2 × 3 Between-Subjects Factorial ANOVA: Study

Environments by Gender

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College of Doctoral Studies

PSY 870: Module 4 Problem Set

2 × 3 Between-Subjects Factorial ANOVA: Study Environments by Gender

This study investigates whether study environment affects academic performance. In addition,

this study investigates whether sex of student “moderates” the effect of study environment on

academic performance (that is, do males and females differ in how much benefit they get from

studying in certain environments).

During the first half of the spring semester, 120 male students and 120 female students in grade

10 at a public high school in a large metropolitan area in the southwestern region of the United

States were randomly assigned to one of three study environment: study in front of the TV, at the

library, or in the food court. The students could ONLY study in the environment to which they

were assigned during the research period. At the end of the 7-week research period, mid-term

GPA was computed for each student. A change score was computed for each student: each

student’s spring midterm GPA was subtracted from his or her GPA for the preceding fall

semester. The difference was each student’s GPA Improvement score. The GPA improvement

score was used to measure academic performance.

Directions:

Using the SPSS 2 × 3 ANOVA data file for Module 4 (located in Topic Materials), answer the

following questions. NOTE: Helpful hints are provided here for you to use while answering

these questions. There is no separate answer sheet/guide to use while doing this assignment.

1. What are the two independent variables in this study? What is the dependent variable?

Independent Variables: Sex, Study Environment

Dependent Variable: GPA Improvement

2. Why is a two-way between-subjects factorial ANOVA the correct statistic to use for this

research design?

Two way ANOVA would the best statistic since this data is complex and it involves

the measure of three effects: the effect of Gender on performance, effect of study

environment on performance and the interaction between gender and the study

environment.

The interaction between gender and study environment simply asks whether there is any

significant difference in performance when you test gender and study environment acting

together.

3. Did you find any errors that the researcher made when setting up the SPSS data file

(Remember to check the variable view)? If so, what did you find? How did you correct

it?

Yes. In the SPSS data file, the data measurements for Sex was recorded as Scale while it

ought to be Nominal. I changed it to Nominal Scale

4. Run Descriptive Statistics on the dependent variable data. What do the skewness and

kurtosis values tell you about whether the data satisfy the assumption of normality?

Skewness: 0.652

This is positive value which shows greater number of smaller values with respect to

deviance from symmetry around the mean.

Kurtosis: -0.63

This is a negative value indicating the distribution is more peaked than normal.

5. Perform a between-subjects factorial ANOVA on the data.

a. What do the results of the Levene’s Test tell you about your data? What does this

mean in terms of interpreting the outcomes of the ANOVA?

Significant Result =0.032,

This is less than 0.05 (0.032< 0.05), this shows that the error variance of
dependent variable is not equal across the groups. The assumption of the
ANOVA has not been met.
What do the results of the Tests of Between-Subjects Effects tell you? Was there a

significant main effect of Environment on GPA improvement? Was there a

significant main effect of Sex on GPA improvement? Was there a significant

interaction effect of Environment X Sex on GPA improvement?

The sig column for Sex and envir*sex are significant since sig is less than 0.05

(<0.05), but there is no effect on Sex (>0.05)

© 2013. Grand Canyon University. All Rights Reserved.

However this does not tell us which environment affects GPA improvement. We

hence look at the post-hoic test.

Post hoc result shows significance in all environmental combinations (000<0.001)
Report the results for each of these questions providing the actual F-value and p value
using the following format: F (df1, df2) = ____, p =.___ or if the p is shown as .000,
write it as p < .001; an example of this formatting is F(1, 400) = 15.4, p = .02).
Reporting.
An experiment was conducted to check whether the Sex of students and the
Study environment had any effect on the GPA improvement. A two way
ANOVA found no effect on Sex, F (1,234) =2.652, p> 0.05 indicating that

students gender does not determine GPA improvement.

Environment, F (2,234) =77.173, p< 0.05 indicating the GPA improvement is
dependent on the study environment.
There was interaction between Sex and study environment F (2,234) = 45.688 p<
0.05.
b. Use eta squared to provide effect size/proportion of variance accounted associated
with each F-value. If the F-value for a main effect and/or for an interaction effect
is statistically significant, what is the eta squared (2) value associated with that
outcome?
HINT:
Report eta squared, 2; ignore partial eta squared that SPSS can provide.
You have to calculate eta squared yourself. It is not given to you by SPSS,
but you can use what SPSS provides to calculate it. Eta squared is calculated
by using the values in the column headed "Type III Sum of Squares" from
the table with the results for Tests of Between-Subjects Effects." To
compute eta squared, which would be notated as 2, take that source's Type
III Sum of Squares and divide it by the value for Corrected Total in the same
column. For example, if the Type III Sum of Squares for Environment had
been 4.5 rather than 4.696, you would divide 4.5 by 14.677 to get the effect
size for Environment. If the Type III Sum of Squares for Sex had been 2.0,
© 2013. Grand Canyon University. All Rights Reserved.
you also would divide that by 14.677, etc. Interpret these eta squared results
for effect size using the following guidelines from Cohen (1988):
.01 ~ small
.06 ~ medium
.14 ~ large
2 Sex =0.081/14.667=0.0055
This implies small proportional variance (effect)
2 Study Environment = 4.696/14.667=0.320
This implies large proportional variance (effect)
c. If the result for the main effect of Environment was statistically significant, what
did you find out when you performed post hoc tests (Tukey HSD) to look at
possible statistically significant differences in the pairs of means for Environment
groups?
.
The Post hoc result shows significance in all environmental combinations (In front of the
TV, the library and the food Court) .All the results for the different environments gave p
value = 000 (000<0.001)
© 2013. Grand Canyon University. All Rights Reserved.
d. If the result for the interaction of Environment X Sex was statistically significant,
what follow up tests did you perform to understand what was going on here? That
is, what did you do to find out what was different for males in the various study
Environments versus for females in the various study Environments in effects on
GPA improvement? What did you learn?
Environment*Sex was found to be Statistically Significant. I hence performed
Estimated Marginal means to understand clearly the effect of Males and Females in
each Study environment and how it affected GPA improvement.
I learned that in front of TV males had a higher GPA improvements than their
female counterparts (0.335 > 0.170)

In the Library Environment Female had a higher GPA improvement than the Male

students (0.305<0.640)
At the environment in the Food Court Males had higher GPA improvement than
the Female counterparts (0.165>0.105)

e. When you have a factorial ANOVA and the interaction effect is significant, does

the researcher give much attention to any significant main effects when

interpreting the results of the study?

Yes, attention should be given to the significance brought about by

interaction. In our case, the researcher will try to know how the mixture in

different study environments affects male and female GPA improvement.

6. Citing the results of your statistical analyses, what is the conclusion you can draw (and

support) regarding research question that was posed in this research (see problem

statement)? Write a results section for this study that expresses and supports this

conclusion.

HINT:

Use the sample write-up of the results for the Two-Way Between-Subjects

ANOVA example that is in the textbook to see what you should report and how to

say it. Just substitute the correct language and values for the analyses you have

done for this problem.

© 2013. Grand Canyon University. All Rights Reserved.

An experiment was conducted to check whether the Sex of students and the

Study environment had any effect on the GPA improvement. A two way

ANOVA was conducted and from the Analysis results, the following were

conclusions:

No effect on Sex, F (1,234) =2.652, p> 0.05 indicating that students gender does

not determine or has no significant effect on the GPA improvement.

However, on the effect of Environment, F (2,234) =77.173, p< 0.05 .This indicates
that the GPA improvement is dependent on the study environment.
There was interaction between Sex and study environment F (2,234) = 45.688 p<
0.05.This implies that a combination of sex and the study area has a significant
impact on the GPA improvement.
© 2013. Grand Canyon University. All Rights Reserved.
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