Statistical Analysis of Gender Pay Gap and Occupation in Australia

This report presents a statistical analysis of the gender pay gap in Australia, utilizing two datasets to investigate salary disparities and occupational representation. The analysis includes descriptive statistics, such as column charts and tables, to illustrate gender distribution across different occupations and salary levels. Inferential statistics, including confidence intervals and hypothesis testing (z-tests and t-tests), are employed to examine the proportion of females in high-paying occupations and to test for the presence of a gender pay gap. The findings reveal significant variations in gender representation across occupations, with under-representation of females in certain high-paying fields. The study supports the existence of a gender pay gap in the Australian workforce, highlighting the need for further research to explore the underlying causes of salary differences and skewed gender distributions in specific occupations. The report concludes by emphasizing the importance of addressing these issues to promote gender equality in the workplace.

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Section 1: Introduction
a) A disturbing trend that is witnessed globally is the lower average salaries witnessed for
females in comparison to males. Such a trend if continued over the long time could lead to
severe labour shortages as the participation level of females may drop owing to lack of
adequate incentive to work. This difference in average salary across the gender is
commonly referred to as gender gap and is reality in Australian workplace as well as
highlighted through various reports. While the critics may criticise such claims citing
difference in occupational representation of genders, report seem to indicate the presence
of gender gap even in workplaces where the numerical strength is with females. Clearly,
more research is required on the topic to highlight the presence and the key contributory
reasons (Livsey, 2017). The given research study would also aim on the issue of gender
gap along with exploring possible interconnections with occupation.
b) A unique dataset is provided in the form of Dataset 1. The sample size for this is 1000
observations. The source of the data is ATO or Australian Taxation Office and since this
data has not been directly retrieved from the respondents or the selected sample, thus data
would be regarded as secondary (Flick, 2015). The information contained in the dataset
pertains to namely four aspects i.e. gender, occupation of taxpayer, underlying annual
salary level coupled with gift amount tax deduction. The first two variables would be
regarded as categorical variables that are measured through the use of nominal scale owing
to absence of any natural order. Besides, the last two are quantitative variables since the
corresponding data values are numerical in nature and belong to interval measurement
scale (Hair et. al., 2015). The initial five cases from the dataset 1 that has been provided
are illustrated as follows.
.
c) Yet another dataset that is utilised for completion of the task is dataset 2 which has not
been provided and hence has been obtained directly from the respondents. The sample size

of this data is 30 observations. This data is limited in variables as only two aspects have
been collected namely the salary level and underlying gender of the taxpayer. The
collection of data would enable further research to highlight if there is gender gap amongst
the Australian population. However, the data collected has issues regarding presence of
bias owing to non-probability sampling technique used coupled with a small sample size.
Thus, the result obtained from the statistical analysis of this data would have limited utility
and more emphasis would be accorded to dataset 1 to reach a meaningful conclusion
(Eriksson and Kovalainen, 2015).
Section 2: Descriptive Statistics
a) Through the use of the following column char the representation of the two genders in
different occupations is indicated.
The key reading from the graphical representation is that the representation of genders across
occupations shows high variation. For instance the female representation in occupation with
code 7 is 0% while in case of occupation with code 5, the representation of females is about
75%. Also, it is noticeable that males do not have lower than 20% representation in any of the
occupations. Thus, it is quite surprising to find certain occupations where presence of women
is almost absent. It needs to be explored as to why the representation of females in certain
occupations is so low.

b) Through the use of the following column chart, the distribution of salary across gender can
be summarised.
A clear reading from the above column chart is that for annual income levels below $ 50,000,
females are in majority while the position reverses as soon as the annual salary becomes
higher than $ 50,000. Further, as the annual salary levels witness an increase, the proportion
of females tends to incrementally decline Thus, there is no denying on the basis of the sample
dataset provided that the average salary levels of female employees is lower than the male
counterparts. However, this does also raise incremental question as to whether this gender
gap is on account of gender based discrimination or due to some other reason such as
different proportion representation in different occupations considering that salary levels
across occupations is different.
c) Through the use of the following table, the salary distribution of the two gender is
summarised as highlighted as follows.

The above table contains information which further builds on the gender gap and the fact that
the salary levels of females tends to be lower when compared to the other gender (i.e. males).
The disparity is particularly stark at higher salary levels when the presence of female seems
an aberration as there is high domination of males. To reach any conclusion based on the data
provided, it needs to be ascertained as to the underlying reason for this gender gap is any
discrimination or just unequal distribution of male and female in high paying occupations.
d) Through the medium of the scatter plot indicated below, the potential relationship between
the given variables can be explored.

The scatter points do not form any definite pattern and seem to indicate random scattering
thus highlighting that no signifciant relationship is visible between the taxpayer’s salary and
deduction for gift. Another crucial evidence further extending support to the above
conclusion is the coefficient of determiantion which has an almost zero value. This indicates
the inability of the salary amount to explain any variation in the deduction amount as gift.
Further, the underlying correlation of correlation would be practically zero (Eriksson and
Kovalainen, 2015).
Section 3: Inferential Statistics
a) In accordance with the relevant instruction, the population proportion of a particular
gender needs to be estimated for the occupations having the highest four median salary
levels. Through the usage of the pivot tables in excel, it has been obtained that the
occupations which offer the highest median salaries are 1,2,3 and 7 (Hillier, 2016). Based
on the sample representation of female, the population proportion of females has been
attempted assuming 95% confidence level. This yields the following confidence intervals.
The above computation leads to the 95% confidence interval determination as
(0.3544,0.5475). Hence, there is 95% likelihood that of all the people in Australia engaged in
occupation code 1, the female proportion should lie between 0.3544 and 0.5475.

The above computation leads to the 95% confidence interval determination as
(0.4815,0.6322). Hence, there is 95% likelihood that of all the people in Australia engaged in
occupation code 2, the female proportion should lie between 0.4815 and 0.6322.
The above computation leads to the 95% confidence interval determination as (0.0426,
0.1636). Hence, there is 95% likelihood that of all the people in Australia engaged in
occupation code 3, the female proportion should lie between 0.0426 and 0.1636.

The above computation leads to the 95% confidence interval determination as (0.000, 0.000).
Hence, there is 95% likelihood that of all the people in Australia engaged in occupation code
7, the female proportion should be 0%.
The computation of the intervals and their interpretation clearly highlight that in occupation
code 3 and 7, there is under-representation of females. The most curious case is that of
occupation code 7 where there is not even a single female from amongst a sample of 1000
people. Further probe is required in order to understand for such skewed gender distribution
observed in some of the occupations such as 7.
b) The requisite hypotheses are indicated below.
For the given hypothesis test, the suitable test statistics will be a z and the test would be right
tailed test. Owing to the preference for p value approach, using excel as an enabling tool, p
value computation has been carried out below.

The above result hints at p value being 0.0002. If this is compared with the assumed level of
significance (5%), then it is apparent that the level of significance is found to be greater. This
in turn highlights the presence of evidence to cause rejection of null hypothesis and
acceptance of alternative hypothesis (Hillier, 2016). Hence, the given sample data provides
support to the claim that more than 80% of the employees in occupation code 7 are males.
c) The requisite hypotheses are indicated below.
For the given hypothesis test, the suitable test statistics will be a t and the test would be two
tailed test. The t test is preferred to z test as the underlying standard deviation of the variable
population is not given. Owing to the preference for p value approach, using excel as an
enabling tool, p value computation has been carried out below.

The above result hints at p value being 0.000. If this is compared with the assumed level of
significance (5%), then it is apparent that the level of significance is found to be greater. This
in turn highlights the presence of evidence to cause rejection of null hypothesis and
acceptance of alternative hypothesis (Flick, 2015). Hence, the given sample data provides
support to the claim of presence of gender gap in the workforce in Australia.
d) The requisite hypotheses are indicated below.
For the given hypothesis test, the suitable test statistics will be a t and the test would be two
tailed test. The t test is preferred to z test as the underlying standard deviation of the variable
population is not given. Owing to the preference for p value approach, using excel as an
enabling tool, p value computation has been carried out below.

The above result hints at p value being 0.364. If this is compared with the assumed level of
significance (5%), then it is apparent that the level of significance is found to be lower. This
in turn highlights the absence of evidence to cause rejection of null hypothesis and
acceptance of alternative hypothesis (Hair et. al, 2015). Hence, the given sample data does
not provide support to the claim of presence of gender gap in the workforce in Australia.
Section 4: Conclusion
a) The hypothesis regarding gender gap persisting in Australia has received support from
Dataset 1 but not so from Dataset 2. However, this is not because the gender gap does not
exist but on account of the dataset 2 being unrepresentative of the underlying population.
The representation of different gender in occupations is quite variable and no uniform
trends are visible. However, there are certain occupations where the females are
essentially absent and further research in this regards is necessary. Further, the precise
contributory reasons for existence of gender gap also need to be explored in wake of the
results obtained.
b) There is ample scope for further research which would focus essentially on two aspects.
One would be on finding reasons as to why female representation in some occupations is
so low. The other would be on comparing the average salary levels of male and females
across occupation to see if there is a significant different or not which would provide a
more concrete evidence with regards to presence of gender gap in Australia.
.

References
Eriksson, P. and Kovalainen, A. (2015) Quantitative methods in business research 3rd ed.
London: Sage Publications.
Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research
project. 4th ed. New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials
of business research methods. 2nd ed. New York: Routledge.
Hillier, F. (2016) Introduction to Operations Research 6th ed. New York: McGraw Hill
Publications.
Livsey, A (2017) Australia's gender pay gap: why do women still earn less than men?
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