Benford's law - using mathematics to detect accounting fraud (Excel)

[@NEDLeducation]

APPLYING BENFORD'S LAW TO THE US 2020 ELECTION: kzbin.info/www/bejne/q2Ong6qqa7eKr8U You can find the spreadsheets for this video and some additional materials here: drive.google.com/drive/folders/1sP40IW0p0w5IETCgo464uhDFfdyR6rh7 Please consider supporting NEDL on Patreon: www.patreon.com/NEDLeducation

[@dustinmyeye8752]

Why is this video now private? Did you tube do that or did you decide to? It was one of the only videos actually running the numbers of the election.

[@Jtking3000]

@@dustinmyeye8752 Came looking for the video too and was sad to see it taken down :(

[@ibealgoody2666]

How relevant this is today

[@NEDLeducation]

Could not be more relevant actually! Will post a video with applications of Benford's law to election data tomorrow, so stay tuned :)

[@ibealgoody2666]

@@NEDLeducation Are you familiar with this study in this regard? www.cambridge.org/core/journals/political-analysis/article/benfords-law-and-the-detection-of-election-fraud/3B1D64E822371C461AF3C61CE91AAF6D

[@spyro3635]

@@ibealgoody2666 www.cambridge.org/core/journals/political-analysis/article/comment-on-benfords-law-and-the-detection-of-election-fraud/BC29680D8B5469A54C7C9D865029FE7C

[@ibealgoody2666]

@@spyro3635 This is perfect, thank you !

[@davidbeckham5579]

Make Benfords Law Great Again!

[@sushantakumarpattnaik525]

Very well explained. Very interesting and educative👍

[@currently7886]

hi everyone! Who is here from Election 2020?

[@mahmoudfaouzichaoubi5855]

Thank you =شُكراً

[@danjensen731]

Can you do this for a company’s net sales over say 20 years? Should it be on a quarterly basis?

[@mahmoudfaouzichaoubi5855]

what software or application for benford's law? THANKS.

[@tn4AH2UC5BhwvnEus]

Thank you so much for this. 👍

[@markusbrownicus01]

Quick question. Most election results depend on populations of counties. Those county populations are not random. Often county lines are drawn with populations in mind. If you applied Benford's Law to county populations, often you'd find manipulation. Wouldn't it stand to reason that votes in those counties would also show signs of "manipulation" as they're largely dependent on populations of counties, which are manipulated?

[@robinhoyas5088]

The size of votes depends on the size of population indeed and this may also affect the distribution of the first digit of votes but even if this can effect the distribution of the first digit, this effect remains random so the answer to you question is no.

[@robinhoyas5088]

The less difference with the theorical frequency, the more p_value. Plus the X² does not depend on the sample size. Does that make sense?

[@bhaiyyu]

This was a great lecture, thank you so much for sharing it with us. Qn - where are the links to the Chi Sq. and Supremum test? I'd love to see them as well

[@NEDLeducation]

Hi, and thanks so much for the feedback! Separate videos on Chi-squared and Kolmogorov-Smirnov test are already there on the channel, please check these out: Chi-squared: kzbin.info/www/bejne/bJK0kIyfoZ6FbZY Kolmogorov-Smirnov: kzbin.info/www/bejne/iF6wc3l5gJijb7M A more advanced test sometimes used for Benford's law is Kuiper test (basically a modified version of K-S): kzbin.info/www/bejne/aniuoZ6Of7Carq8 Hope it helps!

[@muntedme203]

Can do last for the 2 digits of CFD FX quotes by a particular broker?

[@NEDLeducation]

Hi, and thanks for the question! Yes, you can investigate price clustering using the price digit distribution. However, for last digits you would generally test the empirical distribution against the uniform null hypothesis rather than the Benford's law. I have got a video on price clustering, check this out if you are interested: kzbin.info/www/bejne/onWcZoJnZpKbZ9k

[@ahmadzai08]

Hello, what if the p-value is less than Supremum? for example, the p-value is 4% and Supremum is 38%.

[@NEDLeducation]

Hi Shafiq and thanks for the question. It is perfectly fine, the supremum is a test statistic, so you should not really worry about comparing it to the p-value. The sample size held equal, the greater the supremum (the higher the deviation), the less the p-value (the less likely such a deviation to occur from random chance alone).

[@lklim3914]

Hi sir, how do you apply it to accounting data such as financial statements and annual reports?

[@NEDLeducation]

Hi and many thanks for the question! In a similar way, you can look through the financial statements of a company, extract a large set of reported figures and apply Benford's law to the first meaningful digits of the data. The results will provide you with some insight if this company has something suspicious in the books. Alternatively, if you want to see if there are potentially some manipulations with a particular disclosure element (i.e., whether firms at large misreport profits), you could apply Benford's law to reported profits data across a set of companies. Hope it helps!

[@lklim3914]

@@NEDLeducation Good day sir from Singapore and thank you for your kind reply. I really appreciate it. So just to check, for example, with regards to Tesla FY 2019 financial statements, I can pull out all cash flow, balance sheet and income statement numbers and run a benford test to check for consistency with benford's law. I can also do the same for all line items on the balance sheet such as cash, accounting receivables , payables etc.... Is that correct? Can I also do it for 1 line item say cash and cash equivalents, but my worry in this case is that there is a lack of data as I need many years of input. Any advice is appreciated. Thank you so much in advance.

[@NEDLeducation]

Absolutely, you can apply Benford's law in all of the cases you mentioned, but obviously the higher the sample size, the more precise the test results.

[@lklim3914]

@@NEDLeducation Is 10 years of quarterly profit data of any value? That is only 40 data points. I am not sure if there will be any significance to that. How would you do it if there is a shortage of data in this case?

[@NEDLeducation]

​@@lklim3914 40 data points can be enough, but not the ideal case obviously. The larger the sample size, the higher the statistical power of the test. It is possible to detect something fishy is going on even with 40 points, but here using Kolmogorov-Smirnov instead of Chi-squared is strongly advised.

[@ann_vocals]

Nicely explained..Can you also do a video on computing theoretical value of futures using cost of carry model..?

[@NEDLeducation]

Hi Ann, and glad you liked the video! Actually, was planning to dig deeper into derivatives from late December/early January, futures valuation is already up there in the priority list!

[@ann_vocals]

@@NEDLeducation Thank you so much..I'm looking forward to it..

[@sherrybailey3102]

what does it mean if the p-value = zero and do you have videos on 2 digits

[@NEDLeducation]

Hi Sherry and many thanks for the question! P-value is never actually absolutely equal to zero, it just tends to zero as the test statistic tends to infinity. For hypothesis testing, a very low (near zero) p-value means that the null hypothesis can be comfortably rejected in favour of the alternative one. Mathematically, p-value can be interpreted as the probability that the null hypothesis is true. For example, in this video the p-value for the Kolmogorov-Smirnov test shows that the data is distributed according to the Benford's law with probability 66%, which is too high for us to suggest otherwise. As for the second digits, yes, they are also distributed according to the Benford's law, yet the pattern is less prominent than in the case for the first digits. The application of the test for the second digit is pretty much analogous. Hope it helps!

[@dustinmyeye8752]

Why is your video about the elections private? Did you choose to do that or did KZbin do it?

[@cedricvillani8502]

Do all you guys use excel for this?

[@jd8122]

Inb4 this video is censored for "misinformation" lol

[@thuglifebear5256]

HAHAHA hoooh boy, betcha didn't think some random math video had the ability to SAVE DEMOCRACY did ya?