Tax Preferences and Lodgement Methods

This assignment explores Australians' tax lodgement preferences, examining the choice between using tax agents or self-preparing returns. Data analysis techniques like ANOVA and regression are employed to identify factors influencing preference, such as age, income, and total deductions. The study reveals a strong inclination towards tax agents, especially among international students and individuals with higher incomes. Future research directions involve investigating the role of gender in tax lodgement choices.

Running Head: STATISTICAL MODELLING ASSIGNMENT
Statistical Modelling Assignment
Name of the Student
Name of the University
Author Note

1STATISTICAL MODELLING ASSIGNMENT
Table of Contents
SECTION 1....................................................................................................................................................2
Introduction.............................................................................................................................................2
SECTION 2....................................................................................................................................................3
Preference of Lodgement Methods of Australian People........................................................................3
SECTION 3....................................................................................................................................................4
Preference of Lodgement Methods of International Students................................................................4
SECTION 4....................................................................................................................................................6
Lodgement Method and Age Group........................................................................................................6
SECTION 5....................................................................................................................................................8
Lodgement Method and Total Income Amount......................................................................................8
SECTION 6....................................................................................................................................................9
Total Income Amount and Total Deduction Amount...............................................................................9
SECTION 7..................................................................................................................................................11
Conclusion.............................................................................................................................................11
References.................................................................................................................................................12

2STATISTICAL MODELLING ASSIGNMENT
SECTION 1
Introduction
In Australia, at the end of a financial year, a tax return file is lodged by a lot of the Australian
citizens. There are two different ways in which a tax return lodgement can be made. The first one is by
paying a registered tax agent and telling them to lodge the return file for them. The other method is by
lodging the tax returns by themselves (Alghamdi and Rahim 2016). The study here aims at evaluating the
proportion of people who prefer the tax agents to lodge the income tax and the proportion of people
who prefer to do it n their own. The preference has to be assessed based on some factors such as age,
income amount and deduction amount.
For the purpose of this study, data is necessary. Thus, data has been collected from the website
of the Australian Taxation Office (ATO). The dataset that will be considered for this study is actually a
subset of the original dataset that has been obtained from this website. A sample of 1000 people of
Australia has been selected from the whole dataset for this study. The dataset contains information
about the variables such as gender, age range, lodgement methods, total income amount and total
deduction amount. Here. In the gender column, 0 indicates male and 1 indicates female. In the column
age range, 0 indicates the person is aged more than 70 years, 1 indicates that the person is aged
between 65 and 69 years, 2 indicates that the person is aged between 60 and 64 years, 3 indicates that
the person is aged between 55 and 59 years, 4 indicates that the person is aged between 50 and 54
years, 5 indicates that the person is aged between 45 and 49 years, 6 indicates that the person is aged
between 40 and 44 years, 7 indicates that the person is aged between 35 and 39 years, 8 indicates that
the person is aged between 30 and 34 years, 9 indicates that the person is aged between 25 and 29
years, 10 indicates that the person is aged between 20 and 24 years and 11 indicates that the person is
aged below 20 years. In the column lodgement method, A indicates tax agent and S indicates self
preparer. Thus, these three variables are categorical variables. Again, the variables total income amount
and total deduction amount are continuous numeric data. The data collected in this case is secondary
data as it is obtained from the website of ATO. The first five cases of the data is attached in table 1.
Table 1: First five cases of Dataset 1
There is another part to this study. In this part data has to be collected from international
students about their preferences on lodgement methods of tax returns. 40 Students from different
nations studying in the Australian universities were asked this question and their responses were
recorded in the second dataset. In this case the data has been collected as a result of a survey and hence
it is known as a primary data. The variable involved in this case is a categorical variable.

3STATISTICAL MODELLING ASSIGNMENT
SECTION 2
Preference of Lodgement Methods of Australian People
At first, summary of the data on the Australian people has been conducted and it can be seen
clearly from table 2 as well as figure 1 that the tax agents are given preference by 738 people out of
1000 people. Thus, a very high proportion of people (73.8 percent) of Australia prefer lodging their tax
returns by hiring expert and registered tax agents.
Table 2: Types of Lodgement Methods by Australian People
Lodgement_method Frequency Proportion
A 738 0.738
S 262 0.262
Grand Total 1000 1
74%
26%
Lodgement Method
A
S
Figure 1: Proportion of different types of Lodgement Methods
The confidence interval for the given data has been obtained at 95 percent confidence level and
is given in table 3. It can be seen from the table that the 95 percent confidence interval for the
proportion of people preferring tax agents is (71.07%, 76.53%).
Table 3: Confidence Interval for the proportion of people preferring Tax Agents
Data
Sample Size 1000
Count of Successes 738
Confidence Level 95%

4STATISTICAL MODELLING ASSIGNMENT
Intermediate Calculations
Sample Proportion 0.738
z Value 1.9600
Standard Error of the Proportion 0.0139
Margin of Error 0.0273
Assumptions: n.p=738, n.q=262 MET
Confidence Interval
Interval Lower Limit 71.07%
Interval Upper Limit 76.53%
Thus, from the above analysis, it is clear the sample proportion of the people preferring tax
agents over themselves on the account of lodging tax returns is 0.738 and also with 95 percent
confidence, it can be said that the proportion of people of Australia preferring tax agents over
themselves for lodging tax returns lies between 71.07 percent and 76.53 percent.
SECTION 3
Preference of Lodgement Methods of International Students
Here, the preference of the lodgement method for tax returns is to be evaluated for the
international students. It can be clearly seen from table 4 that 80 percent of the students selected prefer
tax agents and 20 percent do not. Thus, quite a high proportion of students also prefer the tax agents
over themselves.
Table 5 shows the necessary calculations for the 95 percent confidence interval for the
proportion of students preferring tax agents. The table shows that with 95 percent confidence, within a
percentage of 67.60 and 92.40 students, there is a preference for tax agents for lodging tax returns.
Table 6 shows the comparisons of the two proportions for the preference of tax agents to lodge
tax returns. In order to run this test, the following hypothesis has been defined:
Null Hypothesis (H0): There is no difference in the proportions.
Alternate Hypothesis (H1): There is significant difference in the proportions.
From the results of the test, it can be seen that the null hypothesis is accepted. Hence there is no
difference in the proportions for the preference of tax agents over self preparers for lodgement of tax
returns by both the international students and the people of Australia (Krishnamoorthy 2016).
Table 4: Types of Lodgement Methods by International Students
Lodgement Method Frequency Proportion
A 32 0.8
S 8 0.2
Grand Total 40 1

5STATISTICAL MODELLING ASSIGNMENT
80%
20%
Lodgement Method
A
S
Figure 2: Types of Lodgement Methods by International Students
Table 5: Confidence Interval for the proportion of International Students
preferring tax agents
Data
Sample Size 40
Count of Successes 32
Confidence Level 95%
Intermediate Calculations
Sample Proportion 0.8
z Value 1.9600
Standard Error of the Proportion 0.0632
Margin of Error 0.1240
Assumptions: n.p=32, n.q=8 MET
Confidence Interval
Interval Lower Limit 67.60%
Interval Upper Limit 92.40%
Table 6: Z Test for Two Proportions

6STATISTICAL MODELLING ASSIGNMENT
Hypotheses
Null Hypothesis H0: p = 0%
Alternative Hypothesis HA: p <> 0%
Test Type Two
Level of Significance
 0.05
Sample Data
Sample Size Group 1 1000
Successes in Group 1 738
Sample Size Group 2 40
Successes in Group 2 32
Hypothesized Difference 0
Intermediate Calculations
Proportion Group 1 0.738
Proportion Group 2 0.8
Average Proportion 0.740385
Difference in Two Proportions -0.062
Z -0.87702
p-value 0.380474
Hypothesis Test Decision
Do not reject Ho
SECTION 4
Lodgement Method and Age Group
The relationship between age group and lodgement methods is given in table 7. It can be seen
from table 7 and figure 3 clearly that people of all age ranges prefer agents to lodge for their tax returns
rather than themselves. The difference in the proportion of preference is quite high in all the age groups
except for the people aged below 24 years. For the people aged below 24 years, the difference in the
proportion of preference for tax agents and themselves are very less.
Table 7: Age range and Lodgement Method (Observed Frequency Table)
Age Range Lodgement Method
A S Grand Total
0 43 10 53
1 29 10 39
2 59 13 72
3 69 14 83
4 89 18 107
5 88 20 108

7STATISTICAL MODELLING ASSIGNMENT
6 70 21 91
7 89 25 114
8 60 33 93
9 79 40 119
10 45 43 88
11 18 15 33
Grand Total 738 262 1000
0 1 2 3 4 5 6 7 8 9 10 11
0
10
20
30
40
50
60
70
80
90
100
Relationship Between Lodgement Method and Age
A
S
Age Range
Frequency
Figure 3: Relationship between Lodgement Method and Age
To test for the association between the age groups and lodgement methods, a chi square test of
association has to be conducted (Sharpe 2015). To conduct this test, the expected frequencies has to be
calculated which us given in table 8. The null and the alternate hypothesis for this test is given below:
Null Hypothesis (H0): There is no significant association between age range and Lodgement Methods.
Alternate Hypothesis (H1): There is significant association between age range and Lodgement Methods.
The significance value for this test has been found to be less than 0.05 (the level of significance).
Thus, the null hypothesis has been rejected. Thus, there is an association between age range and
lodgement methods.
Table 8: Expected Values of Age Range and Lodgement Methods
Age Range A S Grand Total
0 39.114 13.886 53
1 28.782 10.218 39
2 53.136 18.864 72
3 61.254 21.746 83
4 78.966 28.034 107
5 79.704 28.296 108

8STATISTICAL MODELLING ASSIGNMENT
6 67.158 23.842 91
7 84.132 29.868 114
8 68.634 24.366 93
9 87.822 31.178 119
10 64.944 23.056 88
11 24.354 8.646 33
Grand Total 738 262 1000
SECTION 5
Lodgement Method and Total Income Amount
Table 9 gives the summary of the average of the total income amount earned by the people
preferring tax agents and themselves respectively for lodging tax returns. It is very clear from the table
that people with higher income prefer tax agents and lower income count on themselves for lodging tax
returns.
Table 9: Summary of average Total Income
Lodgement Methods Average of Tot_inc_amt
A 67612.57859
S 45202.08397
Grand Total 61741.029
A S
0
10000
20000
30000
40000
50000
60000
70000
80000
Total Income and Lodgement Method
Lodgement Method
Average Total Income
Figure 4: Total Income and Lodgement Methods
It can be seen from table 10 that the average income of the people hiring tax agents are
$67,612.58 and self preparer are $45,202.08. On the other hand, it can also be seen that there are 50
percent of the people who earn more than $46,363 and $35,726 and hire tax agents or prepare by

9STATISTICAL MODELLING ASSIGNMENT
themselves respectively. As there s huge difference between these values and the average is quite high,
this indicates that there are some people who earn a lot higher than the others.
It has been observed that there are 34 such people hiring tax agents who earn a lot higher than
the other people of the group and 10 such people lodge for themselves who earn a lot higher than the
other people of the group. Thus, the incomes are not close to the mean income mostly. There are more
people who earn higher than the average.
Table 10: Summary of Lodgement Methods
A S
Mean 67612.58 45202.08
Standard Error 6398.625 2732.934
Median 46353 35726
Mode 0 0
Standard Deviation 173826 44236.4
Sample Variance 3.02E+10 1.96E+09
Kurtosis 484.0539 18.67934
Skewness 20.36088 3.408487
Range 4308305 380484
Minimum -1942 -7
Maximum 4306363 380477
Sum 49898083 11842946
Count 738 262
First Quartile 25848.75 17830.75
Third Quartile 77811.25 58913
Interquartile Range 51962.5 41082.25
Table 11: Outlier Ranges
Lower Outiler Range -52095 -43792.6
Upper Outlier Range 155755 120536.4
SECTION 6
Total Income Amount and Total Deduction Amount
Figure 5 shows the relationship between the Total Income and Total Deduction of the people of
Australia. It can be seen from the figure only that with the increase in the total income, there is Increase
in the total deduction. Thus, there is a positive relation between the two variables.
The degree of the relationship between the income and the deduction has been obtained as a
result of the regression analysis (Costa 2017). The relationship between Income and Deduction can be
established with the following equation:
Total deduction amount = 470.37 + (0.0325 * Total income amount)

10STATISTICAL MODELLING ASSIGNMENT
54.98 precent of the variability in the deduction amount can be explained by the income. The
model is quite a good fit as the significance value obtained from table 13 is less than the level of
significance (0.05).
-1000000 0 1000000 2000000 3000000 4000000 5000000
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
Total Income Vs. Total Deduction
Total Income Amount
Total Deduction Amount
Figure 5: Relationship between Total Income and Total Deduction
Table 12: Regression Statistics
Multiple R 0.741468594
R Square 0.549775676
Adjusted R Square 0.54932455
Standard Error 4455.001408
Observations 1000
Table 13: ANOVA
df SS MS F Significance F
Regression 1 24187044267 2.42E+10 1218.673 3.9162E-175
Residual 998 19807343468 19847038
Total 999 43994387735
Table 14: Coefficients of Regression Equation
Coefficients
Standard
Error t Stat P-value Lower 95% Upper 95%
Intercept 470.366301 152.164921
3.09116
1
0.00204
9
171.766404
6
768.966197
3
Tot_inc_amt
0.03251584
5 0.000931433
34.9094
9 3.9E-175
0.03068805
3
0.03434363
6

11STATISTICAL MODELLING ASSIGNMENT
SECTION 7
Conclusion
From the analysis conducted in the former sections, it has been observed that the preference
for the tax agents is much higher than self preparers on the account lodging tax returns. Both the people
of Australia and international students prefer to appoint tax agents to lodge their returns. People below
24 years old have shown equal preference towards both the types of lodgement methods. Total income
and Total deduction due to tax has been observed to have a direct relationship. With the increase in
income in the deduction amount increases as well.
In the study so far, the variable gender has not been considered at all. This study can be further
proceeded by considering the factor gender and preference of lodgement methods according to gender
could also be evaluated.

12STATISTICAL MODELLING ASSIGNMENT
References
Alghamdi, A. and Rahim, M., 2016. Development of a Measurement Scale for User Satisfaction with E-
tax Systems in Australia. In Transactions on Large-Scale Data-and Knowledge-Centered Systems
XXVII (pp. 64-83). Springer Berlin Heidelberg.
Krishnamoorthy, K., 2016. Handbook of statistical distributions with applications. CRC Press.
Sharpe, D., 2015. Your chi-square test is statistically significant: Now what?. Practical Assessment,
Research & Evaluation, 20.
Costa, V., 2017. Correlation and Regression. In Fundamentals of Statistical Hydrology (pp. 391-440).
Springer International Publishing.