Statistics Project

Statistics Project
Student Name:
Instructor Name:
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30 May 2019

Introduction
This study sought to apply the statistical concepts on analysis of variance (one-way analysis of
variance, two-way analysis of variance and repeated measures) to analyze different cases. The
first case that the study sought to analyze was on the satisfaction levels of the respondents. The
study aimed to test whether the satisfaction levels of the respondents is affected by the gender of
the respondent or by the income level of the participant. Based on this, both one-way ANOVA
and two-way ANOVA were employed to analyze the cases. In the second part, the study aimed
to test the effect of instruction given to the students on their performance in the quizzes. Using
General Linear Model/repeated measures, a Repeated Measures ANOVA was performed to
analyze the influence of repeating the quiz over time on the quiz scores.
Results
Part 1:
a. One way ANOVA
In this section, the study sought to investigate whether there is significant difference in the
family satisfaction levels based on the income levels. The following hypothesis was tested;
Null hypothesis (H0): There is no significant difference in the average satisfaction for all the
income levels
Alternative hypothesis (HA): At least one of the income levels has different satisfaction level.
To test the above hypothesis, a one-way ANOVA was performed at 5% level of significance.
The results of the ANOVA test are presented below.
Table 1: Tests of Between-Subjects Effects
Dependent Variable: lsatisy

Source Type III
Sum of
Squares
df Mean
Square
F Sig. Partial Eta
Squared
Corrected
Model 18.619a 6 3.103 4.193 .001 .102
Intercept 1934.544 1 1934.544 2613.88
0 .000 .922
Income 18.619 6 3.103 4.193 .001 .102
Error 164.303 222 .740
Total 5492.254 229
Corrected
Total 182.923 228
a. R Squared = .102 (Adjusted R Squared = .078)
A one-way analysis of variance showed that the main effect of income was significant in
determining the satisfaction of a person, F(6, 222) = 4.19, p = .001, η2=.102. Post hoc test by
Tukey HSD showed that significant differences in satisfaction levels exist between those with
income levels of 1 and 3 (p = .002), 1 and 4 (p = .010) and 1 and 5 (p = .004).
b. Two way ANOVA table
In this section, the study sought to investigate whether there is significant difference in the
family satisfaction levels based on the income levels as well as based on gender and the
interaction effect of gender and family income level. The following three hypotheses were tested;
1. Null hypothesis (H0): There is no significant difference in the average satisfaction for all the
income levels
Alternative hypothesis (HA): At least one of the income levels has different satisfaction level.
2. Null hypothesis (H0): There is no significant difference in the average satisfaction for the
males and the females.
Alternative hypothesis (HA): There is significant difference in the average satisfaction for the
males and the females.

3. Null hypothesis (H0): There is no significant effect of the interaction between gender and
family income level on average satisfaction.
Alternative hypothesis (HA): There is significant effect of the interaction between gender and
family income level on average satisfaction.
To test the above hypotheses, a two-way ANOVA was performed at 5% level of significance.
The results of the ANOVA test are presented below.
Dependent Variable: lsatisy
Source Type III
Sum of
Squares
df Mean
Square
F Sig. Partial Eta
Squared
Corrected
Model 25.960a 13 1.997 2.735 .001 .142
Intercept 1765.279 1 1765.279 2418.00
3 .000 .918
Sex 1.999 1 1.999 2.738 .099 .013
income 18.664 6 3.111 4.261 .000 .106
sex * income 4.397 6 .733 1.004 .424 .027
Error 156.962 215 .730
Total 5492.254 229
Corrected
Total 182.923 228
a. R Squared = .142 (Adjusted R Squared = .090)
A two-way analysis of variance was performed on the influence of two independent variables
(gender and income) on the family satisfaction levels. Income level included 7 levels (0, 1, 2,
3, 4, 5 and 6) while gender consisted of two levels (male and female). The effect of gender
was found to be statistically insignificant at the 5% level of significance while the effect of
income was statistically significant at 5% level of significance. The main effect for gender
yielded an F ratio of F(1, 215) = 2.74, p = .099, η2=.013 indicating an insignificant difference
in the satisfaction levels between males and the females. For the income, the main effect