ACS401 Statistics Assignment: Variable Relationship Analysis

This statistics assignment analyzes relationships between variables using SPSS. The assignment is divided into three parts. The first part examines the association between email use and computer use, including cross-tabulation and hypothesis testing. The second part investigates the relationship between happiness and perception of life, again employing cross-tabulation and Chi-square tests. The third part explores the correlation between fathers' and mothers' education levels, utilizing correlation analysis and hypothesis testing. The solution includes SPSS output, statistical tests, and interpretations of the findings. The assignment aims to compare groups, investigate relationships between variables, and draw conclusions based on the statistical analysis.

Statistics
Student name:
Tutor name:
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NUMBER 1
a. Cross tabulation and graph
Case Processing Summary
Cases
Valid Missing Total
N Percent N Percent N Percent
Use e-mail? * Use
computer?
1213 80.9% 287 19.1% 1500 100.0%
Table 1
Use e-mail? * Use computer? Cross tabulation
Use computer? Total
No Yes
Use e-mail? No Count 329 201 530
% within Use computer? 99.1% 22.8% 43.7%
Yes Count 3 680 683
% within Use computer? 0.9% 77.2% 56.3%
Total Count 332 881 1213
% within Use computer? 100.0% 100.0% 100.0%
Table 2
Chi-Square Tests
Value df Asymp. Sig. (2-
sided)
Exact Sig. (2-
sided)
Exact Sig. (1-
sided)
Pearson Chi-Square 570.316a 1 .000
Continuity Correctionb 567.220 1 .000
Likelihood Ratio 681.764 1 .000
Fisher's Exact Test .000 .000
Linear-by-Linear Association 569.846 1 .000
N of Valid Cases 1213
Table 3
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Directional Measures
Value Asymp. Std.
Errora
Approx. Tb Approx. Sig.
Ordinal by Ordinal Somers' d
Symmetric .682 .017 28.405 .000
Use e-mail? Dependent .763 .015 28.405 .000
Use computer? Dependent .616 .021 28.405 .000
Table 4
Symmetric Measures
Value Asymp. Std.
Errora
Approx. Tb Approx. Sig.
Ordinal by Ordinal Gamma .995 .003 28.405 .000
N of Valid Cases 1213
Table 5
Figure 1
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Figure 2
Table 1 above shows the summary statistics of the cases of the respondents that were missing
and those that were non-missing. The total cases that were not missing were 1213 while those
that were missing were 287. The total number of participants was 1500.
Table 2 is a cross tabulation of computer users and email users. The columns represent the use of
computers while the rows represent the email users. Those who use email were 683 (56.3%)
while who do not are 530 (43.7%). Those who use computers were 881 while who do not are
332.
b. Hypothesis test
H0: There is no relationship between use of computer and use of email
H1: There is significant relationship between use of computer and use of email
Alpha = 0.01
From table 4 and 5, it can be observed that the p-values calculated (0.00) were both less than the alpha
value (0.05). The decision is that the null hypothesis is rejected. It is concluded that there is significant
relationship between use of computer and use of email.
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NUMBER 2
a. Cross tabulation and graph
Case Processing Summary
Cases
Valid Missing Total
N Percent N Percent N Percent
GENERAL HAPPINESS * IS
LIFE EXCITING OR DULL
967 64.5% 533 35.5% 1500 100.0%
Table 4
Cross tabulation between happiness and perception of life
GENERAL HAPPINESS * IS LIFE EXCITING OR DULL Crosstabulation
IS LIFE EXCITING OR DULL Total
EXCITIN
G
ROUTIN
E
DULL
GENERAL
HAPPINESS
VERY HAPPY Count 233 85 2 320
% within IS LIFE
EXCITING OR DULL
46.0% 19.4% 9.5% 33.1%
PRETTY HAPPY Count 257 312 11 580
% within IS LIFE
EXCITING OR DULL
50.7% 71.1% 52.4% 60.0%
NOT TOO
HAPPY
Count 17 42 8 67
% within IS LIFE
EXCITING OR DULL
3.4% 9.6% 38.1% 6.9%
Total Count 507 439 21 967
% within IS LIFE
EXCITING OR DULL
100.0% 100.0% 100.0% 100.0%
Table 5
Chi-Square Tests
Value df Asymp. Sig. (2-
sided)
Pearson Chi-Square 113.595a 4 .000
Likelihood Ratio 103.047 4 .000
Linear-by-Linear Association 95.465 1 .000
N of Valid Cases 967
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Table 6
Directional Measures
Value Asymp. Std.
Errora
Approx. Tb Approx. Sig.
Ordinal by Ordinal Somers' d
Symmetric .300 .029 10.210 .000
GENERAL HAPPINESS
Dependent
.303 .029 10.210 .000
IS LIFE EXCITING OR DULL
Dependent
.298 .028 10.210 .000
Table 7
Symmetric Measures
Value Asymp. Std.
Errora
Approx. Tb Approx. Sig.
Ordinal by Ordinal Gamma .546 .046 10.210 .000
N of Valid Cases 967
a. Not assuming the null hypothesis.
b. Using the asymptotic standard error assuming the null hypothesis.
Table 8
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Figure 3
Table 4 above shows the summary statistics of the cases of the respondents that were missing
and those that were non-missing. The total cases that were not missing were 967 while those that
were missing were 533. The total number of participants was 1500.
Table 5 is a cross tabulation of happiness and perception of life. The columns represent
perception while the rows represent happiness. Those who are very happy were 320 (33.1%),
those who are pretty happy were 580 (60%) while who are not happy were 67 (6.9%). When it
comes to perception of life, those who said life was exciting were 507, those who said life was a
routine were 439 while those who said life is dull were 21.
b. Chi square test of association (between happiness and perception of life)
H0: There is no relationship between being happy and perception of life
H1: There is significant relationship between being happy and perception of life
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Alpha = 0.05
From table 7 and 8, it can be observed that the p-values calculated (0.00) were both less than the alpha
value (0.05). The decision is that the null hypothesis is rejected. There is significant relationship
between being happy and perception of life.
Number 3
a. Correlation between fathers education and mothers education
Correlations
HIGHEST
YEAR
SCHOOL
COMPLETED
, MOTHER
HIGHEST
YEAR
SCHOOL
COMPLETED
, FATHER
HIGHEST YEAR
SCHOOL COMPLETED,
MOTHER
Pearson Correlation 1 .605**
Sig. (2-tailed) .000
N 1336 1024
HIGHEST YEAR
SCHOOL COMPLETED,
FATHER
Pearson Correlation .605** 1
Sig. (2-tailed) .000
N 1024 1090
**. Correlation is significant at the 0.01 level (2-tailed).
Table 9
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Figure 3
b. Hypothesis test
Hypothesis
H0: There is no relationship between father highest education and mother highest education.
H1: There is a significant relationship between father highest education and mother highest
education
Alpha = 0.05
From table 9 it can be observed that the p-values calculated (0.00) is less than the alpha value (0.05). The
decision is that the null hypothesis is rejected. It is concluded that there is a significant relationship
between father highest education and mother highest education. It can also be said that the
relationship between the two variables is linear. The R2 value of 0.38 means that the independent
variable explains 38% of the variation that occurs in the dependent variable.
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