Glossary entry (derived from question below)
English term or phrase:
among or between
English answer:
comparing correlation and cross-correlation coefficients
Added to glossary by
Roddy Stegemann
Aug 28, 2004 14:30
19 yrs ago
2 viewers *
English term
among or between
English
Science
Science (general)
among or between
The inter-probe placement relationships of the muscle oxygenation kinetics were evaluated by calculating the cross correlation coefficient between the parameters on the two probe placements. The relationships among the parameters were examined by Pearson
The inter-probe placement relationships of the muscle oxygenation kinetics were evaluated by calculating the cross correlation coefficient between the parameters on the two probe placements. The relationships among the parameters were examined by Pearson
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Responses
+2
42 mins
Roddy Stegemann
United States
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Works in: German to English, Japanese to English, French to English, and 3 more.
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The text is correct. Do not change it.
The two key terms in your text are cross-correlation coefficient and Pearson's correlation coefficient. A cross-correlation coefficient is obtained between two variables. The Pearson's correlation coefficient is obtained between two or more.
With all due respect to the contributions of are other illustrious ProZ.com members the ambiguity of the terms "between" and "among" is best not entertained in this context. The Pearson's correlation coefficient is a single value that measures the degree of distribution across two or more variables. Although in a nonstochastic sense it is not something that is itself distributable, it does measure the degree of relationship among several variables simultaneously -- not as pairs, but as a group. See the link provided below.
The cross-correlation coefficient, on the other hand, is clearly a measure of stochasitic affinity between two variables, and I can think of no reasonable justification for using the term among in this context.
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Note added at 19 hrs 27 mins (2004-08-29 09:57:53 GMT)
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Below you will find what may be thought of as a correlation matrix for four variables. Each element of the matrix represents a single correlation coefficient between a pair of variables. For example, the correlation coefficient for the variables 3 and 4 is given by X34 and X43, and the correlation coefficient for the variables 1 and 2 is given by X12 and X21. The values of X34 and X43 are identical. The same is true for values of X12 and X21. The values X11, X22, X33, and X44 are all equal to one. This is because they represent the correlation of each of the variables with itself. Because of the redundancy of information contained in the matrix, it is very common to provide only its diagonal.
X11 X12 X13 X14
X21 X22 X23 X24
X31 X32 X33 X34
X41 X42 X43 X44
The diagonal matrix is provided for you below.
1
X21 1
X31 X32 1
X41 X42 X43 1
Any element of the diagonal matrix is called a cross-correlation coefficient. Hopefully, the name is by now self-explanatory.
Pearson\'s correlation coefficent is simply the name given to the calculation of any correlation coefficient, whether it appears in a cross-correlation table or not. Now to a careful analysis of your text.
The author tells us that there are two probes. What the author does not tell us is how many parameters (for the purpose of this example, variables) are measured with each probe. It could be one, two, three, or more. Say it were four, as given in my example. Then there would be a total of six useful cross-correlation coefficients. For the purpose of your text and this discussion the number of probes is somewhat immaterial, because it is the information obtained for each of the parameters (variables) that is being compared. Once again, we are never told the number of parameters. If, for example, there were four, then the number of possible comparisons would be quite large. For example, you could compare the pair of coefficents X21 and X32, or you could compare the combination of coefficents X21, X41, and X43, etc.
Usually a single probe of anything yields a large number of observations for each parameter (variable), and thus an ample amount of data to generate appropriate correlation coefficients. The fact that two probes were taken was simply to insure that the examined tissue was adequately represented in the data.
In layman\'s terms, when you stick a fork into a baked cake, you usually probe more than once, so as to be certain that no part of the cake is underbaked. In the same manner, you poke living tissue, so as to be sure that you have an accurate reading of the entire tissue.
In contrast to a single cake probe that reveals only a single value for a single parameter (the number of crumbs stuck to the fork when it is removed from the cake), a single electronic probe can emit a long stream of data for several different variables. It is these long streams of data that provide one with the variances required to produce the covariances between variables that result in the correlation coefficents about which your text and this discussion is so obviously about.
I hope that I have eliminated most of your confusion. Should you have any more questions about the matter, please feel free to write to me at [email protected]
Should you have other questions about statistical terms of a multivariate nature, please see the HKLNA-Project\'s Statistical Toolbox at
http://homepage.mac.com/moogoonghwa/earth/current/hklna/indi...
Bye for now, I do hope I have been of help.
With all due respect to the contributions of are other illustrious ProZ.com members the ambiguity of the terms "between" and "among" is best not entertained in this context. The Pearson's correlation coefficient is a single value that measures the degree of distribution across two or more variables. Although in a nonstochastic sense it is not something that is itself distributable, it does measure the degree of relationship among several variables simultaneously -- not as pairs, but as a group. See the link provided below.
The cross-correlation coefficient, on the other hand, is clearly a measure of stochasitic affinity between two variables, and I can think of no reasonable justification for using the term among in this context.
--------------------------------------------------
Note added at 19 hrs 27 mins (2004-08-29 09:57:53 GMT)
--------------------------------------------------
Below you will find what may be thought of as a correlation matrix for four variables. Each element of the matrix represents a single correlation coefficient between a pair of variables. For example, the correlation coefficient for the variables 3 and 4 is given by X34 and X43, and the correlation coefficient for the variables 1 and 2 is given by X12 and X21. The values of X34 and X43 are identical. The same is true for values of X12 and X21. The values X11, X22, X33, and X44 are all equal to one. This is because they represent the correlation of each of the variables with itself. Because of the redundancy of information contained in the matrix, it is very common to provide only its diagonal.
X11 X12 X13 X14
X21 X22 X23 X24
X31 X32 X33 X34
X41 X42 X43 X44
The diagonal matrix is provided for you below.
1
X21 1
X31 X32 1
X41 X42 X43 1
Any element of the diagonal matrix is called a cross-correlation coefficient. Hopefully, the name is by now self-explanatory.
Pearson\'s correlation coefficent is simply the name given to the calculation of any correlation coefficient, whether it appears in a cross-correlation table or not. Now to a careful analysis of your text.
The author tells us that there are two probes. What the author does not tell us is how many parameters (for the purpose of this example, variables) are measured with each probe. It could be one, two, three, or more. Say it were four, as given in my example. Then there would be a total of six useful cross-correlation coefficients. For the purpose of your text and this discussion the number of probes is somewhat immaterial, because it is the information obtained for each of the parameters (variables) that is being compared. Once again, we are never told the number of parameters. If, for example, there were four, then the number of possible comparisons would be quite large. For example, you could compare the pair of coefficents X21 and X32, or you could compare the combination of coefficents X21, X41, and X43, etc.
Usually a single probe of anything yields a large number of observations for each parameter (variable), and thus an ample amount of data to generate appropriate correlation coefficients. The fact that two probes were taken was simply to insure that the examined tissue was adequately represented in the data.
In layman\'s terms, when you stick a fork into a baked cake, you usually probe more than once, so as to be certain that no part of the cake is underbaked. In the same manner, you poke living tissue, so as to be sure that you have an accurate reading of the entire tissue.
In contrast to a single cake probe that reveals only a single value for a single parameter (the number of crumbs stuck to the fork when it is removed from the cake), a single electronic probe can emit a long stream of data for several different variables. It is these long streams of data that provide one with the variances required to produce the covariances between variables that result in the correlation coefficents about which your text and this discussion is so obviously about.
I hope that I have eliminated most of your confusion. Should you have any more questions about the matter, please feel free to write to me at [email protected]
Should you have other questions about statistical terms of a multivariate nature, please see the HKLNA-Project\'s Statistical Toolbox at
http://homepage.mac.com/moogoonghwa/earth/current/hklna/indi...
Bye for now, I do hope I have been of help.
4 KudoZ points awarded for this answer.
Comment: "Thank you very much."
+1
2 mins
between, since there are two
among indicates more than two
+8
1 min
see explanation
between if there are two p.
among if there are more than two
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Note added at 2 mins (2004-08-28 14:32:46 GMT)
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the rule is as simple as that!
among if there are more than two
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Note added at 2 mins (2004-08-28 14:32:46 GMT)
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the rule is as simple as that!
Peer comment(s):
| agree |
NancyLynn
: quicker than I!
0 min
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Thanks, Nancy!
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| agree |
Saleh Chowdhury, Ph.D.
18 mins
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Thanks, Saleh!
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| agree |
Rajan Chopra
28 mins
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Thanks, langclinic!
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| agree |
nrabate
3 hrs
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| agree |
Alexandra Tussing
3 hrs
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| agree |
airmailrpl
: -
16 hrs
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| agree |
Empty Whiskey Glass
1 day 1 hr
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| agree |
senin
3 days 21 hrs
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+6
7 mins
Kim Metzger
Mexico
Mexico
Native in English
&
English
Mexico
Committed to Quality and Service
Native in: English (Variant: US) 
Works in: German to English
among
I think in the first case (between the parameters on the two probe placements) we're talking about two things. Whereas in the second case we're talking about more than two: many parameters.
The New York Times Manual of Style and Usage -
among/between: "In general, 'between' applies to two things, and 'among' to more than two. But 'between' is correct in reference to more than two when the items are related individually as well as severally: Trade between the United States, Canada and Mexico has grown under Nafta. Each country trades with each of the others, rather than will all simultaneously. When more than two things are related in a purely collective and vague way, use among."
The New York Times Manual of Style and Usage -
among/between: "In general, 'between' applies to two things, and 'among' to more than two. But 'between' is correct in reference to more than two when the items are related individually as well as severally: Trade between the United States, Canada and Mexico has grown under Nafta. Each country trades with each of the others, rather than will all simultaneously. When more than two things are related in a purely collective and vague way, use among."
Peer comment(s):
| agree |
Saleh Chowdhury, Ph.D.
13 mins
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| agree |
Orla Ryan
41 mins
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| agree |
Kevin Pfeiffer (X)
: good point!
54 mins
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| agree |
Alexandra Tussing
3 hrs
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| agree |
Tony M
: Well put, the rule is by no means as hard-and-fast as some answerers seem to be suggesting...
5 hrs
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| neutral |
Katalin Horváth McClure
: Th explanation about the exceptional use of "between" this is precisely the case. The statistical calculations used here apply to two parameters, and there are several pairs like that. "Between" would be correct to use.
12 hrs
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And I also found the exception to be enlightening.
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mportal
: I agree with the explanation given, but, in the text, I think it is confusing because the author does not specify that s/he is talking about a number of groups/pairs of parameters. What is being implied is 'among the groups or pairs', not the parameters
20 hrs
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| agree |
Empty Whiskey Glass
1 day 1 hr
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+8
1 min
Michael Powers (PhD)
United States
United States
Native in English
&
English
United States
US Court Cert. 1980 Ph.D. 1981
Native in: English
Works in: Spanish to English, Portuguese to English, English to Spanish, and 2 more.
depends on number of parameters
"between" is used in a relationship of two parameters (or whatever) and "among" is used when there are more than two parameters (or whatever)
Mike :)
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Note added at 4 mins (2004-08-28 14:34:59 GMT)
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This is the prescriptive rule. However, in actual usage, there is confusion as can be seen in the Merriam-Webster Dictionary explanation of usage regarding \"between\":
usage There is a persistent but unfounded notion that between can be used only of two items and that among must be used for more than two. Between has been used of more than two since Old English; it is especially appropriate to denote a one-to-one relationship, regardless of the number of items. It can be used when the number is unspecified *economic cooperation between nations*, when more than two are enumerated *between you and me and the lamppost* *partitioned between Austria, Prussia, and Russia — Nathaniel Benchley*, and even when only one item is mentioned (but repetition is implied) *pausing between every sentence to rap the floor — George Eliot*. Among is more appropriate where the emphasis is on distribution rather than individual relationships *discontent among the peasants*. When among is automatically chosen for more than two, English idiom may be strained *a worthy book that nevertheless falls among many stools — John Simon* *the author alternates among mod slang, clich*s and quotes from literary giants — A. H. Johnston*.
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Note added at 7 mins (2004-08-28 14:37:34 GMT)
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Quite often prescriptive or school-based rules do not reflect reality. For example, there is a common prescriptive rule stating that the nominative or subject form of the pronoun must be used after the verb \"be\" thus giving \"It is I\" or \"This is he.\" However, in acutal usage, it is extremely common, even among university educated native speakers to hear, \"Yeah, this is me.\" The distinction then becomes one of formality, and is more sociolinguistic in nature from a descriptive point of view.
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Note added at 10 mins (2004-08-28 14:40:41 GMT)
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Other examples in which prescriptive rules are not followed in actuality include the common grammatical rule that you cannot end a sentence in a preposition. This is not true and is violated all the time; however, since the first grammarians were classical scholars and thus greatly influenced by Latin, they applied Romance language rules to the English language, apparently oblivious to the fact that it is a Germanic language.
Mike :)
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Note added at 4 mins (2004-08-28 14:34:59 GMT)
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This is the prescriptive rule. However, in actual usage, there is confusion as can be seen in the Merriam-Webster Dictionary explanation of usage regarding \"between\":
usage There is a persistent but unfounded notion that between can be used only of two items and that among must be used for more than two. Between has been used of more than two since Old English; it is especially appropriate to denote a one-to-one relationship, regardless of the number of items. It can be used when the number is unspecified *economic cooperation between nations*, when more than two are enumerated *between you and me and the lamppost* *partitioned between Austria, Prussia, and Russia — Nathaniel Benchley*, and even when only one item is mentioned (but repetition is implied) *pausing between every sentence to rap the floor — George Eliot*. Among is more appropriate where the emphasis is on distribution rather than individual relationships *discontent among the peasants*. When among is automatically chosen for more than two, English idiom may be strained *a worthy book that nevertheless falls among many stools — John Simon* *the author alternates among mod slang, clich*s and quotes from literary giants — A. H. Johnston*.
--------------------------------------------------
Note added at 7 mins (2004-08-28 14:37:34 GMT)
--------------------------------------------------
Quite often prescriptive or school-based rules do not reflect reality. For example, there is a common prescriptive rule stating that the nominative or subject form of the pronoun must be used after the verb \"be\" thus giving \"It is I\" or \"This is he.\" However, in acutal usage, it is extremely common, even among university educated native speakers to hear, \"Yeah, this is me.\" The distinction then becomes one of formality, and is more sociolinguistic in nature from a descriptive point of view.
--------------------------------------------------
Note added at 10 mins (2004-08-28 14:40:41 GMT)
--------------------------------------------------
Other examples in which prescriptive rules are not followed in actuality include the common grammatical rule that you cannot end a sentence in a preposition. This is not true and is violated all the time; however, since the first grammarians were classical scholars and thus greatly influenced by Latin, they applied Romance language rules to the English language, apparently oblivious to the fact that it is a Germanic language.
Peer comment(s):
| agree |
NancyLynn
: quicker than I!
0 min
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Thank you, NancyLynn - Mike :)
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| agree |
Sonia Heidemann
8 mins
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Thank you, Sónia - Mike :)
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| agree |
Saleh Chowdhury, Ph.D.
20 mins
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Thank you, Saleh - Mike :)
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| agree |
Orla Ryan
47 mins
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Thank you, Orla - Mike :)
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| agree |
J. Leo (X)
2 hrs
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Thank you, James - Mike :)
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| agree |
Katalin Horváth McClure
: I agree with the additional note including the Merriam-Webster Dictionary explanation about the special use of "between". The asker's text is precisely this case, the correlation coefficients are obtained using several variables, but on a one-to-one basis
12 hrs
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| agree |
Empty Whiskey Glass
1 day 1 hr
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| agree |
Ernesto de Lara
: good explanation, Mike!
1 day 4 hrs
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1 day 13 hrs
Katalin Horváth McClure
United States
United States
Works in field
United States
Expert: high-tech, software, engineering
Native in: Hungarian
Works in: English to Hungarian, Japanese to English, Hungarian to English, and 3 more.
between, because it is about several pairs of parameters
The question was posted on the Eng-Jpn KudoZ as well, and there were several answers, just as here.
I just want to point out two things:
1. As several other collegues have already pointed out here, using "between" is correct when referring to a group of (I mean, more than two) items that are related to each other in a one-to-one fashion, in other words, as pairs. Some people may mot know this exception in English grammar, and therefore use "among", since the total number of items is more than two. (I think this was the case with the author of the original text.)I am not saying it is totally incorrect, as I am sure many people use it this way, but "between" in this case would be better.
2. The Pearson's correlation coefficient is calculated using TWO (and not more) variables. I have posted a few sites and quotes, and quite a bit of explanation at the other Kudoz Question:
http://www.proz.com/kudoz/796945
I don't know what Hamo means when he is writing the following things:
A. "The Pearson's correlation coefficient is a single value that measures the degree of distribution across two or more variables. Although in a nonstochastic sense it is not something that is itself distributable, it does measure the degree of relationship among several variables simultaneously -- not as pairs, but as a group."
B. "Cross-correlation coefficients are a special case of Pearson's correlation coefficent. They refer to a pairwise comparison of individual elements of a correlation table. The term 'among' refers to several pairwise comparisons and is therefore correct."
C. "Pearson's correlation coefficent is simply the name given to the calculation of any correlation coefficient, whether it appears in a cross-correlation table or not."
These statements contain a fair amount of contradiction - first he says Pearson's is NOT dealing with pairs, but then later he says it is dealing with pairs...
The thing is, the target audience will probably know how Pearson's is calculated, and from the translation's point of view it doesn't matter whether the original author should have used "between" or "among".
As long as we understand the meaning (that is, the relationships of the parameters are examined in pairs, in other words, how one parameter is related to another, using the same process for all pairs), we should be able to translate it into another language.
I just want to point out two things:
1. As several other collegues have already pointed out here, using "between" is correct when referring to a group of (I mean, more than two) items that are related to each other in a one-to-one fashion, in other words, as pairs. Some people may mot know this exception in English grammar, and therefore use "among", since the total number of items is more than two. (I think this was the case with the author of the original text.)I am not saying it is totally incorrect, as I am sure many people use it this way, but "between" in this case would be better.
2. The Pearson's correlation coefficient is calculated using TWO (and not more) variables. I have posted a few sites and quotes, and quite a bit of explanation at the other Kudoz Question:
http://www.proz.com/kudoz/796945
I don't know what Hamo means when he is writing the following things:
A. "The Pearson's correlation coefficient is a single value that measures the degree of distribution across two or more variables. Although in a nonstochastic sense it is not something that is itself distributable, it does measure the degree of relationship among several variables simultaneously -- not as pairs, but as a group."
B. "Cross-correlation coefficients are a special case of Pearson's correlation coefficent. They refer to a pairwise comparison of individual elements of a correlation table. The term 'among' refers to several pairwise comparisons and is therefore correct."
C. "Pearson's correlation coefficent is simply the name given to the calculation of any correlation coefficient, whether it appears in a cross-correlation table or not."
These statements contain a fair amount of contradiction - first he says Pearson's is NOT dealing with pairs, but then later he says it is dealing with pairs...
The thing is, the target audience will probably know how Pearson's is calculated, and from the translation's point of view it doesn't matter whether the original author should have used "between" or "among".
As long as we understand the meaning (that is, the relationships of the parameters are examined in pairs, in other words, how one parameter is related to another, using the same process for all pairs), we should be able to translate it into another language.
Reference:
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