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bunbury
Post  Post subject: Definition confusion  |  Posted: Wed Dec 11, 2013 10:49 pm
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I am in a mild argument elsewhere on the web with a person who, in the course of discussing some topic stated that a correlation is a causal relationship by definition. I objected and gave a pretty standard response to this fallacy, thinking that was that and we could move on. I said correlation does not imply causation. He disagreed and posted what he says is the Oxford English Dictionary number one definition thus:

"Correlation: 1. A causal relationship or connection between two or more things."

I think this definition is either flat wrong, or at least misleading. A correlation can be a causal relationship if the observed correlation is subsequently shown to be such, and that may be the intent of the "or" in the OED definition. Meanwhile the arguments drags on (ball in my court I guess) with the other guy's latest response here:

"A correlation IS a causal relationship. If any scientist, engineer or statistician "knows" otherwise they're wrong. "

Any comments, or advice how to respond?


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iNow
Post  Post subject: Re: Definition confusion  |  Posted: Thu Dec 12, 2013 1:43 am
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Sounds to me like he's just trying to be clever and no matter how fully you rebut his position, he'll likely maintain it (because he almost certainly believes he's smarter than you).

My immediate thought is that his comment (A correlation IS a causal relationship) is wrong because clear counter examples exist.

The most obvious being that there is a correlation between people carrying umbrellas and it raining. However, people carrying umbrellas clearly doesn't cause it to rain (if it did, we could simply hand umbrellas to people in drought stricken climates or deserts and start growing water-intensive crops in the Sahara).

Likewise, thinking he's more clever than you, he might respond, "Ah, but rain DOES cause people to carry umbrellas," which is itself remedially false. The rain clearly doesn't cause people to carry umbrellas because not everybody carries an umbrellas when it rains (some people wear raincoats or no protection or simply stay inside, etc.). Likewise, people often carry umbrellas when there's no rain at all, for example to shade themselves from the sun.

If it was a causal relationship in the way he's arguing, then by definition the rain would result in everyone carrying an umbrella every single time precipitation falls (or, assuming the other perspective, it would rain every time someone picked up an umbrella). Basically, his comment is ALMOST correct, but is missing a key word. What he needs to be saying instead is that, "A correlation is SOMETIMES a causal relationship."

He's most likely just trolling, but if he sincerely believes what he's saying and refuses to amend his position then he's just an idiot... Either way, pretty much a waste of your time, IMO.


Here's a good link on the topic. I like some of their examples, too: http://rationalwiki.org/wiki/Correlatio ... _causation

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bunbury
Post  Post subject: Re: Definition confusion  |  Posted: Thu Dec 12, 2013 2:36 am
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But if he is using a different definition of correlation then counter examples are not relevant to him. It's actually just a question of what is the right definition.

Why is the OED seemingly at odds with every other source?


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iNow
Post  Post subject: Re: Definition confusion  |  Posted: Thu Dec 12, 2013 2:56 am
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bunbury wrote:
Why is the OED seemingly at odds with every other source?

Based on what I can see, it's not:

http://www.oxforddictionaries.com/us/de ... orrelation
Quote:
correlation

Pronunciation: /ˌkɒrəˈleɪʃ(ə)n, -rɪ-/
Translate correlation | into Italian | into Spanish

noun
a mutual relationship or connection between two or more things:
research showed a clear correlation between recession and levels of property crime

[mass noun]:
there was no correlation between the number of visits to the clinic and the treatment outcome

  • [mass noun] the process of establishing a relationship or connection between two or more things:
    the increasingly similar basis underlying national soil maps allows correlation to take place more easily
  • [mass noun] Statistics interdependence of variable quantities.
  • Statistics a quantity measuring the extent of the interdependence of variable quantities.

Origin:
mid 16th century: from medieval Latin correlatio(n-), from cor- 'together' + relatio (see relation)

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bunbury
Post  Post subject: Re: Definition confusion  |  Posted: Thu Dec 12, 2013 4:02 am
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Yes, I saw that definition, but that's not the actual OED and I don't have access to one. It requires a paid subscription on line. Anyone her have one? I'm only going by what the other guy posted and would like to verify it.

http://www.nature.com/nature/journal/v4 ... 9409a.html


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iNow
Post  Post subject: Re: Definition confusion  |  Posted: Thu Dec 12, 2013 6:03 am
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That seems likely to be a good point of attack on his argument. I've got a funny feeling he's simply lying.

Anyway, even if it really DOES say correlation = causation, then there's this counter:

http://en.wikipedia.org/wiki/Oxford_Eng ... Criticisms
Quote:
...the OED’s "[b]lack-and-white lexicography is also black-and-white in that it takes upon itself to pronounce authoritatively on the rights and wrongs of usage", faulting the Dictionary’s prescriptive, rather than descriptive, usage. To Harris, this prescriptive classification of certain usages as "erroneous" and the complete omission of various forms and usages cumulatively represent the "social bias[es]" of the (presumably well-educated and wealthy) compilers.


Basically, given the way the OED doesn't concern itself much with how words are ACTUALLY used, it really can't serve as a valid definition, especially when essentially ALL others disagree with it.

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marnixR
Post  Post subject: Re: Definition confusion  |  Posted: Thu Dec 12, 2013 7:29 am
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may i jump at this time and point out the potential difference between the vernacular and the statistical meaning of the word ? statistically items may be correlated without the need for a causal relationship - on the other hand, in plain english i wouldn't be surprised that when people say there's a correlation they mean a causal relation
however, i'd say in science we're more likely to use the more precise meaning of statistical correlation rather than the more woolly one of the vernacular

a bit like when statistics says there's a significant difference between 2 populations - a statistically significant difference may not make all that much difference in the real world, but in stats it just means the difference is more than due to chance, whereas in the real world it really must a substantial difference that requires people to treat the populations differently

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bunbury
Post  Post subject: Re: Definition confusion  |  Posted: Thu Dec 12, 2013 10:29 pm
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I agree there's probably a difference between the vernacular and the statistical (or scientific) interpretations, but the overwhelming opinion on the web supports the latter which makes it very surprising to me that the OED takes the opposite and minority position.

Why would the well educated compilers be ignorant of the accepted meaning?


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SkinWalker
Post  Post subject: Re: Definition confusion  |  Posted: Fri Dec 13, 2013 3:26 am
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Here's a link to the OED online page that I clipped to Evernote (hopefully it'll share correctly).

https://www.evernote.com/shard/s11/sh/d ... 5e6f601fac

But let me quote here too.

Quote:
correlation, n.
View as:Outline |Full entryQuotations:Show all |Hide all
Pronunciation: /kɒrɪˈleɪʃən/
Etymology: < cor- prefix + relation n.: compare French corrélation , and see ... (Show More)
1.
Thesaurus »

a. The condition of being correlated; mutual relation of two or more things (implying intimate or necessary connection).

1561 T. Norton tr. J. Calvin Inst. Christian Relig. iv. xvii. §14 If he did set before vs only an empty imaginatiue forme of bred..where were ye correlation or similitude [L. analogia aut similitudo] which should leade vs from the visible thing to the inuisible.
1658 Sir T. Browne Garden of Cyrus in Hydriotaphia iii. 156 How in animall natures, even colours hold correspondencies, and mutuall correlations.
1849 R. I. Murchison Siluria viii. 148 The rocks of Cumberland will be placed in precise correlation with the types of Shropshire and Wales.
1864 F. C. Bowen Treat. Logic iii. 51 The mutual dependence and correlation of these three Axioms.
(Hide quotations)

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†b. Relationship (of persons). Obs.

1649 Bp. J. Taylor Great Exemplar 10 ⁋9 Christian charity is a higher thing than to be confined within the terms of dependence and correlation.
1652 E. Sparke Scintillula Altaris (1663) 89 Christ..made choise of brethren, as..Simon..and Andrew..hereby..providing against schisme..both by corporall and spirituall correlation.
(Hide quotations)

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c. In Statistics, an interdependence of two or more variable quantities such that a change in the value of one is associated with a change in the value or the expectation of the others; also, the value of this as represented by a correlation coefficient. So correlation coefficient or coefficient of correlation : a number between −1 and 1 calculated so as to represent the linear interdependence of two variables or two sets of data; spec. the product-moment coefficient (see product n.1).

1888 F. Galton in Proc. Royal Soc. 45 143 The statures of kinsmen are co-related variables; thus, the stature of the father is correlated to that of the adult son,..and so on; but the index of co-relation..is different in the different cases.
1896 K. Pearson in Proc. Royal Soc. 59 302 Let r0 be the coefficient of correlation between parent and offspring.
1896 K. Pearson in Proc. Royal Soc. 59 303 We conclude that there is a sensible correlation (circa 0·18) between fertility and height in the mothers of daughters.
1909 W. Elderton & E. Elderton Primer Statistics 57 In such cases there is no relationship, therefore, between length and breadth, and we say that the ‘coefficient of correlation’ is zero.
1933 Forestry 7 27 It may be stated that a correlation coefficient is a number expressing the degree of correlation between two variates, as, for example, weight and volume, or specific gravity and strength. A correlation coefficient of +1 indicates a direct linear relation, a coefficient of −1 indicates an inverse linear relation, while one of 0·0 indicates absence of relations between the variates.
1943 N. Balchin Small Back Room i. 8 There's a positive correlation between penetration and the height of the man firing.
1960 F. Land Lang. Math. xiv. 247 We need to be able to describe this gradation from perfect correlation to no correlation at all, and for this purpose we can calculate a ‘correlation coefficient’.
1964 R. von Mises Math. Theory Probability & Statistics xi. 572 Out of 239 patients treated with serum, 9 patients died, and out of 244 left without serum, 29 died. Compute the correlation coefficient between treatment and recovery.
1969 Computers & Humanities 3 145 After correlation coefficients are computed for every pair of variables, they are entered in a correlation matrix which summarizes the degree of similarity between pairs of variables.
(Hide quotations)

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2. correlation of forces (in Physics): a phrase introduced by Grove to express the mutual relation that exists between the various forms of force or energy, by virtue of which any one form is convertible into an equivalent amount of any other. (Cf. conservation n. 3.)

1846 W. R. Grove On Correlation Physical Forces 44 The sense I have attached to the word correlation..[is] a reciprocal production..in other words, that any force capable of producing..another may, in its turn be produced by it.
1869 M. Somerville Molec. Sci. i. ii. 33 Another proof of the correlation of heat and electricity.
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3. Biol. Mutual relation of association between different structures, characteristics, etc. in an animal or plant; ‘the normal coincidence of one phenomenon, character, etc., with another’ (Darwin Origin of Species, Gloss.).

1859 C. Darwin Origin of Species Introd. 5, I shall discuss the complex and little known..laws of variation and of correlation of growth.
1870 G. Rolleston Forms Animal Life 105 The correlation of large size of ova with the completion of development before hatching.
1883 19th Cent. May 763 There is..a mysterious law of correlation of growth between the hair and the teeth.
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4. Geom. The reciprocal relation between propositions, figures, etc. derivable from each other by interchanging the words point and plane, or point and line: cf. correlative adj. 6.


Thesaurus »

5. The action of correlating or bringing into mutual relation.

1879 ‘G. Eliot’ Theophrastus Such xi. 204 It is on such false correlations that men found half their inferences about each other.
1886 A. J. Jukes-Browne Student's Handbk. Hist. Geol. iv. iii. 27 The correlation and classification of rocks on Palæontological principles.
1963 Gloss. Mining Terms (B.S.I.) i. 6 Correlation, the process of orientating underground survey lines or of coordinating underground survey stations to the National Grid.


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bunbury
Post  Post subject: Re: Definition confusion  |  Posted: Fri Dec 13, 2013 4:24 am
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Thanks for posting that.

The top definition says "implying intimate or necessary connection". A connection is not necessarily causal and there's a good example further down where Darwin mentions a correlation between the growth of hair and teeth. Teeth do not cause hair to grow. Some third thing (hormone?) causes both of them to grow.

Also, the correlation between heat and electricity is mentioned but heat does not cause electricity, at least not directly.


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