 1 1 1 1 = 4
![Page 7: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/7.jpg)
Degrees of Freedom
Dftotal N – 1
15 – 114
Dfbetween K – 1
3 – 12
Dfwithin K (n – 1)
3 (5 – 1)12
![Page 8: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/8.jpg)
Mean Square
MSbetween SSbetween / dfbetween
30 / 215
MSwithin SSwithin / dfwithin
16 / 121.33
![Page 9: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/9.jpg)
F Ratio
F Ratio MSbetween / MSwithin
15 / 1.3311.278
Is F > 1? Yes!
Is F big enough to reject Ho?Compare your F value to the F distribution
Dfnumerator = Dfbetween Dfdenominator = Dfwithin
= 2= 12
![Page 10: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/10.jpg)
F Ratio
• What is the critical value of F when = .05?– 3.88
• What is the critical value of F when = .01?– 6.93
• Is your F value greater than the critical values?– Yes!
• Can you reject Ho? At what alpha level?– Yes! At P < .01
![Page 11: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/11.jpg)
Example 2: ANOVA by computer
Group Social Anxiety
1 (Placebo)... 0
1 1
1 3
1 1
1 0
2 (CBT)... 4
2 3
2 6
2 3
Enter the data into SPSS...
![Page 12: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/12.jpg)
Run the ANOVA
• Analyse, Compare Means, One Way ANOVA
– Dependent List: Social Anxiety– Factor: Group– Options: Descriptives
Homogeneity of variance testMeans plot
![Page 13: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/13.jpg)
Examine the means plot
GestaltCBTplacebo
Therapy
4
3.5
3
2.5
2
1.5
1
Me
an
of
so
cia
lan
x
Are the means more or less the same or does one seem a little different?
![Page 14: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/14.jpg)
Examine the test for Homogeneity of Variance
Is Levine’s statistic significant?
Can we assume homogeneity of variance among groups?
Test of Homogeneity of Variances
socialanx
.000 2 12 1.000
LeveneStatistic df1 df2 Sig.
![Page 15: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/15.jpg)
Examine the ANOVA table
•Is it similar to the one you created?•What is the p value?•Is it statistically significant?•What can you conclude from this ANOVA?At least one mean is significantly different from the others
ANOVA
socialanx
30.000 2 15.000 11.250 .002
16.000 12 1.333
46.000 14
Between Groups
Within Groups
Total
Sum ofSquares df Mean Square F Sig.
![Page 16: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/16.jpg)
Multiple Comparisons
•According to the Bonferroni & Tukey posthoc tests, which means are significantly different from the others?
Multiple Comparisons
Dependent Variable: socialanx
-3.000* .730 .004 -4.95 -1.05
.000 .730 1.000 -1.95 1.95
3.000* .730 .004 1.05 4.95
3.000* .730 .004 1.05 4.95
.000 .730 1.000 -1.95 1.95
-3.000* .730 .004 -4.95 -1.05
-3.000* .730 .004 -5.03 -.97
.000 .730 1.000 -2.03 2.03
3.000* .730 .004 .97 5.03
3.000* .730 .004 .97 5.03
.000 .730 1.000 -2.03 2.03
-3.000* .730 .004 -5.03 -.97
(J) TherapyCBT
Gestalt
placebo
Gestalt
placebo
CBT
CBT
Gestalt
placebo
Gestalt
placebo
CBT
(I) Therapyplacebo
CBT
Gestalt
placebo
CBT
Gestalt
Tukey HSD
Bonferroni
MeanDifference
(I-J) Std. Error Sig. Lower Bound Upper Bound
95% Confidence Interval
The mean difference is significant at the .05 level.*.
![Page 17: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/17.jpg)
Example 3: T tests v ANOVAs
Software/ Kevin Thomas/ ANOVA data setAnalyse the ‘age’ & ‘adherence’ variables using an independent samples t test & an ANOVA
Independent Samples Test
.000 1.000 -3.873 8 .005 -3.00000 .77460 -4.78622 -1.21378
-3.873 8.000 .005 -3.00000 .77460 -4.78622 -1.21378
Equal variancesassumed
Equal variancesnot assumed
adherenceF Sig.
Levene's Test forEquality of Variances
t df Sig. (2-tailed)Mean
DifferenceStd. ErrorDifference Lower Upper
95% ConfidenceInterval of the
Difference
t-test for Equality of Means
ANOVA
adherence
22.500 1 22.500 15.000 .005
12.000 8 1.500
34.500 9
Between Groups
Within Groups
Total
Sum ofSquares df Mean Square F Sig.
Similar results?T2 = ?
![Page 18: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/18.jpg)
• Example 4: Research example– Eysenck (1974) used three groups to investigate the impact of
levels of processing (Craik & Lockhart, 1972) on incidental learning - learning in the absence of expectation that the material will need to be recalled later
• Group 1 - count number of letters in each word - lowest level of processing
• Group 2 - think of an adjective that might be used to describe the word
• Group 3 - form a vivid image of the word
– What are Ho & H1?
Ho: There is no difference between the groupsLevel of processing has no effect on recall
H1 : At least one group is significantly differentAs level of processing increases, incidental memory increases
![Page 19: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/19.jpg)
Run the ANOVA
ANOVA dataset: Group & Recall variables
ANOVA
recall
209.067 2 104.533 10.516 .000
268.400 27 9.941
477.467 29
Between Groups
Within Groups
Total
Sum ofSquares df Mean Square F Sig.
•What is the F value?•Is F > 1?•Is it statistically significant?•What can we conclude?
Conclude:•At least one of the means is significantly different from the others•Level of processing does significantly affect incidental recall
![Page 20: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/20.jpg)
Which means are different?
What does the means plot suggest?
imageryadjectivecounting
group
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
Mea
n o
f re
call
![Page 21: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/21.jpg)
Which means are different?
What do the posthoc tests suggest?
Multiple Comparisons
Dependent Variable: recall
-4.00000* 1.41002 .022 -7.4960 -.5040
-6.40000* 1.41002 .000 -9.8960 -2.9040
4.00000* 1.41002 .022 .5040 7.4960
-2.40000 1.41002 .223 -5.8960 1.0960
6.40000* 1.41002 .000 2.9040 9.8960
2.40000 1.41002 .223 -1.0960 5.8960
-4.00000* 1.41002 .026 -7.5990 -.4010
-6.40000* 1.41002 .000 -9.9990 -2.8010
4.00000* 1.41002 .026 .4010 7.5990
-2.40000 1.41002 .301 -5.9990 1.1990
6.40000* 1.41002 .000 2.8010 9.9990
2.40000 1.41002 .301 -1.1990 5.9990
(J) groupadjective
imagery
counting
imagery
counting
adjective
adjective
imagery
counting
imagery
counting
adjective
(I) groupcounting
adjective
imagery
counting
adjective
imagery
Tukey HSD
Bonferroni
MeanDifference
(I-J) Std. Error Sig. Lower Bound Upper Bound
95% Confidence Interval
The mean difference is significant at the .05 level.*.
![Page 22: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/22.jpg)
Effect Size
Calculate Eta squared Calculate Omega squared
2 SSbetweenSStotal
2 SSbetween (k 1)MSwithin
SStotal MSwithin209.09 (3 1)9.94
477.46 9.94189.18
487.4.39209.06 /
477.46
= .44
![Page 23: Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin](https://reader035.vdocument.in/reader035/viewer/2022062320/56649d4d5503460f94a2b713/html5/thumbnails/23.jpg)
• Fully reporting the analysis– A one-way (or one-factor) analysis of variance
(ANOVA) compared the mean number of words recalled across three groups who processed the words differently: count, adjective or imagery. With an alpha level of .05, the analysis was statistically significant, F(2,27) = 10.516, p< .001. A Tukey HSD test indicated that the mean of 7 (SD =1.83) for the count group was significantly different to that of the adjective (M=11, SD=2.5) and imagery (M=13.4, SD=4.5) groups. The difference between the adjective and imagery groups was not significant (p > 10).