![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||||||||
|
"when, in fact, it has several characteristics maximally probable for a pseudorandom stream, such as an equal number of each result (P(O) = P(X)) and an equal number of adjacent results with the same outcome for both possible outcomes (P(O|X) = P(X|O) = P(X|X) = P(O|O))."
O = 10 X = 11
O|X = 5 X|X = 6 X|O = 5 O|O = 4
So neither of these statements are true. Anyway, if they were true the example would be silly - the probability of a 21 character sequence containing perfectly equalized pseudorandom properties would be very low. Actually, given that it's 21 characters, the probability would be zero. — Preceding unsigned comment added by 118.148.3.205 ( talk) 03:42, 3 August 2012 (UTC)
I just removed the reference to Lcamtuf's research on network vulnerabilities caused by Strange Attractors in Pseudorandom Number Generators. Super interesting stuff, but the Clustering Illusion is a psychological phenomenon, and has nothing to do with predictability caused by flaws in PRNGs. —Preceding unsigned comment added by 94.212.58.194 ( talk) 10:29, 5 May 2011 (UTC)
The claim that SAT answers are intentionally declustered should have an attribution.
has this been proven?
In another example, Londoners during World War II developed elaborate theories on the impacts of Nazi V-2 rocket attacks on the city. Dividing up the city in certain ways seemed to produce clusters of bombings that were believed to be intentional. In fact there was no way the V-2 rockets could have been so precise, and any clustering was due solely to random variation.
Lazarus666 07:26, 4 Sep 2004 (UTC)
The example is from the referenced Gilovich book, page 19. Is there any specific part you have doubts about?
-- Taak 23:14, 5 Sep 2004 (UTC)
The following quote is shamelessly borrowed, without permission - from V2ROCKET.COM, make of it what you will.
Several factors come into play for the "modest" number of V-2s Antwerp suffered each day, but the main reasons were the German bottleneck in their alcohol and liquid-oxygen supply and the enormous dispersion of the still imperfect weapon. Antwerp would probably have suffered more direct impacts if the Germans would have equipped all of their units with the Leitstrahl remote guidance apparatis instead of just the single SS 500 Batterie.
From other information on the same site one may notice that the Leitstrahl remote guidance apparatus equipped V-2 rockets had the ability to strike a target within 250 meters, even at a 250 kilometer range, whereas the less accurate version had a typical dispersion at the target of 4 to 11 km.
Lazarus666 18:47, 11 Sep 2004 (UTC)
User:80.175.217.179 removed the following, calling it an erroneous example in the edit summary:
I see why one may find this erroneous, as nothing is really clustering here, but the intro defines the illusion like this:
- and that seems applicable.-- Niels Ø 07:45, 7 May 2006 (UTC)
I'm the one who added the example, and I agree with Niels Ø. While the name of the illusion is clustering, the description encompasses various kinds of "pattern illusions". So could User:80.175.217.179 please give a brief explanation of why the example is erroneous. Thanks. -- Nick 15:06, 12 June 2006 (UTC)
"Consider the sequence "XXOXOXOOOXOXOOOXOX"; is it random?"
YES, i CONSIDERED ! As a practical gambler, I am obsessed with my own theory, that: "all sequences are random sequences if we define some limit.."; Because of that reason, I made a comparison between the given sequence and my database derived from diligent note taking and analyzing gambling outcomes. I wouch for the validity and correctness of all of my data,(they are archived), however a few errors could have crept in. Presently I have a corresponding RANDOM SEQUENCE experienced in the Casino wich match the given one in sixteen (16) places. I suppose, cannot calculate, that even this matching has an extraordinary low probability. (Moreover, the latter day I experienced a series of actions which matched the random binary result eleven or twelve times. Interesting!) When I am ready with my present tasks, I'll return to my search and if I found the matching sequence, I will post the date when it occured and the exact data sequence which caused it. Till then, I hope that my fate allow me to reach the level of knowledge necessary to understand your teaching. Yours with thanks 144.139.11.122 02:51, 21 June 2007 (UTC)
I beg to differ! I am sorry of not being able to determine my point(s) using axiomatic mathematical language,
but my deliberate avoidance of formal mathematics led to my conclusion - which could be falsified as any philosophical
thought. Regarding your fifty zeroes example : I am sure that in the UNIVERSE, there once was, or there will be a random
sequence which corresponds to your sample. Moreover, with my very limited knowledge, I assume, that the first combination
of 37 Roulette outcomes in 37 repeated trials with replacement shall be : 00000000000000000000000000000000000, that is
37 zeroes, which shall be part of the all available outcomes (37 on the power of 37, which is the number of possible events.
Bewersdorff, Luck, Logic and White Lies Ch14, p90). Regarding the "definition" - it is exactly what it says : definition.
By human being, to go around in the UNIVERSE, until they lost their way. Then : We will find a new "definition" of which
transformations I saw quite a few in my life. Yours
121.210.9.3
21:04, 4 December 2007 (UTC)
Another way of looking at Robin's argument (above) is to say, "Is there a way to 'compress' the data?" Obviously the statement "write fifty zeros" is more "compressed" than "00000000000000000000000000000000000000000000000000", just as "write the first 20 natural numbers" is more compressed than "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19". So one way of saying a sequence is random is to say "there is no more compressed way to describe this sequence."
But this is exactly why I believe the article is incorrect to say that "OXXOXOXOOOXOXOOOXOX" is non-random. Simply attaching meaning to the sequence doesn't mean it's not random. Saying "an X stands for a prime number" doesn't predict when the next X will occur; in fact, it is well known that the distribution of prime numbers is (in one sense) random.
One might say, "But you can 'compress' the sequence by saying, 'X stands for a prime number.'" But this ignores the fact that calculating the next prime number takes more informations that simply stating what the next prime number is. The algorithm for creating fifty zeros or twenty natural numbers is much shorter than a prime computing function.
So I believe the statement about "OXXOXOXOOOXOXOOOXOX" being non-random should be remove or re-written. -- KSnortum 21:57, 2 December 2007 (UTC)
The intro says: "see patterns where actually none exist". I say: if one can see a pattern, then it definitely exists. SJ2571 ( talk) 11:36, 30 January 2008 (UTC)
Gravity's Rainbow has a plot? — Preceding unsigned comment added by 216.31.238.114 ( talk) 22:52, 21 June 2012 (UTC)
I'm rewriting this article as it has lost sight of the original definition of the clustering illusion. "The natural human tendency to 'see patterns where actually none exist'" is an overgeneralization from its more specific meaning, Gilovich's defines it as "the intuition that random events such as coin flips should alternate between heads and tails more than they do... Random distributions seem to us to have too many clusters or streaks of consecutive outcomes of the same type, and so we have difficulty accepting their true origins." As this person defines it: "The observation that people frequently view random distributions, for example, sequences of coin-tosses, as seeming to have too many clusters or ‘streaks’ of consecutive outcomes of the same type" [1].
Much of the deleted content would be better placed in apophenia or pareidolia.
I'm not 100% sure what the above means, but the clustering illusion refers to seeing "clusters" or "streaks" in typical and most small samples of random data, not patterns that will eventually appear in a large amount of data.
The clustering illusion is not about any kind of pattern, it's about streaks or clusters specifically, and in small sets of data, not large ones.
-- Taak ( talk) 00:23, 29 April 2008 (UTC)
Is the clustering illusion more for analyzing existing data and searching for a pattern or predicting a possible outcome given a certain set of existing data? While similar, I don't think they are quite the same.
Take this example, I remember seeing it in countless math and reasoning tests:
However, the probability of 100 consequective flips landing on heads is certainly not 50%. This is the phenomenom where people bet against the odds. The odds will always be 50/50, but it seems people will tend to perceive a pattern. Or, they will think the odds are too great for it to happen 100 times in a row, and go against the establishment of a pattern. If it's being used to predict the outcome, is it still the clustering illusion? Lime in the Coconut 16:57, 23 December 2009 (UTC)
I think it would be good if the article had a picture that people often would find clusters in but that statistical analysis says there are none, and a picture where people would not say there clusters but that statistical analysis says there are. -- TiagoTiago ( talk) 03:05, 31 October 2011 (UTC)
Shouldn´t the formula be P(O|X)+P(X|O)=P(X|X)+P(O|O)? According to my understanding this is what Gilovich mentions 92.72.246.123 ( talk) 09:52, 6 July 2012 (UTC) Witek
I propose that Hot-hand fallacy be merged into Clustering illusion. I think that the content in the Hot-hand Fallacy article can easily be explained in the context of Clustering Illusion. The merger will be especially helpful for those who read the " List of cognitive biases"-article. Because they will avoid confusion. Spannerjam 11:04, 19 October 2013 (UTC)
Goose121 ( talk) 22:48, 19 September 2015 (UTC)
Don't people expect to see MORE variability than what is actually observed, ie, things appear to be less random than we expect? SpxB fan ( talk) 13:46, 14 October 2015 (UTC) SpxB Fan
Hello fellow Wikipedians,
I have just added archive links to one external link on
Clustering illusion. Please take a moment to review
my edit. If necessary, add {{
cbignore}}
after the link to keep me from modifying it. Alternatively, you can add {{
nobots|deny=InternetArchiveBot}}
to keep me off the page altogether. I made the following changes:
When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{
Sourcecheck}}
).
This message was posted before February 2018.
After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than
regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
RfC before doing mass systematic removals. This message is updated dynamically through the template {{
source check}}
(last update: 5 June 2024).
Cheers.— cyberbot II Talk to my owner:Online 12:28, 28 February 2016 (UTC)