Statistical Analysis: T-Test for Income Differences, SPSS

This assignment applies the t-test to analyze income differences between male and female employees using a sample dataset. The student used IBM SPSS Statistics and the "Example Dataset" to assess the hypothesis: "Men and women have different incomes in this city." The solution includes the t-test output, calculations, and a discussion of the appropriate t-test type, including the rationale for using a two-tailed test. The student calculated the test statistic, critical value, and effect size (r2), and interpreted the results by stating the reason for the study, presenting the main results, explaining the results' meaning, and suggesting future research directions. The analysis concluded that there was no significant difference in the average income of male and female workers, and the student recommended increasing the sample size and using random sampling methods for future research.

Difference in the Average Income between Male and Female Employees
1. A t-test was performed at 0.05 level of significance based on the hypothesis below.
2.
H0: there is no significant difference between the average income of male and female employees
Versus
H1: there is a significant difference between the average income of male and female employees
3. Summary of the t-tests are represented in the sections below.
4. A two-tailed t-test was necessary to investigate the difference since the one-sided test
would be biased on one side either male have higher or lower average income than
females and vice versa(Corty, 2016).
5. The output of the t-test was reported as follows t (28) =0.801 and p-value=0.430 as
shown in the output below.
6. The effect size of the test was calculated using r2 and below is the output of the effect
size for the difference in the average income between male and female employees. Below
is the output of the test.
Correlations
maleIncome femaleIncome

maleIncome
Pearson Correlation 1 .287
Sig. (2-tailed) .300
N 15 15
femaleIncome
Pearson Correlation .287 1
Sig. (2-tailed) .300
N 15 15
7.
a) The independent two-sided t-test was performed to investigate whether there was a
significant difference between the average income for male and female employees. It was
necessary because the sample size was small and the population standard deviation was
unknown (De Winter, 2013). The effect size was used for investigating the kind of
difference that existed between the average income between the income of males and
females (Fritz, Morris, & Richler, 2012).
b) The t-test had a p-value of 0.43 which was greater than 0.05 level of significance.
Therefore the null hypothesis was accepted and the test concluded that there was no
significant difference in the average income of male and female workers (De Winter,
2013).
c) The effect size between the average income of the income between the two genders was
0.287 this implied that there was a low effect size (Fritz, Morris, & Richler, 2012).
The two tests indicated that there was no significant difference in the average income
between male and female employees.
d) In the future to improve the efficiency of the results the sample size should be increased.
Additionally, random sampling methods should be used to minimize the bias and
variability that may occur during sampling. Finally, since the null hypothesis was not

rejected this implied that there was a need to include other factors that may determine the
income of the employees (Kifle & Desta, 2012).
References
Kifle, T., & Desta, I. H. (2012). Gender Differences in Domains of Job Satisfaction: Evidence
from Doctoral Graduates from Australian Universities. Economic Analysis &
Policy, 42(3).
De Winter, J. C. (2013). Using the Student's t-test with extremely small sample sizes. Practical
Assessment, Research & Evaluation, 18(10).
Fritz, C. O., Morris, P. E., & Richler, J. J. (2012). Effect size estimates: current use, calculations,
and interpretation. Journal of experimental psychology: General, 141(1), 2.
Corty, E. (2016). Using and Interpreting Statistics A practical text for the behavioral, social,
and health sciences (3 ed.). New York, NY: Worth Publishers.