Exploratory Data Analysis and Factorial ANOVA

This document provides a step-by-step guide on performing exploratory data analysis and factorial ANOVA using SPSS. It includes descriptive statistics, main effects of gender and classroom size, interaction effects, and interpretation of the results.

Problem Analysis and Statistics
Name:
Institution:
20th March 2019

Part A. SPSS Assignment
Exploratory Data Analysis.
a. Perform exploratory data analysis on all variables in the data set. Realizing that you have six
groups, be sure that your exploratory analysis is broken down by the group. When possible,
include appropriate graphs to help illustrate the dataset.
Answer
Gender
Frequency Percent Valid Percent Cumulative
Percent
Valid
Female 30 50.0 50.0 50.0
Male 30 50.0 50.0 100.0
Total 60 100.0 100.0
Classroom size
Frequency Percent Valid Percent Cumulative
Percent
Valid
10 or less 20 33.3 33.3 33.3
11-19 20 33.3 33.3 66.7
20 or more 20 33.3 33.3 100.0
Total 60 100.0 100.0

Descriptive Statistics
Classroom size N Minimum Maximum Mean Std. Deviation
10 or less Math_Score 20 87.00 99.00 93.2500 3.64005
Valid N (listwise) 20
11-19 Math_Score 20 82.00 95.00 89.1000 3.25900
Valid N (listwise) 20
20 or more Math_Score 20 72.00 98.00 85.2000 7.14953
Valid N (listwise) 20
Descriptive Statistics
Gender N Minimum Maximum Mean Std. Deviation
Female Math_Score 30 72.00 98.00 87.1667 7.26865
Valid N (listwise) 30
Male Math_Score 30 86.00 99.00 91.2000 3.19914
Valid N (listwise) 30
b. Give a one to two paragraphs write up of the data once you have done this.
Answer
Results shows that an equal proportion of male and female respondents were included in the
sample (50%, n = 30). Also, an equal proportion of class groups were included in the sample

(33.3%, n = 20). The average math score for the male respondents were found to have a
higher mean score (M = 91.20, SD = 3.20) as compared to the average score of the female
respondents (M = 87.17, SD = 7.27).
c. Create an APA style table that presents descriptive statistics for the sample.
Answer
A descriptive analysis was performed to explore the data before performing inferential
analysis. Results shows that an equal proportion of male and female respondents were
included in the sample (50%, n = 30). Also, an equal proportion of class groups were included
in the sample (33.3%, n = 20). In terms of average score in math scores, male respondents
were found to have a higher mean score (M = 91.20, SD = 3.20) as compared to the average
score of the female respondents (M = 87.17, SD = 7.27).
In terms of the classroom size, classes with small number of students had on average larger mean
as compared to those with large number of students. For instance, the average scores in math
exam for classes with 10 or less was 93.25 (SD = 3.64), the average was 89.10 (SD = 3.26) for a
classroom of 11-19 and lastly the average was 85.20 (SD = 7.15) for a classroom of 20 or more.

Factorial ANOVA. Perform a factorial ANOVA using the “Activity 9.sav” data set.
Answer
Between-Subjects Factors
Value Label N
Gender F Female 30
M Male 30
Classroom size
1 10 or less 20
2 11-19 20
3 20 or more 20
Descriptive Statistics
Dependent Variable: Math_Score
Gender Classroom size Mean Std. Deviation N
Female
10 or less 93.8000 3.93841 10
11-19 88.5000 3.97911 10
20 or more 79.2000 4.18463 10
Total 87.1667 7.26865 30
Male
10 or less 92.7000 3.43350 10
11-19 89.7000 2.40601 10
20 or more 91.2000 3.22490 10
Total 91.2000 3.19914 30
Total
10 or less 93.2500 3.64005 20
11-19 89.1000 3.25900 20
20 or more 85.2000 7.14953 20
Total 89.1833 5.92750 60
Tests of Between-Subjects Effects
Dependent Variable: Math_Score
Source Type III Sum of
Squares
df Mean Square F Sig.
Corrected Model 1381.483a 5 276.297 21.576 .000
Intercept 477220.017 1 477220.017 37266.639 .000
Gender 244.017 1 244.017 19.056 .000
Classroom 648.233 2 324.117 25.311 .000
Gender * Classroom 489.233 2 244.617 19.102 .000

Error 691.500 54 12.806
Total 479293.000 60
Corrected Total 2072.983 59
a. R Squared = .666 (Adjusted R Squared = .636)
1. Gender
Dependent Variable: Math_Score
Gender Mean Std. Error 95% Confidence Interval
Lower Bound Upper Bound
Female 87.167 .653 85.857 88.477
Male 91.200 .653 89.890 92.510
2. Classroom size
Dependent Variable: Math_Score
Classroom size Mean Std. Error 95% Confidence Interval
Lower Bound Upper Bound
10 or less 93.250 .800 91.646 94.854
11-19 89.100 .800 87.496 90.704
20 or more 85.200 .800 83.596 86.804
3. Gender * Classroom size
Dependent Variable: Math_Score
Gender Classroom size Mean Std. Error 95% Confidence Interval
Lower Bound Upper Bound
Female
10 or less 93.800 1.132 91.531 96.069
11-19 88.500 1.132 86.231 90.769
20 or more 79.200 1.132 76.931 81.469
Male
10 or less 92.700 1.132 90.431 94.969
11-19 89.700 1.132 87.431 91.969
20 or more 91.200 1.132 88.931 93.469

Multiple Comparisons
Dependent Variable: Math_Score
Bonferroni
(I) Classroom size (J) Classroom size Mean Difference
(I-J)
Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
10 or less 11-19 4.1500* 1.13162 .002 1.3539 6.9461
20 or more 8.0500* 1.13162 .000 5.2539 10.8461
11-19 10 or less -4.1500* 1.13162 .002 -6.9461 -1.3539
20 or more 3.9000* 1.13162 .003 1.1039 6.6961
20 or more 10 or less -8.0500* 1.13162 .000 -10.8461 -5.2539
11-19 -3.9000* 1.13162 .003 -6.6961 -1.1039
Based on observed means.
The error term is Mean Square(Error) = 12.806.
*. The mean difference is significant at the .05 level.
a. Is there a main effect of gender? If so, explain the effect. Use post hoc tests when
necessary (or explain why they are not required in this specific case).
Answer

Results shows that there is a main effect of gender on math score [F(1, 54) = 19.056, p
= 0.000]. Male respondents (M = 91.20, SD = 3.20, N = 30) have higher mean score in
the mathematics exam as compared to the female respondents (M = 87.17, SD = 7.27, N
= 30). We don’t need post hoc tests since there are two factors being compared in this
case (male and female).
b. Is there a main effect of classroom size? If so, explain the effect. Use post hoc tests when
necessary (or explain why they are not required in this specific case).
Answer
Results shows that there is a main effect of classroom size on math score [F(2, 54) = 25.31, p
= 0.000]. Post hoc comparisons using the Bonferroni test indicated that the mean math score for
the class size of 10 or less (M = 93.25, SD = 3.64, N = 20) was significantly different from the
class size of 11-19 (M = 89.10, SD = 3.26, N = 20). The mean math score for the class size of 10
or less (M = 93.25, SD = 3.64, N = 20) was significantly different from the class size of 20 or
more (M = 85.20, SD = 7.15, N = 20). We also found out that the mean math score for the class
size of 11-19 (M = 89.10, SD = 3.26, N = 20) was significantly different from the class size of 20
or more (M = 85.20, SD = 7.15, N = 20).
Male respondents (M = 91.20, SD = 3.20, N = 30) have higher mean score in the mathematics
exam as compared to the female respondents (M = 87.17, SD = 7.27, N = 30). We don’t need
post hoc tests since there are two factors being compared in this case (male and female).
c. Is there an interaction between your two variables? If so, using post hoc tests, describe
these differences.
Answer

Results shows that there is an interaction effect between the two variables (gender and
classroom size) on math score [F(2, 54) = 19.102, p = 0.000]. Post hoc test showed that all the
interactions effects between gender and classroom size were significantly different (p < 0.05).
d. Is there support for the researcher’s hypothesis that girls would do better than boys in
classrooms with fewer students? Explain your answer.
Answer
Yes there is significant evidence and support for the researcher’s hypothesis that girls would
do better than boys in classrooms with fewer students. Results showed that female
respondents in a class size of 10 or less (M = 93.80) performed much better than male
respondents in the same class size (M = 92.70). It is however important to note that the
performance of female respondents decreases as the classroom size increases. Hence the
researcher’s hypothesis that girls would do better than boys in classrooms with fewer students
is valid.
e. Write up the results in APA style and interpret them. Be sure that you discuss both main
effects and the presence/absence of an interaction between the two.
Answer
A factorial ANOVA was performed to compare the main effects of classroom size and gender
and the interaction effect between gender and classroom size on the math scores (Miller &
Chapman, 2011) . Classroom size included three levels (10 or less, 11-19 and 20 or more). All
the effects were found to be statistically significant at 5% level of significance. The main
effect of gender on math score yielded an F-ratio of [F(1, 54) = 19.056, p = 0.000] indicating a
significant effect of gender on math score. Male respondents (M = 91.20, SD = 3.20, N = 30)
have higher mean score in the mathematics exam as compared to the female respondents (M =

87.17, SD = 7.27, N = 30). The main effect of classroom size on math score yielded an F-ratio
of [F(2, 54) = 25.31, p = 0.000] indicating a significant effect of classroom size on math score.
Post hoc comparisons using the Bonferroni test indicated that the mean math score for the class
size of 10 or less (M = 93.25, SD = 3.64, N = 20) was significantly different from the class size
of 11-19 (M = 89.10, SD = 3.26, N = 20). The mean math score for the class size of 10 or less
(M = 93.25, SD = 3.64, N = 20) was significantly different from the class size of 20 or more (M
= 85.20, SD = 7.15, N = 20). We also found out that the mean math score for the class size of 11-
19 (M = 89.10, SD = 3.26, N = 20) was significantly different from the class size of 20 or more
(M = 85.20, SD = 7.15, N = 20). The interaction effect was also statistically significant, [F(2, 54)
= 19.102, p = 0.000].
Part B. Applying Analytical Strategies to an Area of Research Interest
1. Briefly restate your research area of interest. Analysis of Covariance. Using your area of
interest, identify one independent and two dependent variables, such that the dependent
variables would likely be covariates. Now, assume you conducted an ANCOVA that shows
both the first independent variable as well as the covariate significantly predicts the dependent
variable. Create a mock ANCOVA output table (see SPSS Output 12.6 in your text for an
example) that supports the relationship shown above. Report your mock finding APA style.
Answer
A One-Way Analysis of Covariance (ANCOVA) was performed to evaluate the use of
Instagram on the narcissism scores obtained by the respondents. The independent variable was
the Instagram use. The covariate was the age of the respondent.
Variable name Variable Type
Narcissism Dependent variable
Instagram Use Independent variable

Age Covariate variable
Results shows that there is significant effect of Instagram use on the narcissism score after
controlling for the age of the respondent, F(4, 98) = 21.65, p < 0.05.Respondents who use of
Instagram always had statistically significant higher narcissism scores as compared to those who
rarely or never use Instagram (Engqvist, 2005).
References
Engqvist, L. (2005). The mistreatment of covariate interaction terms in linear mode analyses of
behavioral and evolutionary ecology studies. Animal Behavior, 70, 967-971.
Miller, G. A., & Chapman, J. P. (2011). Misunderstanding Analysis of Covariance. Journal of
Abnormal Psychology, 110, 40-48.