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RMIT Bachelor of Business Marketing Business ECON1030 Statistics 1

Roksana Hematizadeh

Amelia May Lois Bennett Easton

S3786141

A Comparative Report of Australia’s Private and Public Sectors Executive Summary This report provides analysis and evaluation of the private sector in comparison to the public sector, taking into account many factors including age, hourly wage, marital status and whether or not each sample has a degree. In this report, Histograms are utilized as data to help identify similarities and differences between the public and private sectors in order to provide a comprehensive and systematic analysis. This report used various methods including performing hypothesis tests to come to conclusive outcomes assisting the Australian Productivity Commission to analyse the pay gap between the public and private sectors in Australia. Future summaries should include data from a larger sample pool, as the sample size for both public and private labour sectors were relatively small and therefore the conclusions made are difficult to generalise to the population.

Introduction The private sector is run by individuals and companies for profit and is not under the state’s control. Conversely, companies and corporations that are government run are in the public sector. This report makes clear comparisons between each sector and carefully examines the pay gap using data from the 2017 Household, Income and Labor Dynamics in Australia survey. In a viable labor market people with the same qualities and attributes should be paid equally, irrespective of their sector. When this is not the case the procurement of public goods, the labor market and equality suffer. Through my analysis it can be concluded that there are a number of key differences between these groups, however a key finding was that in general people are more likely to have a higher hourly wage in the public sector than the private sector. This report will be professionally presented employing useful graphical data to assist in the analysis.

Section 1 – Descriptive Analysis 1a. Public Sector Table 1. Descriptive statistics of hourly wage for public sector

1b. Private sector Table 2. Descriptive statistics of hourly wage for private sector

Public Sector Mean Standard Error Median Mode Standard Deviation Sample Variance

Private Sector

41.90614 2.355428 38.88889 20

Mean Standard Error Median Mode Standard Deviation Sample Variance

16.148 260.7578 1

35.83736 1.428651 31.96667 25 17.67144 312.2798

Kurtosis Skewness Range Minimum Maximum Sum Count

0.946854 0.879301 74.12202 14.6875 88.80952 1969.589 47

Kurtosis Skewness Range Minimum Maximum Sum Count

The Location:  Mean is 41.90614  Median is 38.88889  Mode is 20 The Spread:  Sample variance is 260.7578  Range is 74.12202  IQR is 19.22957 The Shape:  Skewness is 0.879301  Kurtosis is 0.046854

3.346758 1.551679 108 7 115 5483.116 153

The Location:  Mean is 35.83736  Median is 31.96667  Mode is 25 The Spread:  Sample variance 312.2798  Range is 108  IQR is 19.55556. The Shape:  Skewness is -1.551679  Kurtosis is 3.346758

Section 2 – Hourly Wage Distribution 2a. Public sector Figure 1: Public sector hourly wage distribution 18 16 14

Frequency

12 10 8 6 4 2 0 14.6875

27.04117

39.39484

51.74851

64.10218

76.45585

More

Hourly Wage ($)

This histogram highlights the hourly wage and the frequency each wage was earned by the participants in the public sector. The graph is not evenly distributed as it has a slight right skew. This can be proven by comparing the mean and the median of the hourly wages. Because the mean value is higher than the median it can be concluded that the hourly wage is positively skewed. Testing for outliers IQR = Q3 - Q1 2

51.74984-32.52027 = 19.22957 UPPER FENCE: Q3 + (1.5*IQR) 51.74984 + (1.5*19.22957) = 80.594195 LOWER FENCE: Q1 - (1.5*IQR) 32.52027 - (1.5*19.22957) = 6.675915 Hence the number of outliers is 2 both being on the high end of the distribution. 2b. Private sector Figure 2: Private sector hourly wage distribution 50 45 40

Frequency

35 30 25 20 15 10 5 0 5

15

25

35

45

55

65

75

85

More

Hourly wage ($)

The above figure demonstrates a positive skew distribution. This is consistent with the mean being higher in value than the median depicting a right skew. Whilst most frequently people are paid between $20 and $40 per hour, in the private sector there is greater distribution along the higher end of the graph. Testing for outliers IQR = Q3 - Q1 43.75 -24.19444 = 19.55556 UPPER FENCE: Q3+ (1.5*IQR) 43.75 + (1.5*19.55556) = 73.08334 LOWER FENCE: Q1 - (1.5*IQR) 24.19444 - (1.5*19.55556) 3

= -5.1389 From this we can see there are 41 outliers.

Section 3 – Employee characteristics Figure 3: Proportion of females and males in the public sector

23

Figure 6: Proportion of females and males in the private sector

24

Female

Female

Male

Figure 4: Proportion of people married in public sector

70

83

Male

Figure 7: Proportion of people married in private sector

17

73

80 30

No

No

Yes

Figure 5: Proportion of people with a degree in the public sector

Figure 8: Proportion of people with a degree in the private sector

68

22

25

No

Yes

85

No

Yes

Yes

Through the analysis of the data we see that in regards to wage in the private sector the mean, being the average found by adding all of the wages provided by the survey together before dividing by the number of participants, was $35.837 per hour whereas in the public sector it was $41.906. Following this trend, the median wage, the middle value when the data entries are ordered from least to greatest, was $31.967 in comparison to the public sector median of $38.889. Although the mode, the number that occurs most frequently in the data, was also 4

higher in the private sector at, $25 versus the public's $20 per hour. In regard to standard deviation, being how spread out the data is or how far away from the mean each data value is, the private sector had a standard deviation of $17.671 as compared with the public sector of $16.14. This analysis of the wages suggests on average those working in the public sector make more money as a whole despite the fact that there is a greater number of individuals earning more money per hour than the public sector. When considering whether or not those employees hold a university degree seems to be somewhat unrelated with 44.44% of the private sector comprising university graduates compared to the 51.63% in the public sector. It appears that those who don't hold university degrees but that are still in a higher age bracket tend to be older than others in the survey. Suggesting that experience may make up for no degree. The mean age for those in the private sector is 38.261 years old opposed to the public’s older 47.787 years, this may help to explain the increased percentage of married people in the private sector being 63.83% opposed to the privates 47.71% as the individuals are older thus more likely to be settled down and married. When comparing gender, the public sector has more women at 51.06% against the privates 47.71%. Although interestingly in both sectors women are overrepresented in the lower income brackets whilst males are overrepresented in the top brackets.

Section 4 – Confidence intervals Derive the 95% confidence interval for the average hourly wage for the public and private sector respectively. Clearly label your diagram and indicate any assumptions made. Is the width of the intervals the same? Explain carefully. [Topic 5-7] 95% / 0.05 significance level Public Sector M = 41.90614 Confidence level = 4.74123 Lower limit = 37.16491 Upper limit = 46.64737 The confidence interval of the values is 37.16491 ± 46.64737

∴ You can be 95% con/dent that the popula(on mean (μ) is between 0.04602305 and 3.12591495. ∴ You can be 95% con/dent 5

that the popula(on mean (μ) is between 0.04602305 and 3.12591495. From this, we are 95% confident that the weekly return rates for MAC is between -0.053% and 0.729%. From this, we are 95% confident that the average hourly wage for the public sector is between 37.16491 and 46.64737. Private Sector M = 35.8374 Confidence level = 2.8225777459776 Lower limit = 33.01478 Upper limit = 38.65994 The confidence interval of the values is 33.01478 ± 38.65994 From this, we are 95% confident that the average hourly wage for the public sector is between 33.01478 and 38.65994.

At a 95% level of confidence, the confidence interval for the slope is -1.4888448; 1.49872949. Therefore, making 6

us confident that 95% of DLT’s return will be between -14.89% and 14.99%. The width of the private sector confidence interval is smaller than the width of the public sector confidence interval. The same size of the private sector was 153 whereas the sample size of the public sector was 47. The width of the confidence interval decreases as the sample size increases; therefore, it would be expected that the private sector would have a smaller confidence interval than the public sector. A narrower confidence interval enables more precise population estimates, and can therefore be more confident in the location of the mean wage.

Section 5 – Hypothesis testing 5a. A media report claims that the average hourly wage for the private sector in Australia in 2017 was 40 AU$. Do you agree? Perform a hypothesis test at the 5% significance level. Clearly label your diagram and indicate any assumptions made. [Topic 8-9] Null hypothesis = 40 Test hypothesis ≠ 40

μ a = 0.05, n = 153, degrees of freedom = 152, σ = unknown t = +/-1.9757

=

35.83736 - 40

= -2.913685243

17.67144 √153

If the t-test statistic is between t-critical values -1.9757 and 1.9757, we do not reject the null hypothesis.

However, -2.913685243 < -1.9757, therefore we reject null hypothesis. Conclusion 7

We can reject the null hypothesis and support the test hypothesis that at a 5% significance level, there is sufficient evidence to reject the claim that the average hourly wage for the private sector was $40. 5b. Is the average hourly wage equal for the public and private sector? Perform a hypothesis test at the 5% significance level. Clearly label your diagram and indicate any assumptions made. [Topic 8-9] Null hypothesis: public $ = private $ Test Hypothesis = public $ ≠ private $ a = 0.05, n1 = 47, n2 = 153, degrees of freedom = 46, σ = unknown

41.90614 - 35.83736 - 0

=

√

= 2.202961

260.7578 + 312.2798 47

153

If the t-test statistic is between t-critical values -2.0129 and 2.0129, we do not reject the null hypothesis.

However, 2.202961 > 2.0129, therefore we reject null hypothesis. Conclusion We can reject the null hypothesis and support the test hypothesis that at a 5% significance level, there is sufficient evidence that the average hourly wage is not equal for the public and private sector.

Conclusions This report estimates the wage differentials between the public sector and the private sector in Australia. After observing individual characteristics and data based on the HILDA survey data from 2017, it is shown that on average workers in the public sector earn more hourly wages than those in the private sector.

References 8

1. Andreas Makridis, C., 2020. [online] Belfercenter.org. Available at: [Accessed 20 September 2020]. 2. Cai, Lixin & Liu, Amy. (2008). Public-Private Wage Gap in Australia: Variation Along the Distribution. Centre for Economic Policy Research, Research School of Economics, Australian National University, CEPR Discussion Papers 3. Birch, E 2006, 'The Public-Private Sector Earnings Gap in Australia: A Quantile Regression Approach', Australian Journal of Labour Economics, vol. 9, no. 2, pp. 99-123.

Part B: Ministerial brief Figure 3: Distribution of male and female hourly wages in the public sector 18 16 14

Frequency

12 10 8 6 4 2 0

$5

$15

$25

$35

$45

$55

$65

$75

Hourly wage Male

Female

Figure 3: Distribution of male and female hourly wages in the private sector

9

$85

$95

50 45 40

Frequency

35 30 25 20 15 10 5 0

$5

$15

$25

$35

$45

$55

Male

$65

$75

$85

$95

More

Female

Multiple studies have conducted inquiries into the pay gap of the public and private sectors of Australia. Many show that the full-time male employees in the public sector earn 10-15% more weekly earnings than those in similar roles in the private sector. This is true for women, also demonstrating that female public sector employees are found to earn around up to 25% more than those in the private sector. What is important to note is that whilst men and women earn similar amounts in the moderately paid jobs women are vastly underrepresented in highpaying jobs in both the public sector. Although whilst consistent with the private sector as well it is not as prevalent, considering the highest-paid participant in the survey is a woman earning $115 per hour.

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