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Utilizing Benford's Law to Spot Earning and Revenue Management Practices in
Jordanian’s Listed Companies.
Omar Alsinglawi1
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Mohammad Aladwan2
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Sadam AL Wadi3
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Abstract
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Introduction
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Literature Review
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Table (1): Benford's Law: Anticipated Digital Frequencies, (Nigrini, 2005):
Position of Digits in Number.
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Digit First Digit Second Digit Third Digit Fourth Digit
0 0.11968 0.10178 0.10018
1 0.30103 0.11389 0.10138 0.10014
2 0.17609 0.10882 0.10097 0.1001
3 0.12494 0.10433 0.10057 0.10006
4 0.09691 0.10031 0.10018 0.10002
5 0.07918 0.09668 0.09979 0.09998
6 0.06695 0.09337 0.0994 0.09994
7 0.05799 0.09035 0.09902 0.0999
8 0.05115 0.08757 0.09864 0.09986
9 0.04576 0.085 0.09827 0.09982
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Research Hypotheses
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Methodology and Data Analysis:
Methodology
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5.2 Data Analysis:
5.2.1 Descriptive Statistics:
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Companies’ category Statistic Revenue Net income
Reported positive net
income mean 70,869,066 10,334,373
median 10,263,829 1,296,707
skewness 11.26058 7.06472
minimum 2,798 261
maximum 4,855,334,0
92 378,182,700
Number of
observations 2360 2360
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Reported Negative net
income (absolute) mean 18,406,622 2,292,057
median 3,436,647 546,192
skewness 9.21595 7.06141
minimum 3,417 1,780
maximum 807,720,34
272,298,079
Number of
observations 1300 1300
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Number
1 2 3 4 5 6 7 8 9
Observed
proportion (%)
30.674 16.265 13.54
112.824 10.38
710.53 9.02
57.735 7.018
Expected
proportion (%)
32.103 19.609 14.49
411.691 9.918 8.695 7.79
97.115 6.576
Deviation rate
(%) -1.429 -3.344 -
0.953 1.133 0.469 1.835 1.22
60.62 0.442
Z-statistics 1.135 3.244 1.036 1.386 0.6 2.689 1.90
20.99 0.726
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Number 1 2 3 4 5 6 7 8 9
Observed
proportion
(%)
34.212 14.156 13.604 6.151 6.151 8.576 7.454 5.404 5.59
Expected
proportion
(%)
30.405 17.785 12.619 9.788 8.006 6.762 5.855 5.167 4.622
Deviation
rate (%) 3.807 -3.629 0.985 -3.637 -1.855 1.814 1.599 0.237 0.968
Z-statistics 1.885 2.168 0.64 2.775 1.519 1.61 1.502 0.152 0.971
P-value 0.06 0.030* 0.522 0.006* 0.129 0.107 0.133 0.879 0.331
The number of observations (N) is 1300.
The Chi-square calculated for all digits is 22.40343882, exceeding the tabulated Chi-
square value of 15.682 at 8 degrees of freedom.
The Mean Absolute Deviation (M.A.D) is 0.02024206, indicating nonconformity.
indicates significance at the 5% level for the two-tailed test.
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3DDistribution of Second Digit for revenue figures for companies that have Positive
net income
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Table 7: Distribution of Second Digit for revenue figures – for companies which have
Negative net income
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Number
0 1 2 3 4 5 6 7 8 9
Observed
proportion
(%)
13.81
411.438 10.122 10.17
8
10.17
2
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58.79 9.608 10.34
28.499
Expected
proportion
(%)
12.30
611.729 11.214 10.76
2
10.33
19.953 9.62 8.797 9.022 8.755
Deviation
rate (%) 1.508 -0.291 -1.092 -
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0.159 0.172 -0.83 0.811 1.32 -0.256
Z-
statistics 1.612 0.284 1.316 0.617 0.128 0.148 0.98
90.323 1.642 0.295
P-value 0.107 0.776 0.188 0.537 0.898 0.883 0.32
30.746 0.329 0.762
The number of observations (N) is 1300.
The Chi-square calculated for all digits is 10.368764, exceeding the tabulated Chi-square
value of 17.265 at 9 degrees of freedom.
indicates significance at the 5% level for the two-tailed test.
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Table 8: Distribution of First Digit for companies which have Positive net income
Number 1 2 3 4 5 6 7 8 9
Observed
proportio
n (%)
29.78 18.9 12.9
6
10.6
49.773 5.285 5.211 4.199 5.34
7
Expected
proportio
n (%)
30.4 17.7
7
12.6
2
9.78
88.006 6.762 5.854 5.166 4.62
1
Deviation
rate (%)
-
0.629
1.12
9
0.34
1
0.85
51.767 -
1.477
-
0.643
-
0.967
0.72
6
Z-
statistics 0.764 1.09
2
0.34
7
1.03
52.539 2.19 0.965 1.574 1.25
4
P-value 0.445 0.27
5
0.72
90.3 0.011
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0.029
*0.335 0.116 0.21
Number of observations (N) = 2360
CHI square calculated for all digits is 18.67185497, compared to the tabulated Chi-
square value of 15.507 at 8 degrees of freedom.
Mean Absolute Deviation (M.A.D) is 0.010717479 (Acceptable conformity).
Significance at 5% (two-tailed test).
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Table 9: Distribution of first digit for companies which have negative net income.
Number 1 2 3 4 5 6 7 8 9
Observed
proportio
n (%)
30.54 16.87 15.15 8.435 8.81 7.113 5.244 3.745 5.619
Expected
proportio
n (%)
30.57 17.88 12.73 9.833 8.041 6.793 5.884 5.194 4.646
Deviation
rate (%)
-
0.036
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1.004 2.424 -
1.398 0.769 0.32 -0.64 -
1.449 0.973
Z-
statistics 0.019 0.557 1.635 1.031 0.579 0.21 0.542 1.417 0.975
P-value 0.985 0.579 0.102 0.302 0.563 0.834 0.588 0.157 0.329
Number of observation (N) = 1300
CHI square calculated to all of digit 8.20304947, where Chi-square tabulated 15.507 at 8
degrees of freedom
Mean absolute deviation (M.A.D) is 0.010106441 (Acceptable conformity)
significance at 5% (two-tailed test)* significance at 5% (two-tailed test)
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28DDistribution of second digit for companies which have positive net income
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Number
Observed
proportion
(%)
Expected
proportion
(%)
Deviation
rate (%) Z-statistics P-value
012.69 11.98 0.705 0.792 0.4295
112.69 11.4 1.284 1.491 0.1345
210.9 10.89 0.01 0.022 0.9855
310.39 10.44 -0.044 0.052 0.9615
48.962 10.04 -1.075 1.292 0.1975
510.54 9.673 0.866 1.06 0.2915
610.61 9.342 1.268 1.592 0.1115
77.313 9.041 -1.728 2.203 0.0265*
88.245 8.763 -0.518 0.635 0.528
97.671 8.505 -0.835 1.068 0.2875
- Number of observations (N) = 2360
- CHI square calculated for all digits = 13.977582, where the Chi-square tabulated value
is 16.971 at 9 degrees of freedom
- *Significance at 5% (two-tailed test)
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Number
Observed
proportion (%)
Expected
proportion (%)
Deviation
rate (%) Z-statistics P-value
011.55 11.95 -0.407 0.333 0.739
19.791 11.36 -1.573 1.639 0.101
29.791 10.86 -1.066 1.363 0.174
310.53 10.41 0.121 0.491 0.62
411.45 10.01 1.445 0.44 0.66
2+
59.422 9.643 -0.221 0.708 0.479
611.27 9.312 1.955 0.866 0.387
711.27 9.01 2.257 1.123 0.26
89.975 8.732 1.243 0.306 0.759
911.82 8.475 3.345 2.065 0.038
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