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among or between

Japanese translation: between (when the relationships are pairwise)

GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
English term or phrase:among or between
Japanese translation:between (when the relationships are pairwise)
Entered by: Katalin Horváth McClure

13:18 Aug 28, 2004
English to Japanese translations [PRO]
Science - Electronics / Elect Eng
English term or phrase: 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’s correlation coefficients. A probability level of 0.05 was considered to be an indication of a statistical significance.

Is it the relationships among prarameters or between the parameters?
Mitsuko
Local time: 00:00
between (plus see explanation)
Explanation:
I think the author use of "among" is slightly misunderstandable.
Here is the explanation of the situation.
(There will be some statistics involved, so please bear with me.)
There are two probe placements, and I believe there are several parameters read (measured, calculated, whatever) for each placement.
Let's say we have parameters "A", "B", and "C" for the first placement, and we also have "a", "b", "c" for the second placement. To be exact, a parameter will have several values, actually a series of values, in this case, probably some sort of value measured over time. (For example, a parameter could represent temperature, or voltage, or PH value, or weight, whatever.)
So, for eaxmple, parameter A could have values : 1,3,4,3,5,6,7, whatever.
Parameter B could have another series of values, and so does parameter C.
Same thing goes for parameters a, b, c for the second placement, those also have a series of values.
Correlation is calculated between TWO things, between two parameters. It describes the relationship between those two parameters, simply said, would a certain change in the values of one parameter result in the same kind of change in the other, or would it cause the opposite type of change?
For example, if the values of parameter "A" are increasing over time, and the values of parameter "a" are also increasing over time, they have a positive correlation. If the values of parameter "A" are decreasing over time, but the values of parameter "a" are increasing over time, the have a negative correlation. Correlation can have a value between -1 and 1, where -1 is a perfect negative correlation, and 1 is a perfect positive correlation. Two parameters are perfectly correlated when one is doing exactly the same thing as the other.

Anyway, the point is that correlation is always calculated between two things.
Here, you are dealing with PAIRS of parameters. I believe they are calculating correlations between parameter pairs, such as "A" and "a", "B" and "b", "C" and "c", using one parameter from each placement for one correlation calculation.

This way, you have several pairs, in other words, several relationships to describe.
Since the author is talking about the relationships between these parameter pairs, he/she is using the word "among". But don't misunderstand it, it does not mean the relationship or relationships where all parameters are considered at the same time.



--------------------------------------------------
Note added at 13 hrs 32 mins (2004-08-29 02:50:59 GMT)
--------------------------------------------------

Additional explanation (after Hamo¥'s posting):
I will quote several sites below that explain how the Pearson¥'s correlation coefficient is calculated. They all explain it slightly differenty, using different version of the formula, but they all agree that it uses TWO (and not more) variables for the calculation.
If you have more than two variables, it is possible to build a correlation matrix, where (it¥'s gonna be hard to explain verbally here) you have the correlation values (that were obtained using two variables) arranged in rows and columns, each row and column corresponding to one variable.
Let me try it with an example.
You have variables x, y, z (that is 3 variables).
You calculate the correlation (or Pearson¥'s) between each pair, let¥'s call them
Cxy, Cxz, Cyz
Then you have a correlation matrix that looks like this:
Cxx, Cxy, Cxz
Cyx, Cyy, Cyz
Czx, Czy, Czz
(Cxx=Cyy=Czz=1, because a variable is in perfect correlation with itself)
In this case, we can talk about the ¥"the relationships among the parameters¥", but it still refers to PAIRS.

Again, a ¥"parameter¥" or ¥"variable¥" is a set of values, a vector, a one dimensional array if you wish, so maybe that is causing the confusion about whether Pearson¥'s is dealing with ¥"only two¥" or ¥"two or more¥" parameters.
There is no point in calculating correlation between two values (e.g two scalar points) because it is either 1 (if they are equal) or 0 (if they are not equal).

Now, there is a way to mathematically (statistically) describe the relationship among several variables, that is called ¥"n-way correlation¥".
There is one paper related to that here, but more can be found:
http://atesit.phys.uniroma1.it/pdf/L89,207901.pdf

As for the correctness of the original English, I see no particular problem with it. It could be that the author did not feel comfortable using ¥"between¥" because there are more than two parameters involved, even though each of the relationships refer to the relationship between two of these parameters. The same question was posted on the English monolingual KudoZ forum, and one reply talks about this.

In my opinion, it doesn¥'t matter whether the original should be between or among, as long as you understand what the situation is and translate it correctly, according to the meaning, not word by word.

Now, back to the quotes on Pearson¥'s:

¥"Pearson¥'s correlation coefficient, r

Correlation is a technique for investigating the relationship between two quantitative, continuous variables, for example, age and blood pressure. Pearson¥'s correlation coefficient (r) is a measure of the strength of the association between the two variables.¥"
http://hsc.uwe.ac.uk/dataanalysis/quant_pear_coeff.htm

¥"Pearson¥'s Correlation Coefficient
Brian T. Luke, Ph.D.
LearningFromTheWeb.net

Pearson¥'s product-moment correlation coefficient, r, or simply the sample correlation coefficient, is a measure of extent to which two samples are linearly related. For example, if two samples X1 and X2 contain five measurements and X1={1,2,3,4,5} and X2={2,4,6,8,10}, there is a perfect linear relationship between them since X2 is just two times X1. In this case, r=1.0. If, on the other hand, X1={1,2,3,4,5} and X2={10,8,6,4,2}, there is a negative correlation between the samples and r=-1.0. ¥"
http://members.aol.com/btluke/pearson.html

Pearson¥'s Correlation Coefficient

The correlation coefficient r (also called Pearson¥'s product moment correlation) is calculated by ...
Assumptions:
* linear relationship between x and y
* continuous random variables
* both variables must be normally distributed
* x and y must be independent of each other
http://www.vias.org/tmdatanaleng/cc_corr_coeff.html

The next one has a good explanation, also about the 0.05 value that is in the context:
http://www.medcalc.be/manual/mpage06-03a.php

¥"Karl Pearson¥'s Correlation Coefficient

This formula was created for calculating a measure of linear association between pairs of values (x, y) that are ranked or unranked.

Karl Pearson, (1857-1936), was a British statistician. His coeffient, just like Spearmen¥'s, indicates the direction (+ or -) and strength (near 1 or -1 versus near 0) of the association between the two variables.¥"

http://www.msad54.k12.me.us/MSAD54Pages/skow/MathDept/CPMP/M...








--------------------------------------------------
Note added at 13 hrs 38 mins (2004-08-29 02:57:08 GMT)
--------------------------------------------------

Oh, last thing:
Read this carefully:
¥"The relationships among the parameters were examined by Pearson’s correlation coefficients.¥" Pay attention to the last ¥"S¥". It is in plural!
The text is talking about several Pearson¥'s correlation coefficients - that means it is NOT a single value describing the relationship among several variables simultenously.


--------------------------------------------------
Note added at 13 hrs 48 mins (2004-08-29 03:07:04 GMT)
--------------------------------------------------

Sorry for the long posting.
The reason is that there was another answer arguing that the Pearson¥'s correlation coefficient measured (with a single value) the relationship among several (more than two) parameters at the same time, as a group, not in pairs.
Since I posted my disagreement with his statement, he removed his posting.

--------------------------------------------------
Note added at 2 days 6 hrs 20 mins (2004-08-30 19:38:48 GMT)
--------------------------------------------------

To Hamo:
This is a quote from the message you posted on the English KudoZ, where your link was pointing. (Just becasue you say I stated something that is not true.)
Hamo wrote: ¥"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.¥"

It says ¥"single value¥", ¥"two or more variables¥", ¥"several variables simultaneously¥", ¥"not as pairs, but as a group¥".

I posted my long discussion about coefficients, coeff. matrices, etc. to clarify and support my point that Pearson¥'s correlation is calculated using two (and not more) variables at the same time. (As opposed to your argument.)

Later on, you added more notes, where you discussed the pairwise nature of the coefficients, which is correct. The only problem is that it is contradicting your very first statement. If by now you agree, that the text is talking about studying the variables in pairs, then we are on the same platform, and there is nothing to argue about.

I think the other readers are getting tired of this by now, so this is my last posting on the topic. At least nobody has to suffer through my poorly argued discussions anymore...
;-)
Selected response from:

Katalin Horváth McClure
United States
Local time: 11:00
Grading comment
Thank you very much.
4 KudoZ points were awarded for this answer



Summary of answers provided
5 +5between (plus see explanation)
Katalin Horváth McClure
5It depends on the number of parameters.
Kurt Hammond
4テクストが平気です。
Roddy Stegemann
1 +1between and then among/between
Maynard Hogg


  

Answers


1 hr   confidence: Answerer confidence 5/5
It depends on the number of parameters.


Explanation:
It is unusual to use the word 'among' here. You may consider getting clarification from the author if possible.

"Among" is used when there are three or more parameters. "Between" is used when there are exactly two parameters. In the first usage of "between", it is clearly stated that there are two parameters.
In the second usage, there is no direct mention of how many parameters there are, but the word "the" seems to indicate we are talking about the same set of parameters.

Note: It appears this paragraph was written by a non-native, so it is highly possible he or she simply misused "among" and should have used "between" (in the final sentence, "statistical significance" is more natural than "a statistical significance").

Kurt Hammond
United States
Local time: 08:00
Native speaker of: English
PRO pts in category: 4

Peer comments on this answer (and responses from the answerer)
agree  conejo: It seems like the author is talking about the same parameters, but has used two different words. I agree with Kurt's assessment.
3 hrs
neutral  Katalin Horváth McClure: Correlation is calculated between two parameters. There could be more parameters here, but they are handled in pairs. See explanation separately.
5 hrs
  -> Possible and likely. I vote for your response.
disagree  Maynard Hogg: Paragraph 1: The author uses BOTH, so is no help. Paragraph 2: Too simplistic. Japanese does not have a monopoly on 学校文法. See Katalin's post for an important exception to your "rule".
13 hrs
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15 hrs   confidence: Answerer confidence 1/5Answerer confidence 1/5 peer agreement (net): +1
between and then among/between


Explanation:
The first sentence talks about comparing the same parameter for two probes; the second about the total set of relationships among all possible pairings of those parameters. Those fixated on the size of the set might prefer among, but I'd go for between. After we distinguish "relations/trade between countries" from "Bobby Fisher circulated among five countries avoiding arrest."

Maynard Hogg
Canada
Local time: 08:00
Specializes in field
Native speaker of: English
PRO pts in category: 11

Peer comments on this answer (and responses from the answerer)
agree  Katalin Horváth McClure: Yes, this is it, I like your example. This is the point: we are talking about pairings of those parameters (who cares how many).
23 hrs
Login to enter a peer comment (or grade)

6 hrs   confidence: Answerer confidence 5/5 peer agreement (net): +5
between (plus see explanation)


Explanation:
I think the author use of "among" is slightly misunderstandable.
Here is the explanation of the situation.
(There will be some statistics involved, so please bear with me.)
There are two probe placements, and I believe there are several parameters read (measured, calculated, whatever) for each placement.
Let's say we have parameters "A", "B", and "C" for the first placement, and we also have "a", "b", "c" for the second placement. To be exact, a parameter will have several values, actually a series of values, in this case, probably some sort of value measured over time. (For example, a parameter could represent temperature, or voltage, or PH value, or weight, whatever.)
So, for eaxmple, parameter A could have values : 1,3,4,3,5,6,7, whatever.
Parameter B could have another series of values, and so does parameter C.
Same thing goes for parameters a, b, c for the second placement, those also have a series of values.
Correlation is calculated between TWO things, between two parameters. It describes the relationship between those two parameters, simply said, would a certain change in the values of one parameter result in the same kind of change in the other, or would it cause the opposite type of change?
For example, if the values of parameter "A" are increasing over time, and the values of parameter "a" are also increasing over time, they have a positive correlation. If the values of parameter "A" are decreasing over time, but the values of parameter "a" are increasing over time, the have a negative correlation. Correlation can have a value between -1 and 1, where -1 is a perfect negative correlation, and 1 is a perfect positive correlation. Two parameters are perfectly correlated when one is doing exactly the same thing as the other.

Anyway, the point is that correlation is always calculated between two things.
Here, you are dealing with PAIRS of parameters. I believe they are calculating correlations between parameter pairs, such as "A" and "a", "B" and "b", "C" and "c", using one parameter from each placement for one correlation calculation.

This way, you have several pairs, in other words, several relationships to describe.
Since the author is talking about the relationships between these parameter pairs, he/she is using the word "among". But don't misunderstand it, it does not mean the relationship or relationships where all parameters are considered at the same time.



--------------------------------------------------
Note added at 13 hrs 32 mins (2004-08-29 02:50:59 GMT)
--------------------------------------------------

Additional explanation (after Hamo¥'s posting):
I will quote several sites below that explain how the Pearson¥'s correlation coefficient is calculated. They all explain it slightly differenty, using different version of the formula, but they all agree that it uses TWO (and not more) variables for the calculation.
If you have more than two variables, it is possible to build a correlation matrix, where (it¥'s gonna be hard to explain verbally here) you have the correlation values (that were obtained using two variables) arranged in rows and columns, each row and column corresponding to one variable.
Let me try it with an example.
You have variables x, y, z (that is 3 variables).
You calculate the correlation (or Pearson¥'s) between each pair, let¥'s call them
Cxy, Cxz, Cyz
Then you have a correlation matrix that looks like this:
Cxx, Cxy, Cxz
Cyx, Cyy, Cyz
Czx, Czy, Czz
(Cxx=Cyy=Czz=1, because a variable is in perfect correlation with itself)
In this case, we can talk about the ¥"the relationships among the parameters¥", but it still refers to PAIRS.

Again, a ¥"parameter¥" or ¥"variable¥" is a set of values, a vector, a one dimensional array if you wish, so maybe that is causing the confusion about whether Pearson¥'s is dealing with ¥"only two¥" or ¥"two or more¥" parameters.
There is no point in calculating correlation between two values (e.g two scalar points) because it is either 1 (if they are equal) or 0 (if they are not equal).

Now, there is a way to mathematically (statistically) describe the relationship among several variables, that is called ¥"n-way correlation¥".
There is one paper related to that here, but more can be found:
http://atesit.phys.uniroma1.it/pdf/L89,207901.pdf

As for the correctness of the original English, I see no particular problem with it. It could be that the author did not feel comfortable using ¥"between¥" because there are more than two parameters involved, even though each of the relationships refer to the relationship between two of these parameters. The same question was posted on the English monolingual KudoZ forum, and one reply talks about this.

In my opinion, it doesn¥'t matter whether the original should be between or among, as long as you understand what the situation is and translate it correctly, according to the meaning, not word by word.

Now, back to the quotes on Pearson¥'s:

¥"Pearson¥'s correlation coefficient, r

Correlation is a technique for investigating the relationship between two quantitative, continuous variables, for example, age and blood pressure. Pearson¥'s correlation coefficient (r) is a measure of the strength of the association between the two variables.¥"
http://hsc.uwe.ac.uk/dataanalysis/quant_pear_coeff.htm

¥"Pearson¥'s Correlation Coefficient
Brian T. Luke, Ph.D.
LearningFromTheWeb.net

Pearson¥'s product-moment correlation coefficient, r, or simply the sample correlation coefficient, is a measure of extent to which two samples are linearly related. For example, if two samples X1 and X2 contain five measurements and X1={1,2,3,4,5} and X2={2,4,6,8,10}, there is a perfect linear relationship between them since X2 is just two times X1. In this case, r=1.0. If, on the other hand, X1={1,2,3,4,5} and X2={10,8,6,4,2}, there is a negative correlation between the samples and r=-1.0. ¥"
http://members.aol.com/btluke/pearson.html

Pearson¥'s Correlation Coefficient

The correlation coefficient r (also called Pearson¥'s product moment correlation) is calculated by ...
Assumptions:
* linear relationship between x and y
* continuous random variables
* both variables must be normally distributed
* x and y must be independent of each other
http://www.vias.org/tmdatanaleng/cc_corr_coeff.html

The next one has a good explanation, also about the 0.05 value that is in the context:
http://www.medcalc.be/manual/mpage06-03a.php

¥"Karl Pearson¥'s Correlation Coefficient

This formula was created for calculating a measure of linear association between pairs of values (x, y) that are ranked or unranked.

Karl Pearson, (1857-1936), was a British statistician. His coeffient, just like Spearmen¥'s, indicates the direction (+ or -) and strength (near 1 or -1 versus near 0) of the association between the two variables.¥"

http://www.msad54.k12.me.us/MSAD54Pages/skow/MathDept/CPMP/M...








--------------------------------------------------
Note added at 13 hrs 38 mins (2004-08-29 02:57:08 GMT)
--------------------------------------------------

Oh, last thing:
Read this carefully:
¥"The relationships among the parameters were examined by Pearson’s correlation coefficients.¥" Pay attention to the last ¥"S¥". It is in plural!
The text is talking about several Pearson¥'s correlation coefficients - that means it is NOT a single value describing the relationship among several variables simultenously.


--------------------------------------------------
Note added at 13 hrs 48 mins (2004-08-29 03:07:04 GMT)
--------------------------------------------------

Sorry for the long posting.
The reason is that there was another answer arguing that the Pearson¥'s correlation coefficient measured (with a single value) the relationship among several (more than two) parameters at the same time, as a group, not in pairs.
Since I posted my disagreement with his statement, he removed his posting.

--------------------------------------------------
Note added at 2 days 6 hrs 20 mins (2004-08-30 19:38:48 GMT)
--------------------------------------------------

To Hamo:
This is a quote from the message you posted on the English KudoZ, where your link was pointing. (Just becasue you say I stated something that is not true.)
Hamo wrote: ¥"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.¥"

It says ¥"single value¥", ¥"two or more variables¥", ¥"several variables simultaneously¥", ¥"not as pairs, but as a group¥".

I posted my long discussion about coefficients, coeff. matrices, etc. to clarify and support my point that Pearson¥'s correlation is calculated using two (and not more) variables at the same time. (As opposed to your argument.)

Later on, you added more notes, where you discussed the pairwise nature of the coefficients, which is correct. The only problem is that it is contradicting your very first statement. If by now you agree, that the text is talking about studying the variables in pairs, then we are on the same platform, and there is nothing to argue about.

I think the other readers are getting tired of this by now, so this is my last posting on the topic. At least nobody has to suffer through my poorly argued discussions anymore...
;-)


Katalin Horváth McClure
United States
Local time: 11:00
Specializes in field
Native speaker of: Native in HungarianHungarian
PRO pts in category: 8
Grading comment
Thank you very much.

Peer comments on this answer (and responses from the answerer)
agree  Nobuo Kawamura: I am impressed by Katalin's analytical mind and logical presentation.
1 hr
  -> Thank you. I had several years of training in mathematics - I am glad if I can use it to help out.
agree  snowbees: Katalin's in-depth comment is laudable.
4 hrs
  -> Thank you.
agree  Minoru Kuwahara: we'd request more context, while the first 'between' relates to "parameters on the two probe placements", which apparently indicates the PAIR Katalin-san points out. they'd be sets of group of parameters to be examined. -
6 hrs
  -> Yes, I assume there are more than two parameters at each placement. The calculations are done using PAIRS (several pairs) of these parameters.
agree  Maynard Hogg: Even when there are three or more objects, "between" creeps in when there is some "pairwise" connotations--between two probes, between two coefficients, among the coefficients. B.Sc. (Math Honours) 1970
8 hrs
  -> Thank you.
agree  Kurt Hammond: As always, great observations. It sounds logical that there are in whole several pairs of coefficients, hence the usage of "among".
11 hrs
  -> Thank you.
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20 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5
テクストが平気です。


Explanation:
簡単で理解しやすい説明は下記のリンクにご参照ください。

--------------------------------------------------
Note added at 2 days 1 hr 22 mins (2004-08-30 14:41:14 GMT)
--------------------------------------------------

Note to Katalin: The following statement ¥"The reason is that there was another answer arguing that the Pearson¥'s correlation coefficient measured (with a single value) the relationship among several (more than two) parameters at the same time, as a group, not in pairs¥" is simply untrue. Either you misunderstood what I wrote, or you are trying to make your own poorly argued discussion look better than it is, by discrediting mine. The reason I squelched my previous message was because the links were not working properly. It had nothing to do with what either you or I had written.


--------------------------------------------------
Note added at 2 days 10 hrs 25 mins (2004-08-30 23:43:54 GMT)
--------------------------------------------------

Further note to Katalin: By definition a correlation coefficient is the correlation between TWO variables. Please refer to my discussion in the link provided on this page. There you will find both my original and final take on the matter. The text should not be altered.

There is nothing misunderstandable in what the author has written, as you originally claimed, and your discussion is both misleading and erroneous. Although you admit to the possibillty of two or more variables, you insist that the correlation measured is between the same variables of two different probes. I have clearly demonstrated why this approach is wrong in my example of the baked cake. Moreovoer, you have failed to distinguish clearly the difference between a correlation coefficient and a cross-corrleation coefficient. Your entire discussion centers around a definition of what a correlation coefficient is -- not a clear understanding of statistics, the experiment, or the text. I find your internecene warfare both petty and dilutive.

--------------------------------------------------
Note added at 2 days 11 hrs 14 mins (2004-08-31 00:32:35 GMT)
--------------------------------------------------

Upon rereading your entry on the English-English bulletin board I note that you did finally distinguish clearly between a simple correlation coefficient and a cross-correlation coefficient. So, I apologize for my mistatement above in this regard. I make no apology for the rest, however. Certainly I hope that through your own muddled discussion you have somehow made it clear to yourself what a correlation coefficient is. Simply I feel sorry for the asker, who has been made to suffer throughout your confusion.


    Reference: http://www.proz.com/kudoz/796987
Roddy Stegemann
United States
Local time: 08:00
Native speaker of: Native in EnglishEnglish

Peer comments on this answer (and responses from the answerer)
neutral  Katalin Horváth McClure: I like your correlation coefficient matrix example over there - hmm - where did I see that before??? Hint: Look at mine, scroll up on your screen.....
17 hrs
  -> I have no idea, but if you are looking for another I suggest that you begin your search with the prhase "cross-correlation coefficent" as your key phrase. Why you would want to find another I have no idea, however. Was mine not clear enough? // No need.
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