Statistics in Research Methods

This research study examines the relationships between achievement and variables like gender, self-esteem, age, and optimism. The study uses statistics to analyze the data and presents findings through tables and graphs. The results show strong and positive correlations between optimism and achievement, positive affect, self-esteem, and life satisfaction. However, age has a weak correlation with life satisfaction and self-esteem. The study concludes that optimism plays a significant role in achieving success in life.

Statistics
Research methods in language study
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Statistics
Introduction
The main objective of this research study was to find out whether there were relationships
between achievement and variables like gender, self-esteem, age and optimism. The study also
sought to fight the summary statistics to know how the data was spread. The results of the study
have been presented in form of tables and graphs as shown in the subsequent sections.
QUESTION 1
CORRELATIONS
Test for relationship between achievement and optimism.
Correlations
Achievement Optimism
Achievement
Pearson Correlation 1 1.000**
Sig. (2-tailed) .000
N 99 99
Optimism
Pearson Correlation 1.000** 1
Sig. (2-tailed) .000
N 99 99
**. Correlation is significant at the 0.01 level (2-tailed).
Table 1
Pearson correlation coefficient r computed is 1. This means that there is a strong and positive
correlation between optimism and achievement. The p-value (0.00) means that the correlation is
significant.
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Test for relationship between achievement and positive affect.
Correlations
Achievement Positive affect
Achievement
Pearson Correlation 1 .489**
Sig. (2-tailed) .000
N 99 99
Positive affect
Pearson Correlation .489** 1
Sig. (2-tailed) .000
N 99 100
**. Correlation is significant at the 0.01 level (2-tailed).
Table 2
Pearson correlation coefficient r computed is 0.49. This means that there is a strong and positive
correlation between optimism and positive affect. The p-value (0.00) means that the correlation
is significant.
Test for relationship between achievement and self-esteem.
Correlations
Achievement Self esteem
Achievement
Pearson Correlation 1 .589**
Sig. (2-tailed) .000
N 99 99
Self esteem
Pearson Correlation .589** 1
Sig. (2-tailed) .000
N 99 100
**. Correlation is significant at the 0.01 level (2-tailed).
Table 3
Pearson correlation coefficient r computed is 0.59. This means that there is a strong and positive
correlation between optimism and self-esteem. The p-value (0.00) means that the correlation is
significant.
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Test for relationship between achievement and life satisfaction.
Correlations
Achievement Life satisfaction
Achievement
Pearson Correlation 1 .449**
Sig. (2-tailed) .000
N 99 99
Life satisfaction
Pearson Correlation .449** 1
Sig. (2-tailed) .000
N 99 100
**. Correlation is significant at the 0.01 level (2-tailed).
Table 4
Pearson correlation coefficient r computed is 0.45. This means that there is a strong and positive
correlation between optimism and life satisfaction. The p-value (0.00) means that the correlation
is significant.
QUESTION 2
Test for relationship between age and life satisfaction.
Correlations
Life satisfaction Age
Life satisfaction
Pearson Correlation 1 .039
Sig. (2-tailed) .699
N 100 100
Age
Pearson Correlation .039 1
Sig. (2-tailed) .699
N 100 100
Table 5
Pearson correlation coefficient r computed is 0.04. This means that there is a weak but positive
correlation between age and life satisfaction. The p-value (0.7) means that the correlation is
insignificant.
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Statistics
Test for relationship between age and self-esteem.
Correlations
Age Self esteem
Age
Pearson Correlation 1 .239*
Sig. (2-tailed) .017
N 100 100
Self esteem
Pearson Correlation .239* 1
Sig. (2-tailed) .017
N 100 100
*. Correlation is significant at the 0.05 level (2-tailed).
Table 6
Pearson correlation coefficient r computed is 0.24. This means that there is a relatively strong
and positive correlation between age and self-esteem. The p-value (0.02) means that the
correlation is significant.
Test for relationship between age and self-esteem.
Correlations
Age Achievement
Age
Pearson Correlation 1 .317**
Sig. (2-tailed) .001
N 100 99
Achievement
Pearson Correlation .317** 1
Sig. (2-tailed) .001
N 99 99
**. Correlation is significant at the 0.01 level (2-tailed).
Table 7
Pearson correlation coefficient r computed is 0.32. This means that there is a relatively strong
and positive correlation between age and life achievement. The p-value (0.02) means that the
correlation is significant.
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QUESTION 3
a. Testing whether there is a difference in life satisfaction between the males and the
females
Independent sample t-test
Hypothesis
H0: There is no difference in life satisfaction between the males and the females
H1: There is a significant difference in life satisfaction between the males and the females
The level of significant is set at 0.05
Table of results
independent Samples Test
Levene's Test for
Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
Life
satisfaction
Equal variances
assumed
.951 .332 .078 98 .938 .11342 1.45578 -2.77553 3.00238
Equal variances
not assumed
.078 92.962 .938 .11342 1.44489 -2.75586 2.98271
Table 8
To be able to make decision and conclusion, the p-value is compared to the level of significance.
In this case, the p-value (0.33) is greater than the level of significance. The decision thus is not to
reject the null hypothesis. The conclusion therefore is that there is no difference in life
satisfaction between the males and the females.
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b. Testing whether there is a difference in self-esteem between the males and the
females
Independent sample t-test
Hypothesis
H0: There is no difference in self-esteem between the males and the females
H1: There is a significant difference in self-esteem between the males and the females
The level of significant is set at 0.05
Table of results is as below;
Independent Samples Test
Levene's Test
for Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
Self
esteem
Equal variances
assumed
.164 .687 1.071 98 .287 1.20359 1.12416 -1.02728 3.43446
Equal variances
not assumed
1.089 95.340 .279 1.20359 1.10557 -.99115 3.39833
Table 9
To be able to make decision and conclusion, the p-value is compared to the level of significance.
In this case, the p-value (0.69) is greater than the level of significance. The decision thus is not to
reject the null hypothesis. The conclusion therefore is that there is no difference in self-esteem
between the males and the females.
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Statistics
c. Testing whether there is a difference in achievement between the males and the
females
Independent sample t-test
Hypothesis
H0: There is no difference in achievement between the males and the females
H1: There is a significant difference in achievement between the males and the females
The level of significant is set at 0.05
Table of results is as below;
Independent Samples Test
Levene's Test for
Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
Achieveme
nt
Equal variances
assumed
.262 .610 .180 97 .857 .16541 .91675 -1.65408 1.98491
Equal variances
not assumed
.180 87.013 .858 .16541 .92088 -1.66493 1.99575
Table 10
To be able to make decision and conclusion, the p-value is compared to the level of significance.
In this case, the p-value (0.26) is greater than the level of significance. The decision thus is not to
reject the null hypothesis. The conclusion therefore is that there is no difference in achievement
between the males and the females.
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Statistics
DESCRIPTIVE STATISTICS
Statistics
Age Optimism Positive affect Self esteem Life
satisfaction
N Valid 100 99 100 100 100
Missing 0 1 0 0 0
Mean 36.8300 21.6667 33.7000 32.5000 22.5400
Median 37.0000 22.0000 35.0000 34.0000 23.0000
Mode 22.00a 21.00a 32.00a 38.00 20.00
Std. Deviation 12.4186 4.48581 6.88799 5.56958 7.17096
Variance 154.223 20.122 47.444 31.020 51.423
a. Multiple modes exist. The smallest value is shown
Table 11
Table 11 above shows the summary statistics for different variables. To add on, measures of
dispersion were also established. It can be observed that the mean age of the respondents who
took part in the survey was 36.83 years while the median age was 37 years. The standard
deviation and variance for the age were 12.41 and 154.22 respectively. The mean optimism level
was 21.67 while the median optimism level was 22. The standard deviation and variance for the
optimism level were 12.41 and 154.22 respectively. The mean positive affect was 33.7 while the
median positive affect was 35. The standard deviation and variance for the positive affect were
6.89 and 47.44 respectively. The mean self-esteem was 32.5 while the median self-esteem was
34. The standard deviation and variance for the self-esteem were 5.57 and 31.02 respectively.
Lastly, the mean life satisfaction was 22.54 while the median life satisfaction was 22. The
standard deviation and variance for the life satisfaction were 7.17 and 51.42 respectively.
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Graph showing distribution of respondents by gender
Figure 1
The graph above shows the distribution of participants by gender. It can be observed that there
were more males than females. The males were 57 while the females were 43.
Conclusion
From the analysis and findings of the research study several insights came out that led to various
conclusions. It can be concluded that optimism in life has significant correlation with
achievements in life. This could mean in other words that people who are pessimistic in life do
not achieve much. Optimism and positive affect also have strong correlation. When it comes to
achievement, we can conclude that it is strongly correlated with self-esteem and life satisfaction.
However, it is insignificantly related to age of an individual. With satisfaction, it can be
concluded that it has a very insignificant correlation with age. This means that an increase in age
does not influence an individuals’ satisfaction.
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