Intermediate Quantitative Methods for Accounting
The Business Council of Australia (BCA) provides a forum for Australian business leaders to contribute directly to public policy debates. One of the issues that BCA is currently working on is the debate on gender pay gap at Australian executives. You are a business analyst working in the Research Department of the BCA. As part of your job requirement, you are asked to submit a report on the gender pay gap of Chief Executive Officers (CEOs) to your Head of your Department so that it can be discussed at the next meeting of BCA board of directors.
There are 10 industry sectors within the Australian market. They are Consumer Discretionary, Consumer Staples, Energy, Financials, Health Care, Industrials, Information Technology, Materials, Telecommunication Services, and Utilities. To address the requirement of the business report (below questions), you choose 4 non-industrial sectors that traditionally have more women representation, i.e. Consumer Discretionary, Consumer Staples, Financials and Health Care. The information on CEO total compensation and CEO characteristics of all firms in each industry sector for the year 2017.
Column A: Firm ID
- To describe the ID of each firm in the sample, ranging from Firm 1 to Firm 277
Column B: Industry sector
- There are 4 industry sectors in the sample. They are Consumer Discretionary, Consumer Staples, Financials and Health Care.
Column C: CEO Total compensation
- Report the total compensation figures for CEO of each firm in the year 2017.
Column D: CEO with financial background
- Indicate the financial background of the CEO of each company
Y = CEO has background in the financial accounting area
N = CEO does not have background in the financial accounting area
There are four questions need to be addressed in the business report:
- Are there differences in CEO gender and CEO financial accounting background?
- Is the proportion of female CEOs that have financial accounting background different from that of male CEOs? How can you calculate the p-value of the test? Without calculation, can you tell the range of the p-value in this case, explain why?
- Is CEO total compensation different among the four chosen industry sectors?
- Is there a gender pay gap, i.e., do male CEOs earn more than female CEOs?
Answers:
1.
| Male CEO with financial background |
Female CEO with financial background |
| 1 |
2 |
| 1 |
2 |
| 1 |
2 |
| 1 |
2 |
| 1 |
2 |
| 1 |
2 |
| 1 |
2 |
| 1 |
2 |
Hypothesis
H0: There is no difference in CEO gender and Financial accounting background
H1: There is difference in CEO gender and Financial accounting background
Test:
Decision Rule: Reject H0 whenver P-value is less than the Aplha value, Alpha=0.05
Test Value: 0.096675978
Decision : Fail to Reject the null hypothesis
Conclusion: Statistically there is no sufficient evidence to prove tha there is no difference in CEO gender and Financial accounting background Anova: Single Factor
| SUMMARY |
|
|
|
|
| Groups |
Count |
Sum |
Average |
Variance |
| Male CEO with financial background |
39 |
39 |
1 |
0 |
| Female CEO with financial background |
39 |
78 |
2 |
0 |
| ANOVA |
|
|
|
|
|
|
| Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
| Between Groups |
19.5 |
1 |
19.5 |
65535 |
0.096675978 |
3.966759784 |
| Within Groups |
0 |
76 |
0 |
|
|
|
| Total |
19.5 |
77 |
|
|
|
|
2.
H0: There is no difference in the proportion of female and male CEOs that have finacial accounting background.
H1: There is a difference in the proportion of female and male CEOs that have accounting backround.
Test: Single factor ANOVA since the test involves comparison of means
Decision Rule: Reject H0 whenver P-value is less than the Aplha value, Alpha=0.05
Test Value: P- value= 0.651721
Decision : Fail to Reject H0
Conclusion: There is no sufficient evidence to show that there is difference in the proportion of female and male CEOs that have finacial accounting background.
Anova: Single Factor
Summary
| Groups |
Count |
Sum |
Average |
Variance |
| Background = Y |
2 |
164 |
82 |
3698 |
ANOVA
| Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
| Between Groups |
650.25 |
1 |
650.25 |
0.276085341 |
0.651720908 |
18.51282051 |
| Within Groups |
4710.5 |
2 |
2355.25 |
|
|
|
| |
|
|
|
|
|
|
| Total |
5360.75 |
3 |
|
|
|
|
3.
| Consumer Staples CEO Total compensation ($) |
Financials CEO Total compensation ($) |
Healthcare CEO Total compensation ($) |
| 892,543 |
127,313 |
454,393 |
| 287,567 |
191,050 |
120,000 |
| 214,000 |
105,728 |
499,028 |
| 186,000 |
291,139 |
518,672 |
| 190,000 |
257,729 |
132,000 |
| 723,153 |
476,075 |
373,139 |
| 1,140,107 |
1,230,768 |
514,268 |
| 192,975 |
907,848 |
546,093 |
| 456,067 |
256,000 |
336,290 |
| 2,079,610 |
1,581,415 |
509,868 |
| 2,407,705 |
329,052 |
359,000 |
| 2,184,213 |
365,040 |
275,772 |
| 556,520 |
261,485 |
574,301 |
| 4,398,243 |
3,693,762 |
452,502 |
| 3,373,367 |
307,278 |
727,971 |
| 1,364,121 |
269,804 |
2,500,000 |
| 133,450 |
2,696,728 |
719,866 |
| 491,068 |
346,591 |
1,140,904 |
| 2,048,704 |
741,281 |
860,132 |
| 280,000 |
728,155 |
1,427,230 |
| 1,330,000 |
9,827,281 |
679,570 |
| 613,746 |
582,982 |
175,000 |
| 1,032,517 |
994,871 |
273,125 |
| 514,574 |
3,350,334 |
424,390 |
| 2,047,242 |
740,526 |
697,837 |
Hypothesis:
H0: There is no difference in CEO total compensation among the four chosen Industry sectores
H1: There is a difference in CEO total compensation among the four chosen industry sectors.
Test Single factor ANOVA since the test involves mean comparion
Decision Rule: Reject H0 whenever p-value is less than the Alpha value=0.05
Test Value P-value=0.2843 which is less than the alpha vele.
We Fail to Reject the H0
Statistically, there is no sufficient evidence to prove that there is a difference in CEO total compensation among the four chosen
Industry sectores
Anova: Single Factor
| SUMMARY |
|
|
|
|
| Groups |
Count |
Sum |
Average |
Variance |
| Consumer Discretionary CEO Total compensation ($) |
25 |
35090532 |
1403621.28 |
3.48728E+12 |
| Consumer Staples CEO Total compensation ($) |
25 |
29137492 |
1165499.68 |
1.21223E+12 |
| Financials CEO Total compensation ($) |
25 |
30660235 |
1226409.4 |
4.16735E+12 |
| Healthcare CEO Total compensation ($) |
25 |
15291351 |
611654.04 |
2.42857E+11 |
| ANOVA |
|
|
|
|
|
|
| Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
| Between Groups |
8.77311E+12 |
3 |
2.92437E+12 |
1.284065408 |
0.284300852 |
2.699392598 |
| Within Groups |
2.18633E+14 |
96 |
2.27743E+12 |
|
|
|
| Total |
2.27406E+14 |
99 |
|
|
|
|
4.
| Male CEO Total compensation ($) |
Female CEO Total compensation ($) |
| 788,755 |
263,468 |
| 1,563,836 |
369,852 |
| 894,147 |
109,985 |
| 4,826,298 |
7,588,095 |
| 357,009 |
490,922 |
| 5,215,837 |
698,510 |
| 695,274 |
282,018 |
| 2,250,091 |
892,543 |
| 2,862,271 |
287,567 |
| 651,750 |
214,000 |
| 657,073 |
186,000 |
| 865,747 |
127,313 |
| 667,460 |
191,050 |
| 472,788 |
454,393 |
| 1,139,084 |
120,000 |
| 148,446 |
499,028 |
| 852,093 |
518,672 |
| 2,571,348 |
132,000 |
| 1,763,825 |
373,139 |
| 171,637 |
514,268 |
| 6,466,016 |
546,093 |
| 692,061 |
336,290 |
| 440,061 |
509,868 |
| 474,489 |
359,000 |
| 484,145 |
275,772 |
| 1,810,000 |
574,301 |
| 836,250 |
452,502 |
| 271,124 |
727,971 |
| 1,451,854 |
2,500,000 |
| 2,512,987 |
719,866 |
| 3,071,799 |
1,140,904 |
| 1,468,750 |
860,132 |
| 978,805 |
1,427,230 |
| 348,184 |
679,570 |
| 456,067 |
521,000 |
| 2,079,610 |
1,384,330 |
| 2,407,705 |
874,540 |
| 2,184,213 |
505,013 |
| 556,520 |
420,500 |
| 4,398,243 |
148,777 |
| 3,373,367 |
2,769,564 |
| 994,871 |
211,672 |
| 3,350,334 |
469,896 |
| 740,526 |
985,660 |
| 8,444,023 |
2,655,574 |
| 400,998 |
190,000 |
| 1,060,783 |
723,153 |
| 810,220 |
1,140,107 |
| 181,833 |
192,975 |
| 314,406 |
105,728 |
| 290,540 |
291,139 |
| 1,074,990 |
257,729 |
| 337,254 |
476,075 |
| 593,836 |
1,230,768 |
| 585,700 |
907,848 |
| 465,652 |
256,000 |
| 1,847,044 |
1,581,415 |
| 2,853,452 |
329,052 |
| 478,930 |
365,040 |
| 321,678 |
261,485 |
| 4,118,586 |
3,693,762 |
| 822,091 |
307,278 |
| 295,136 |
269,804 |
| 3,475,720 |
2,696,728 |
| 712,542 |
346,591 |
| 344,341 |
741,281 |
| 572,909 |
728,155 |
| 328,447 |
9,827,281 |
| 971,195 |
582,982 |
| 297,962 |
175,000 |
| 212,224 |
273,125 |
| 380,207 |
424,390 |
| 339,583 |
697,837 |
Anova: Single Factor
| SUMMARY |
|
|
|
|
| Groups |
Count |
Sum |
Average |
Variance |
| Male CEO Total compensation ($) |
73 |
104195032 |
1427329.205 |
2.50419E+12 |
| Female CEO Total compensation ($) |
73 |
65441576 |
896459.9452 |
2.25277E+12 |
| ANOVA |
|
|
|
|
|
|
| Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
| Between Groups |
1.02865E+13 |
1 |
1.02865E+13 |
4.324821826 |
0.039333269 |
3.906848991 |
| Within Groups |
3.42501E+14 |
144 |
2.37848E+12 |
|
|
|
| |
|
|
|
|
|
|
| Total |
3.52788E+14 |
145 |
|
|
|
|
Hypothesis:
H0: There is no pay gap between the male and female CEOs
H1: There is is a pay gap between the male and female CEOs
Test Single factor ANOVA since the test involves Mean comparison of the pay between males and females
Decision Rule: Reject H0 whenever p-value is less than the Alpha value=0.05
Test Value P-value=0.037 which is less than the alpha vele.
Reject the H0
Conclude that statistically, there is no sufficient evidence to show that there is no pay gap between the male and female CEOs.
