I have been fascinated by Benford for a while, so I finally decided to create a small Ruby script that will take a CSV file and compute the frequency distribution of the first digit.
An example of the use of this script can be found in the population_example.rb file. Note that to compensate for the lack of accuracy of this graph, the margin of error is computed between the result obtained from the dataset and Benford's predictions. When run, the output should look like this.
1: ---------------------------------------------------------|result:56.86% - error:88.9%
2: ---------------------|result:20.68% - error:17.43%
3: --------|result:8.15% - error:34.75%
4: -----|result:5.37% - error:44.58%
5: ---|result:2.98% - error:62.37%
6: --|result:2.19% - error:67.26%
7: -|result:0.99% - error:82.93%
8: -|result:1.19% - error:76.76%
9: --|result:1.59% - error:65.28%
Benchmark: 20.000000 0.000000 20.000000 ( 16.088452)
You can also pass it a --log option to display the data in a log graph. There is also the --hash option which displays the Hash generated to calculate the graph. Running ruby population_example.rb --log --hash would give us this.
{"1"=>56.86, "2"=>20.68, "3"=>8.15, "4"=>5.37, "5"=>2.98, "6"=>2.19, "7"=>0.99, "8"=>1.19, "9"=>1.59}
1: ----------------------------------------------------------|result:5.83 (56.86%). - error:88.9%
2: --------------------------------------------|result:4.37 (20.68%). - error:17.43%
3: ------------------------------|result:3.03 (8.15%). - error:34.75%
4: ------------------------|result:2.42 (5.37%). - error:44.58%
5: ----------------|result:1.58 (2.98%). - error:62.37%
6: -----------|result:1.13 (2.19%). - error:67.26%
7: |result:-0.01 (0.99%). - error:82.93%
8: ---|result:0.25 (1.19%). - error:76.76%
9: -------|result:0.67 (1.59%). - error:65.28%
Benchmark: 20.000000 0.000000 20.000000 ( 16.088452)
There is also a possibility of using the script with the --ascii_chart option (without the other options, they will be ignored anyway), whose result would look like this.
60.0|
55.0|*
50.0|
45.0|
40.0|
35.0|
30.0|
25.0|
20.0| *
15.0|
10.0| *
5.0| * *
0.0+----------*-*-*-*-
1 2 3 4 5 6 7 8 9
Benchmark: 20.000000 0.000000 20.000000 ( 16.563178)
Overall, two external (non-standard-library) libraries are used. The first one being the colored gem which allows us to add color to the output. The second is the ascii_charts library which helped to plot the other chart (the one that is generated once the --ascii_chart option is passed in).
- https://testingbenfordslaw.com/
- https://en.wikipedia.org/wiki/Benford's_law
- https://www.youtube.com/watch?v=XXjlR2OK1kM
- https://www.isaca.org/Journal/Past-Issues/2011/Volume-3/Pages/Understanding-and-Applying-Benfords-Law.aspx
- Create a dataset with Fibonacci series and test it