The full version of this aphorism: “There are three types of lies: lies, damned lies and statistics.” (English)There are three kinds of lies: lies, damned lies, and statistics). Its authorship is attributed to various people, and it gained fame thanks to M. Twain after the publication of “A Chapter of My Autobiography” in the North American Review on July 5, 1907: “The numbers are deceptive,” he wrote, “I have learned this from my own experience; Disraeli rightly spoke about this: “There are three types of lies: lies, damned lies and statistics.” Some believe that the original phrase sounded like “There is an old joke that there are three kinds of liars: common liars, outrageous liars and scientific experts,” and only later began to say something slightly different: “There are three degrees of lies: lies, shameless (blatant ) lies and statistics."
It is unlikely that it is so important who is the author of this aphorism; what is important is that it well illustrates the situation with what “expert” doctors say to most people with serious (and not so serious) diseases.
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In 1992, doctors diagnosed the famous American paleontologist and biologist Stephen Gould with cancer (peritoneal mesothelioma) and reported that on average, people with this diagnosis live 8 months. Gould put his affairs in order, but did not give up, but began to undergo treatment - surgery, chemotherapy and radiation. And he died. In twenty years.
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Two years after the diagnosis was announced in Discover magazine, he published his article “The Median Isn’t the Message,” in which he clearly described how statistics and specific cases from life relate. The original text is at the link , below is an almost complete translation and then my comments.
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Preface to the article - S. Dunn (Steve Dunn, creator of the website http://cancerguide.org, to whom doctors diagnosed stage 4 kidney cancer, after which the kidney was removed. After such “treatment” he led a very active lifestyle for 17 years , got married, had children, was involved in mountaineering and skiing, died in August 2005 from a completely different disease (infectious meningitis).
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Stephen Jay Gould was an influential evolutionary biologist, lecturer at Harvard University, and author of at least a dozen popular books on various fields of science.
As far as I can tell, this article is the wisest, most humane article ever written about cancer and statistics. It is an antidote both to those who say that “statistics don’t matter” and to those who are in the habit of pronouncing “death sentences” on patients facing dire prognoses. Anyone looking for answers in the official medical literature will find there “terrible statistics” for almost any disease. Anyone who reads this article will take on hope.
Don't believe the median "The
Median
Isn"
t
the
Message"
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Lately, my life has been constantly illustrated by two famous jokes by Mark Twain. I'll save one for now for the end of this article, and the second (sometimes attributed to Disraeli) talks about three types of lies, each worse than the last - lies, damned lies and statistics.
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Let's consider a standard example of “smearing” the truth in space or time - which turned out to be very relevant for my personal story. Statistics recognizes different ways of defining "average" or "average tendency." Our usual concept of definition average value
is quite simple - add up the values of all the elements and divide the resulting sum by the number of elements (100 candies collected by five children on Halloween gives 20 candies to each child in this ideal world). - another measure of average tendency, is the value of the function in the middle of the graph. For example, if I rank five children by height, the middle child will be shorter than the previous two and taller than the next two (however, these two short children may have problems sharing candy in a group with taller children...).
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Another way to illustrate this is that a political leader might proudly make the statement, “The average income of our citizens is $15,000 a year,” to which an opposition leader might retort, “But half of our citizens have a real income of less than $10,000 a year.” And they will both be right, although neither of them uses statistics with dispassionate objectivity. The first one talks about arithmetic average
, second - o median
(the arithmetic mean is greater than the median in such cases because one millionaire can outweigh hundreds of poor people when calculating the average, but he can only outweigh one pauper when calculating the median).
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The more important (deeper, more dangerous, difficult, etc.) the question, the greater the distrust and contempt for statistics when considering it. Many people allow a tragic and unacceptable gap between their heart and mind, their feelings (sensations) and their intellect. In some modern traditions, on the contrary, too much emphasis is placed on feelings as the basis for action, while the intellect is relegated to the background as an “outdated tool.” Statistics are often labeled the “enemy” in this absurd dichotomy.
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This article is a personal story of friendship with correctly interpreted statistics that are inspiring and give hope. This is a short story about the usefulness of unbiased scientific knowledge and the fact that the head and heart are coordinators of the actions of one body, one person.
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In July 1982 I learned that I had
, a rare and serious form of cancer. When I came out of anesthesia after surgery, my first question to the doctor and chemotherapy doctor was: “What is the best literature on mesothelioma?” To which I received an answer with a clear diplomatic overtone that there was nothing in the medical literature that was really worth reading.
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Well, of course, advising a scientist to stay away from books is as effective as advising homo sapiens to be chaste and abstain from sex. As soon as I could walk, I went straight to the Harvard Medical Library and entered a query into the computer about everything,
. An hour later, surrounded by all the available literature on abdominal mesothelioma, I understood why my doctor had given me such humane advice. In all the literature I found, the information could not be more unequivocal: Mesothelioma is incurable, with a median mortality rate of just eight months after diagnosis.
for about fifteen minutes, then he smiled and said to himself: so that’s why they won’t let me read anything! Thank God, then my mind started working again.
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I came across a classic example of when
" And this has a direct bearing on the fight against cancer. Perhaps because our mental state “feeds” the immune system, but people with the same type of cancer, differing in age, social class, conditions for receiving medical care, in general - have a positive attitude towards life, a strong will and life goals - and live longer, they will definitely fight or at least look for ways out of the disease, and not just passively accept anything said by doctors. A few months later, I asked Medawar Sir, my personal scientific guru and Nobel Prize winner in immunology, what could be the best recipe for success against cancer? “Personality of a sanguine person,” he answered briefly. Fortunately (since you cannot change yourself in a short time and with one specific goal), I have always been a balanced and self-confident person with exactly this type of character.
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This raises a dilemma for doctors: after all, if a person’s personal attitude to what happens to him is so important, why make such gloomy conclusions (predictions? ..), especially when only a few people have enough understanding of the principles of statistics to evaluate what In fact does this or that statement mean? Personally, I had this understanding, and I am convinced that this played an important role in saving my life. Knowledge is real force!
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Briefly, the first (and perhaps the most important) question might be: what exactly does the phrase “median mortality rate is eight months” mean? I suspect that most people, without much statistical knowledge, would translate this phrase as "I'll probably be dead in eight months" - which is exactly the jumping conclusion that should be avoided because... The very attitude towards the situation and forecasts is of great importance.
Of course, I wasn't overjoyed, but I didn't interpret the data that way either. My technical background allowed me to have a different perspective on the “eight-month medial mortality rate.”
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We still carry the historical burden of Plato's legacy, striving for an explanation of everything, for clear definitions and distinctions, thus trying, for example, to find an unambiguous “beginning of life” or a precise definition of death, although nature often appears to us as a continuum with a smooth transition of one to another. This Platonic heritage, with its emphasis on clear distinctions and the separation of indivisibles, leads us to false estimates of statistical data. In short, we perceive the mean and median as a hard “reality”, and on the contrary, we do not take into account a whole range of different variables and the imperfections of measurement. If you simply take the median as a given and consider what is around it for deeper analysis and calculation, then the interpretation “I will probably be dead in eight months” may lose its relevance. (by the way, the opposite situation is also possible - E.M.)
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But all evolutionary biologists, of which I also am, know that it is the variability of certain parameters that is the unchanging essence of all living things. It is changes, variations of the same thing that are the harsh reality. The statistical mean and median are just abstractions. So I looked at the mesothelioma statistics in a completely different way - and not only because I am an optimist who strives to see the donut itself instead of the hole, but first of all because I know that only variation is reality. And I had to place myself among these different variations.
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When I learned about the eight-month median, my first intellectual reaction was, “great, half the people live longer than that eight months. What about my chances of getting into this half? After an hour of nervous and frantic calculations, I came to the conclusion with relief: my chances are damn good. I had each of the characteristics that make me more likely to live longer: I was young; my disease was diagnosed at a relatively early stage; I can get better medical treatment; I want to live; I know how to properly interpret the data and I am not discouraged.
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Another technical issue also added even more comfort to me. I immediately realized that the actual distribution of variation at the "eight-month median" would almost certainly be what statisticians call "right skewed" (with a symmetric distribution, the profile of the graph to the left of the median is a mirror image of the profile to the right; with skewness, the distribution on one half is more "elongated" ).
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I reasoned that in the case of my mesothelioma, the graph should have been skewed to the right (positive skewness), because, after all, the part of the graph to the left of the median describes only those cases when mesothelioma is diagnosed either posthumously or a short time before the death of a person. Thus, there are not many opportunities to fall into this range, since it is only between zero and eight months. But the upper (or right) half can extend for many years, even if none of the people diagnosed ultimately survive. The distribution should have exactly this right skew, and I need to know how far the “tail” of the graph is located - because I have already come to the conclusion that my favorable "patient profile" made me a good candidate for this half of the schedule.
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The distribution is indeed strongly distorted to the right; it has a long “tail”, albeit not so large in amplitude, but extended several years beyond the median of eight months. I no longer saw any reason why I shouldn't be in this tail, and I took a very long sigh of relief. My technical knowledge helped me this time too. I read the chart correctly. I asked the right question and found the answers. I received, in all likelihood, the most valuable of all possible gifts under existing conditions - significant time. Nothing held me back and nothing could force me to immediately follow the words of Isaiah to Hezekiah - “Put your house in order, because you will die and not live!”
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One more thing about statistical distributions: the current “official” graph only applies to a very specific set of circumstances and shows the survival rate for mesothelioma under conventional treatment regimens. But if circumstances change, the distribution may also change. I was prescribed an experimental treatment protocol, and if Fortune smiles, I will be in the first group of a new distribution with a high median and the right “tail” of the graph, which lasts until death from natural causes in old age.
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In my opinion, it has become too fashionable to consider acceptance of death to be tantamount to inner dignity. Of course, I agree with the sermons of Ecclesiastes that “there is a time to love and a time to die,” and when my source of life runs dry, I hope to meet my end calmly and with dignity. In most cases, however, I prefer to have a different opinion, namely that life must be fought for.
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The choice of weapons in this fight is very wide, but nothing is more effective than humor. My death was announced at a meeting of my colleagues in Scotland, and I took great pleasure in reading my own obituary, written by one of my best friends (by the way, it can hardly be considered an accident that he is a statistician and that he believed in my inevitable death , because I didn’t expect to find me so far in the right “tail” of the above graph). However, this incident was the first that gave me a chance to laugh after hearing my diagnosis. Just think, I almost repeated another famous aphorism of M. Twain: “rumors about my death are greatly exaggerated.”
Afterword by S. Dunn
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Sadly, S. Gould died in May 2002 at the age of 60, but he lived another twenty very productive years after his diagnosis and thus exceeded the “statistical” eight-month median survival rate by thirty times! Although he died of cancer, it was not the same mesothelioma, but a completely different type.
In March 2002, Dr. Gould published his 1,342-page book, Opus Magnum - The Structure of Evolutionary Theory. And it seems very logical that Dr. Gould, one of the world's most prolific scientists and writers, was able to complete the final account of his scientific activities and the account of his philosophy just in time. This book is too long for the average person - but S. D. Gould's work will live on. Especially, I hope, the article " TheMedianIsn"ttheMessage".
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In fact, there will be practically no comments from me on this article - neither about “experimental treatment protocols”, nor about “prophecies of doctors” - there is already a lot of material about this in my LiveJournal. But there will be separate posts about the fact that statistics are often interpreted completely “crookedly”.
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I just want to note that it is no coincidence that in this article Dr. Gould mentioned the phrase “patient profile” - since he also used the words “sanguine personality”, this has to do with psychology, and not just with a person’s financial condition or his social status. Nothing happens by chance in this world. A couple of days ago I saw a post on LiveJournal with the title “The Role of Personality in Oncology,” where links were given to experiments (yes, those same statistics) and the final conclusion was that this role is “too exaggerated.” But no matter how much individual citizens want to isolate themselves from their psyche (from their personality), no matter how much they want to believe that the disease “comes down from somewhere above for reasons beyond my control,” commenting on all this with words like “I’ve had enough of it already.” all these believers in the psychological nature of cancer” - you can’t throw the words out of the song - you can’t run away from yourself.
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But the next post is about this.
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Be healthy. Live with humor.
Mark Twain
The laws of probability theory are not abstract, but mathematically express the real patterns of mass random natural phenomena.
The development of methods for recording, describing and analyzing statistical experimental data obtained as a result of observing mass random phenomena is the subject of MATHEMATICAL STATISTICS.
1
Determination of the law of distribution of a random variable from statistical data.
Since in practice we have to deal with a limited amount of experimental data, the results of observations will always contain an element of chance.
Therefore, the task arises of smoothing statistical data and describing them using simple analytical dependencies.
2
Testing the plausibility of hypotheses.
This task is related to the previous one. For example, it can answer the question: are the results of an experiment consistent with the hypothesis that the random variable obeys a given distribution law?
3
Determination of unknown parameters distribution
Often it is necessary to determine not the law of SW distribution itself on the basis of experimental data, but some numerical characteristics. In a small number of experiments, only “estimated” values of these parameters are determined, i.e. such approximate values that lead on average to smaller errors than
The marketing department of a clothing factory conducted a survey of 100 customers. Among the survey questions were questions about men's suits. Processing of the questionnaires gave the following results about preferences:
By place of manufacture: 40% - domestic, 60% - imported.
2. By cost in US dollars:
« Lies, damn lies and statistics"(full version: There are three types of lies: lies, damned lies and statistics., English There are three kinds of lies: lies, damned lies, and statistics ) - a statement attributed to British Prime Minister Benjamin Disraeli, and it became famous thanks to Mark Twain after the publication of “A Chapter of My Autobiography” in the North American Review on July 5, 1907: “Figures are deceptive,” he wrote, “I am convinced of this from personal experience; Disraeli rightly spoke about this: “There are three types of lies: lies, damned lies and statistics.” However, this phrase does not appear in Disraeli's works. Also, she was not known either during his lifetime or shortly after his death. From the point of view of modern ideas, the most likely candidate for authorship is Charles Dilk (1843-1911).
This saying has been attributed to many others besides Disraeli: the journalist and politician Henry Labouchere (1831-1912) and Leonard Courtenay (1832-1918), who used the phrase in 1895. Two years later he became president of the Royal Statistical Society.
It is now known that the first use of the phrase was in a letter written on June 8, 1891 and published on June 13, 1891 in the National Observer (p.93(-94): NATIONAL PENSIONS London, 8th June, 1891): “Sir, ... very wittily observed “that there are three types of lies: the first is untruth, the second is outright lies, and, finally, the worst thing is statistics.” A little later, in October 1891, in the journal Notes and Queries, a person under the pseudonym “St Swithin” sent a question about the authorship of this phrase, which indicates its widespread use already in those days. In October 1891, Charles W. Dilke, without any attribution, used this statement twice. "Sir Charles Dilke (1843-1911) said the other day that in his opinion 'lies' may be classified in increasing degrees as: white lies, lies and statistics" (The Bristol Mercury and Daily Post, Monday, October 19 1891 G.). Dr. E.R.L. Gould, who used the phrase in 1892, also cited Charles Dilke's authorship: "Sir Charles Dilke was right in a certain sense when he said: 'There are three levels of lies - fiction, lies and statistics...'."
As Robert Giffen (assistant editor of The Economist and 1882-84 president of the Statistical Society) mentions in 1892, the statement “about statistics” is only an interpretation of the phrase “There is an old joke that there are three kinds of liars: ordinary deceivers, outrageous liars and scientific experts. Later they began to say things a little differently: there are three degrees of lies: lies, shameless lies and statistics.” .
The origin of the original (“about experts”) is attributed to an earlier period than the statement “about statistics,” namely in the journal Nature dated November 26, 1885 (note that Disraeli had already died by this time) on page 74 we find: “... It occurred to one well-known lawyer, currently a judge, to divide witnesses into three groups: simple liars, damned liars, and experts.”
Notes
Wikimedia Foundation. 2010.
See what “Lies, blatant lies and statistics” are in other dictionaries:
The most accurate of all pseudosciences. Jin Ko Statistics can prove anything, even the truth. Noel Moynihan Statistics is the science of how, without being able to think and understand, you can make numbers do it. Vasily Klyuchevsky Statistics are like a swimsuit...
There are four types of lies: lies, damned lies, statistics and citations. You should not lie shamelessly; but sometimes evasiveness is necessary. Margaret Thatcher Believe only half of what you see and none of what you hear. English proverb... ... Consolidated encyclopedia of aphorisms
Histogram (method of graphic images) This term has other meanings, with ... Wikipedia
Statistics- (Statistics) Statistics is a general theoretical science that studies quantitative changes in phenomena and processes. State statistics, statistical services, Rosstat (Goskomstat), statistical data, query statistics, sales statistics,... ... Investor Encyclopedia
- (1835 1910) American writer Hell is the only truly significant Christian community in the Universe. A banker is a person who will lend you an umbrella on a sunny day and take it away the moment it starts to rain. Bill... ... Consolidated encyclopedia of aphorisms
Quote: incorrect repetition of someone else's words. Ambrose Bierce Quote is a risk under someone else's responsibility. Vladislav Grzeszczyk If you are quoted, you are already someone. If someone steals from you, you are an outstanding person. But real glory begins only when you... Consolidated encyclopedia of aphorisms
Garry Kasparov Garry Kimovich Kasparov Garry Kasparov, 2007 Date of birth: April 13, 1963 (46 years old) Place of birth ... Wikipedia
There is a very “bearded” saying. Surely you heard her. So…
There are three types of lies:
- Nasty lie
- Statistics
Usually at this point they say the word “shovel” and everyone laughs. But let's look at the facts that are currently flashing in the latest news.
Fact #1
"Levada-Center" conducted a social survey (Russians of all ages were surveyed), which showed that the most popular social network in our country is Odnoklassniki. It consists approximately 76% of respondents.
Cool! We urgently run to open an account there! For those who are in the tank, how to register with Odnoklassniki is described in great detail on akak.ru at the link. This is a site that contains instructions on how to do what.
But these, as you understand, are statistics provided by Levada Center.
Fact #2
- The most popular network according to their data is VKontakte. Comes into it 38 million visitors per day.
- Odnoklassniki has 30 million visitors.
- “My World” - 16 million.
Question #1: Who to believe?
Because it's a statistic third kind of lie, then you can’t trust anyone. How can you calculate the popularity of a social network solely based on indirect data?
Survey. What did he show? Focus group preferences only.
Where was she selected? How were you interviewed? In what region? Were they telling the truth?
According to opinion polls, 100% of Russians use the Internet! The survey was conducted on the website.
Number of visitors per day. What does it show?
Imagine the average office worker. He has VKontakte installed on his phone, he goes there from work, and then in the evening from home. This is already 3 visitors with different IP, browser, etc.
At the same time, Odnoklassniki has an older target audience. This means that mobile applications and access from the office are closed for them.
Worpos #2: What to do with this information?
Conclusion No. 1- You can’t blindly trust statistics!
Conclusion No. 2— Obviously, the most popular social networks are VKontakte and Odnoklassniki. I think that LJ (even though they are “social media”) is also in the top three.
Conclusion No. 3— If you have something to tell or offer to people, create accounts on the most popular social networks. You definitely can't go wrong.
Afterword
As the catchphrase of Dr. House (TV series “Dr. House”) says, “...Everyone lies...”. Remember this.
And Doctor Lexium was with you
Remember that the need to think with your own head has not yet been canceled.
The site found out what is the percentage of statistical data falsification in scientific papers on psychology, what errors were revealed by the verification program and how it is similar to T9.
Programs can not only postmodern song lyrics, a path on the London Underground, simulate processes in a bank, but also look for errors in the work of dishonest or inattentive psychologists. the site tells how a computer identifies inaccuracies in scientific papers and what this can lead to.
The brilliance and poverty of modern psychology
Balancing between “everyday wisdom” and philosophical and metaphysical categories on a thin thread of consistent data, the “science of the soul” is constantly in danger of excesses. Digging into the inner world of people (if you do not consider the anatomical side of the issue) has never been easy, so the research of psychologists is difficult to verify. Having a very subjective subject of study, psychology in some of its branches and sections intersects with medicine and neurobiology, and in others goes beyond the scientific: even Doctor of Psychology and Deputy Director of the Institute of Psychology of the Russian Academy of Sciences Andrei Yurevich defined the place of psychology between science and parascience. Even when applied according to all the rules of scientific methodology, psychological approaches sometimes do not give satisfactory results. If in more careful and long-term work with one person one can assume the uniqueness of the case and state that it is impossible to extrapolate conclusions to all people, then in a large group it is difficult to understand what unified questions and answers actually mean for each participant in the study. In addition, subjects may always have internal reasons to hide some information and answer questions not completely honestly. Therefore, reflection (turning a person’s attention inward) cannot be considered a tool that allows one to obtain absolutely reliable information. about a computer algorithm that identified potential errors in almost eight thousand psychological articles (and this only in the period from 1985 to 2013 and only in eight scientific psychological journals) worked like a stick that stirred up a hornet's nest, already troubled due to constant controversy . Under the leadership of Michelle Nuyten, 30,717 articles were analyzed, of which 16,695 used statistical data. Half of these papers had at least one suspected statistical error that was pointed out by the program.
When a study is conducted on a large group of subjects, statistical methods are used for processing. The popular saying “there are three kinds of lies: lies, damned lies and statistics,” whose authorship is so vague that more than a hundred years ago Mark Twain attributed it to Benjamin Disraeli (but was no longer sure where it actually came from), is not so far from the truth. In the field of human knowledge, where it is so difficult to create theories with reliable predictive power (remember the same Sigmund Freud or Alfred Adler), the risk of accidental error and the temptation to deliberately “adjust” the actual result to the desired one is quite high.
How a computer caught dishonest psychologists red-handed
The program that confirmed the validity of this ironic observation is called Statcheck. It analyzes the P-value, a quantity that scientists use to test statistical hypotheses. This figure shows how likely the result is if the null hypothesis underlying the study is true. The paper, which was published in the journal Behavior Research Methods, shows that the program assessed the validity of more than 258,000 p-values (roughly 11 per scientific paper) in two hours, finding that 13% of papers contained an error that "flipped" received data. As a result, for example, P< 0,05 превращается в P = 0,05, или некоторые знаки после запятой просто отбрасываются, а не влияют на следующий знак по правилам округления чисел. Казалось бы, такое маленькое различие не должно серьезно влиять на результат, однако чаще всего P = 0,05 принимается как пограничное значение между статистически достоверным и недостоверным результатом. В итоге малейшее отклонение в одну или в другую сторону делает вывод в статье ложноположительным или ложноотрицательным.
Initially, the program worked with literature in general, but one of the study's co-authors, Chris Hartgerink, a specialist in scientific methodology from Tilburg University (Netherlands), suggested focusing on more specific texts - scientific articles. Later, in August of this year, he uploaded 50,000 articles for verification and posted the results on Pub Peer (a forum for scientists where they often discuss published scientific articles), causing a huge resonance in the professional community. According to Hutgerink, such posts will inform authors about possible errors and “will bring much more benefit to science than just a data dump.” Not everyone agrees with him, as Monia Baker's discussion article in Nature reports. Some scientists, including representatives of the German Psychological Association, warn that false negative results (here we mean a computer correcting correct data for incorrect ones) may harm the reputation of scientists rather than help the development of psychology as a science. The executive director of the Association for Psychological Science in Washington responded to the publication by saying he condemned the "endemic vilification" of psychologists on blogs and social media, making it clear that publishing the results of a computer analysis with possible errors should be considered an insult.
Statcheck and P-value: who is in the firebox, who is in the top?
On the other hand, such posts promote the concept of open science (by the way, both Nuyten and Hartgerink have awards from organizations that encourage the development of this field), which will allow statistical inaccuracies to be found and corrected more quickly. According to Nick Brown, a psychological scientist at the University of Groningham in the Netherlands, such algorithms will only help if researchers read them and evaluate them from the point of view of experts, rather than simply being distrustful of a journal that published questionable papers with errors.
At the moment, several thousand people, inspired by this opportunity, have downloaded this program, written in the R programming language, for free.
However, Statcheck itself can make mistakes, as Thomas Schmidt states in his criticism of the program. For example, it does not always take into account the necessary statistical errors and sometimes cannot understand what is wrong in the article: the P-value or the relative parameter. After scanning two articles with a lot of statistical data, he found that the program failed to evaluate 43 parameters, checked 137 and identified 35 as “potentially incorrect.” Two of these were errors that did not affect the result, three were errors in other parameters not related to the P-value, and the remaining 30 were the result of “false alarms.”
Some psychological journals are even beginning to abandon the p-value for testing the validity of hypotheses, considering this parameter to be insufficiently reliable.
The creators themselves do not deny that their program “will never be as accurate as checking manually,” but they emphasize the speed of its work: if it takes about ten minutes to check the reliability of the P-value of one average psychological article, then the program can cope with dozens thousands in a matter of hours, which is indispensable for conducting a meta-analysis or initial verification of articles sent to editors of scientific journals. The editors of the journal Psychological Science have been using it in this capacity since July of this year. They compare this program with Word or T9 proofreaders, the absurdity of which everyone laughs at, but few would agree to give up. Like these auto-correctors, Statcheck, in their opinion, can be considered “a convenient tool that sometimes says stupid things.”