Tag: stats

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Wisdom of chance

The advantage to toss a coin is that a decision made by chance is usually perceived as acceptable to all parties involved. The wisdom of Greek philosophers also trusted in decisions by chance. In decision-making it is good scientific practice to mention error margins, a bit like in weather forecasts. In case error margins are very high it, therefore, can make sense to leave the ultimate decision to a toss of a coin as this might be just as valuable as making one or the other choice with high uncertainty. Of course we feel uneasy about such a procedure as we tend to be convinced that we have sufficient information to make a better decision than just a shortcut by chance decision. Hence, there may be many more cases than we would like to admit to which can be left to a by chance decision. 

Random choice decoration of kindergarden Berlin 2026
Random choice decoration of kindergarden Berlin 2026
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Practice Web analytics

For all people, especially webmasters, it is useful to understand and deal with web analytic reports of webpages. From time to time I do my own little research to check what is going on and how changes I implemented can be evaluated. During the month of October 2026 I have changed from a 30 entry long scroll landing page on https://schoemann.org to only a 10 entries before a kind of stop or follow-up click is needed to pursue reading. How has this changed the visits on the webpage? Well, (1) the number of visitors in 2026-10 (56.000) and page views (84.000) remained remained relatively stable, but after an initial rise in time spent on the webpage (report on Frankfurt book fair 2026) a significant drop in average duration on the page has occurred. As the retention rate on the webpage remained stable, my conclusion based on this real-world experiment is that the scroll limit set on purpose to 10 images and blog entries before more active engagement is necessary has the expected effect. Scroll limits shorten time spent on the same page and, most likely would also work in the “not-so-social” social media realm.

www.schoemann.org
web analytics 2026-10 of www.schoemann.org
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Climate, time and space

For statistical analyses is good practice to not only study averages, but whole distributions over time and space. Climate change is an obvious candidate to apply such a methodology. The analysis of US data on temperature changes across quantiles of the distribution in 48 regions over 70 years finds distinct patterns of temperature changes. The authors María Dolores Gadea Rivas and Jesús Gonzalo published their findings in PLOS Climate, which showed different patterns of climate warming. Taking into account that it is not only average temperatures that may shift, but only the lower winter temperatures or the warmer summer peaks, they find overall 84% of the regions experienced a statistically significant warming effect. Whereas a higher summer peak is commonly perceived as a climate warming problem, a warmer winter usually is less associated with climate change. This leads to an overall misinterpretation or lower perception that climate warming is and has been happening over the last decades. With yellow daffodils on 2026-2-8, usually a winter day in Brussels (see image), the warm winter days are also evidence that global warming is well under way all year round and across the planet.  

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Deep Fake Threat

Our Western democracies are aware that “deep fake videos”, radio, online-newspapers and most of all social media platforms are all around us already. However, more scientific voices alert us that this threat to our easy or comfortable way of life to consume information eventually threatens the survival of our democracies. Previously, interference in elections used to focus on rigged election procedures, but in the 21st century powerful other alternatives can do the dirty job to bias elections against the original intentions of the electorate. The widespread use of AI will exacerbate the already practiced ways to produce deep fakes. In a preparatory self-test of an AI-assisted chatbot I was surprised myself of the quality of the output. A person not very familiar with my original voice in a second language would assume that it is me who is being interviewed in person. Based on a fake news text, any form will be automatically translated into voice only and/or video based on basic visuals.
Statisticians used to joke some decades ago: “Don’t believe in any statistics, unless you faked it yourself.” This is meant to encourage people to be aware of dangers of the use of statistics to influence opinions or official decision-making, like in policy making of central banks, which might be based on biased accounting for shrinkflation, cheatflation or greedflation to name just a few,
Hence, the need to strengthen awareness, analytical skills and critical thinking should be high on the agenda to defend our democracies. There are not only external military threats, but additional ones masked as internal threats.
(Image:: mice as humans in living room 2 couch potatos 1 on rocking chair, tea time)

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Failure time

In mechanical as well as medical components it is interesting to know about the usually hidden failure time of a product. The failure time simply means probability the component will seize to function properly or altogether. Usually, this probability of failure increases with the duration and the intensity of use. We might know this from cars or heating systems, but airplanes and heart valves obey the aame basic statistical models. Programmed failure time is a nuisance, which works against all efforts of sustainability, Over-engineered products would work much longer than the actual use case. Locomotives with steam engines that still function well even today might serve as an example of the latter case. The issue becomes a bit more complex if we consider not only the product but each single component. Maximizing profits often leads to taking risks with failure times or failure rates over a fixed time (a more general term than the guaranteed lifetime of a product). This sounds rather abstract thinking, but in modern military equipment the consideration of failure time, self-destruction or destruction by enemy play an important role again. Failure time of military equipment has moved to the forefront of issues of equipment and is part of strategic planning, like it or not.  

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Biased Results

The use of statistics in presenting results of research is common practice. Empirical studies are summarized using statistics and statistical methods based on samples of bigger populations are cost efficient. However, care needs to be exercised when interpreting results to guard against inappropriate conclusions derived from biased estimates. Since the topic has been highlighted and methods proposed to handle them, these methods were deemed worthy of a Nobel prize.  The basic problem of a bias due to a selective sample has been demonstrated by Stockwell et al. (2024). The authors investigate the old question, whether a little bit of alcohol consumption (per day) could be beneficial for our health. The statistical issue which needs careful examination is the construction of the control group against which the results are compared. Apparently many studies have biased control groups which included persons in the not drinking control group who had stopped drinking for bad health previously. Compared to those persons with other health conditions those drinking a little bit compared rather well. But of course such individuals should not be present in a control group. Of the control group is biased due to many persons with below average health the groups of interest consuming higher levels of alcohol do not perform so badly. Hence, interpretation of results from medical or social science studies has to consider carefully the actual or potential sources of bias. Not really a new results in statistics, but still not well known or understood by the public at large. Drug consumption as well as studies of this consumption could deserve the same sticker: handle with care. (Image: Extract from Tenier II David, Les fumeurs, also entitled Chanson à boire, 17th century, Paris Petit Palais).

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Hallucinations

In the 21st century hallucinations have become a daily experience. The origins of the word can be followed back at least to the Latin verb “alucinor”, best translated with “to hallucinate”. As a verb to can conjugate it, meaning that I can do it, you can do it, s/he can do it, and we may do it in groups. Roman emperors did it, American presidents do it and, of course, AI does it. Hence, it is a great subject to study.
In “Nature” 2025 we find ways to limit hallucinations of AI systems. The strategy consists mainly in repeated queries of the same type, but from different angles. It is a bit like cubism applied to informatics. On “github.com” we can follow the rankings of AI-models using LLMs based on the “hallucination-leaderboard” developed by Vectara. On “huggingface.com” you can test the Hughes Hallucination Evaluation Model. For example it is possible to run a test of your own small text documents (just like any blog entry on this webpage) and what the AI systems will do them in an attempt to summarize your ideas. According to the “hallucination-leaderboard” we are confronted with a 1.3%-4% hallucination rate of the top 25 LLMs as AI-systems. In text based systems the quantity of “errors” is a first indicator only. The seriousness of the omission, addition of wrong information or an erroneous judgment will be left to the reader or analyst to uncover.
There is now a lot to do to test various AI-systems on their “trustworthiness” in summarizing my own work. My very own daily hallucinations have become a large data base as a test case for the capacity of LLMs to make sense of them.
Based on the series of passed blog entries I shall test the capacity of AI to predict the n+1 blog entry. It would be great to know today what I am going to write about tomorrow etc. Thanks to AI I shall have (finally) a sort of intellectual life after death (not sure whether I should want this). Enough of hallucinations and on hallucinations for now, back to serious readings or fictionalized science. (Image: extract from Delphine Diallo, Kush, 2024 at Hangar Gallery Brussels).

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Paralympic Counting

The classification system of the Paralympic disciplines is well worked out. This ensures that competitions are on a more equal footing. The counting of medals, points and penalties is an easy task. It is more difficult to keep track of equipment and infrastructure and the adaptation status of it to Paralympic needs in a country or region. Statistics and monitoring of installations is one important step in preparing for participation and success in Paralympic disciplines. On an European open data platform we find the regional data set of “Parasportive equipment in clubs and committees of the Pays de la Loire”, for example. Transparency of structures is a first step in improving access to it. For Paralympic athletes it is the same process to gain access to sport equipment as for all other athletes. The monitoring of infrastructure and equipment is a laborious task, but the documentation of helps people on their way to obtain access. Paralympic counting, therefore, is much more than counting medals and trophies even if they are really nice looking.

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Webpage Analytics

I do not collect data of detailed webpage analytics. Therefore, I thought I do not know anything and do not want to know anything about webpage visits of this webpage. However, the most basic information of how many times the webpage is visited per months is given by the hosting service of the webpage. The previous jump beyond 20.000 visits/month had the implication to move the security level of the webpage for me and all visitors to a higher level. Additional information of how many seconds an “internaut” is staying on the webpage tells, maybe a little bit about the interest in the content or image of a specific entry. Reaching 84.000 visitors/month was a surprise that asks for an explanation. Apparently, the most visited page is the blog entry on “geo-politics”. The longest time people stayed on a page or blog entry is a recent entry on “nutrition policy”.
Other statistics show that people who visited an entry on “find trust”, trusted in the webpage to click on many other entries or pages on “www.schoemann.org”.
I do not collect data or statistics on where visitors go after a visit. The hosting service, however, measures the so-called “jump-off” rate. This indicates the importance of the webpage as spring board to jump to other pages on the internet. It is usually = 1, just showing that you left somewhere. For some pages this reaches higher levels according to the number of links you offer on a blog entry, for example. It gives an indication whether you manage to lead on readers to explore the topic further. This is a usual evaluation question of lectures and seminars given at universities.
Last but not least, even without collecting any “real data” about visitors, it is part of the minimum information your browser transmits is the “operating system” used for access. Your smartphone provides the information on IOS, Android, Linux, or Windows versions used. These technical purposes remind me that there are still vast amounts of users of what we believe are outdated operating systems. Windows 7 and Windows 10 are still heavily in use across the globe. The hype around the latest operating system and smartphone is most likely only a phenomenon of the rich and wealthy in the rich parts of the western world. This reminds me to include images, which are small in data size to allow fast downloads in all parts of the world. We should embrace this as an important topic of geo-political relevance.

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Science Transparent

Every year there is only one special big event (Lange Nacht der Wissenschaften) to make science more transparent to the population at large. Mostly hidden behind impressive walls and buildings guarded by porters,
science is not as transparent for the large public as it would like to be. In general people are rather intimidated or feel quickly out of place if scientist start to “explain” in lengthy formats their topics, ideas, questions and intermediate solutions. Even if the distributed open science fair is running only from 5 p.m to midnight, there are lots of things to learn and look into.
The website lists 1500+ sessions, 230 are in English language. You have to be selective or spread your interest over several years. I chose to start with, maybe, the toughest choice the Weierstrass-Institute near the Naturkundemuseum. Several projects of applied mathematics and stochastic processes were exposed and explained in more or less transparent and/or understandable form to the audiences. The talk by Julian Kern “Why chance doesn’t happen by chance” had a nice interactive format with “Kahoot-quizzes” and gave a good introduction, why it is useful to understand, statistics and stochastic processes in fields from biology, physics to social phenomena. The White board replaced already the black board and chalk.
The open doors policy, at least one day per year, raises interests and awareness for topics few people would only think that they existed already. The  volume “Mathematics and Society” (Wolfgang König ed. 2016) is something I shall follow up on eventually. There are lots of applications of mathematics to social phenomena (time seen from the perspective of generations for example, image below from talk), which we have a hard time to come to grips with without the aid of mathematicians.