FOUN 823_Final Exam
Final Exam
FOUN 823
Directions:
1. The significance level (α) for all significance tests on this exam will be .05.
2. Please use the SPSS data files in the same Blackboard folder for this final exam.
3. No partial credit will be assigned for a co
ect ve
al conclusion supported by the
inco
ect statistics or an inco
ect ve
al conclusion supported by the co
ect statistics.
4. Please submit the exam by the designated submission deadline. Zero point will be
assigned to an overdue exam.
A researcher intended to investigate various effects of Teaching Method (i.e., teaching
methods 1, 2, 3, & 4), and Personality Style of teachers (i.e., 1: liberal; 2: rigid) on
students’ Reading learning outcome (on a 0 – 20 scale, the higher the better).
Therefore, in the beginning of the semester, he randomly selected 60 fifth-grade
students from the N City then randomly assigned them to 8 groups representing
different combinations of Teaching method and Personality Style. Prior to the actual
implementation of different teaching methods by teachers of different personality styles,
the IQ of those students were measured with a standardized IQ test. Then, after one
semester of teaching, students were measured on reading learning outcome with a
standardized reading test.
Please conduct a two-way analysis of variance (ANOVA) with the SPSS data file
entitled FOUN 823_Final Exam-1 using Teaching Method and Personality Style of
teachers as the independent variables and Reading as the dependent variable. Then
use the results to answer the questions 1 - 3:
1. Will the effect of teaching method on reading learning outcomes among fifth-grade
students in the N City change across personality styles of teachers? Please support
your ve
al conclusion with the relevant significance test results and effect size index in
APA style. (3 points)
2. Will teaching method affect reading learning outcomes among fifth-grade students in
the N City? Please support your ve
al conclusion with the relevant significance test
esults and effect size index in APA style. (3 points)
3. Will personality style of teachers affect reading learning outcomes among fifth-grade
students in the N City? Please support your ve
al conclusion with the relevant
significance test results and effect size index in APA style. (3 points)
SAMPLE EXPECTED RESPONSES:
Please conduct an analysis of covariance (ANCOVA) with the SPSS data file entitled
FOUN 823_Final Exam-1 using Teaching Method as the focal independent variable,
IQ as the covariate, and Reading as the dependent variable. Then use the results to
answer the questions 4 - 6:
4. Is the homogeneity of regression assumption violated? In other words, can the same
pooled within-group regression coefficient of IQ be applied to all Teaching Method
groups to statistically adjust Reading? Please support your ve
al conclusion with the
elevant significance test results and effect size index in APA style. (3 points)
5. Will there be an effect of teaching method on reading learning outcomes among
fifth-grade students in the N City controlling for IQ? Please support your ve
al
conclusion with the relevant significance test results and effect size index in APA style.
(3 points)
6. According to the ANCOVA results, which teaching method group will receive the
largest adjustment in absolute value and how much adjustment will be made to that
group? (3 points)
SAMPLE EXPECTED RESPONSES:
A researcher studied the effect of a new antidepressant by measuring the depressive
symptoms of 30 patents over time (Time 1: 2 weeks before the treatment; Time 2; 1
week before the treatment; Time 3: 1 day after the treatment; Time 4: 1 week after the
treatment; Time 5: 2 weeks after the treatment). Please conduct a within-subjects
(repeated measures) ANOVA with the SPSS data file entitled FOUN 823_Final
Exam-2 to answer the questions 7 - 10:
7. According to the Mauchly’s test results, is the sphericity assumption violated? Please
support your ve
al conclusion with the relevant significance test results in APA style. (3
points)
8. Did the patients’ depressive symptom change over time? Please support your ve
al
conclusion with the relevant significance test results and effect size index in APA style.
(3 points)
9. Please implement a planned comparison of depressive symptoms between the
pre-treatment time period (Time 1 + Time 2) and the post-treatment time period (Time 3
+ Time 4 + Time 5) to assess the possible effect of the new antidepressant. Then
support your ve
al conclusion with the relevant significance test results and effect size
index in APA style. (3 points)
10. Please implement a planned comparison of depressive symptoms between the
pre-treatment time period (Time 1 + Time 2) and the post-treatment time period (Time 4
+ Time 5) to assess the possible effect of the new antidepressant. Then support you
ve
al conclusion with the relevant significance test results and effect size index in APA
style. (3 points)
SAMPLE EXPECTED RESPONSES (next page)
SAMPLE EXPECTED RESPONSES:
Questions/6foun-823two-way-anova-nnxr1huf.pdf
1
Two-Way Fixed-Effect
ANOVA
FOUN 823
Cherng-Jyh Yen, Ph.D.
2
Two-Way ANOVA
• ANOVA with 2 independent variables
• Two-way ANOVA and Factorial
Experimental Designs
• Two types of effects
• Interaction effect between 2 independent
variables on the dependent variable
• Main effect of each independent variable
on the dependent variable
• The test of the interaction effect
precedes the test of main effect
• Given the presence of the interaction effect,
the results from the main effect assessment
can be partially co
ect or even completely
inco
ect
3
Two-Way ANOVA
• Interaction effect between 2
independent variables
• Effect of the combination of levels in 2
independent variables
• Is the “simple effect” of an independent
variable constant across levels of the other
independent variable?
• Main effect of an independent variable
• Effect of an independent variable without
egard to the other independent variable
• Variation among column means or row
means
4
Two-Way ANOVA
• Numerical example
Type of teacher 1 Type of teacher 2
Method XXXXXXXXXX, 5, 2, XXXXXXXXXX, 4, 3, XXXXXXXXXX1Y = 4.75
XXXXXXXXXX11Y = XXXXXXXXXX12Y = 6
Method XXXXXXXXXX, 4, 3, XXXXXXXXXX, 4, 2, XXXXXXXXXX2Y = XXXXXXXXXXrow means)
XXXXXXXXXX21Y = XXXXXXXXXX22Y = 4.5
Method XXXXXXXXXX, 7, 8, XXXXXXXXXX, 9, 10, XXXXXXXXXX3Y = 7.75
XXXXXXXXXX31Y = XXXXXXXXXX32Y = XXXXXXXXXXcell means)
XXXXXXXXXXY = XXXXXXXXXXY = 6.417
XXXXXXXXXX2 column means XXXXXXXXXXTY = XXXXXXXXXXgrand mean)
Independent Variable #1: Teaching Method (TM 1, TM 2, & TM 3)
Independent Variable #2: Type of Teacher
1: Junior teachers with < 5-year teaching experiences
2: Senior teachers with 5-year or more teaching experiences
Dependent Variable: Reading Achievement
5
Two-Way ANOVA
• Research questions in an
experimental design:
• Is there any interaction effect between Method and
Teacher on student Reading Achievement?
• Interaction effect: Does the effect (simple effects) of
Method vary across different levels of Teacher? Does
the effect (simple effects) of Teacher vary across
different levels of Method?
Given the presence of interaction effect
• Interaction contrast: Where does the effect (simple
effects) of Method vary across different levels of
Teacher? Where does the effect (simple effects) of
Teacher vary across different levels of Method?
Specificity of the finding
Given no interaction effect
• Main effect of Method: Does Method affect reading
achievement of students regardless of Teacher?
• Main effect of Teacher: Does Teacher affect reading
achievement of students regardless of Method?
Generalizability of the finding
6
Two-Way ANOVA
• An example of the presence of the
interaction effect between Method and
Teacher on Reading
XXXXXXXXXXTeacher XXXXXXXXXXTeacher 2
Method XXXXXXXXXX11Y = XXXXXXXXXX12Y = XXXXXXXXXX1Y = 5
Method 2 XXXXXXXXXX21Y = XXXXXXXXXX22Y = XXXXXXXXXX2Y = 8
XXXXXXXXXXY = XXXXXXXXXXY = 9