Correlation and variablity

[Humphrey Paulie]

Dear folks,
In a corralational research with a hypothesis of "There is a positive relationship between X and Y ( X and Y both being some foreing language proficiency

variables) the researcher wants to introduce language proficiency as a moderator variable. That is, the researcher hypothesises that the correlation between

X and Y changes for different language ability groups. She wants to divide the sample into 3 homogeneous language ability groups and study the correlations

separately for each group. My apprehension is that since correlation is a highly population-dependdent statistic, the correlations get depressed as a result

of homogenization of the subjects on the variable of interest. Is it common to introduce such moderator variables in correlational stuides?
Isn't it better to have more variability in the data to get better results?
Your comments are appreciated.
Regards
Humphrey

 

[Burleson,Joseph A.]

Not sure what you mean by “highly population-dependent statistic,” or “homogenization of the subjects on the variable of interest.” Maybe you could explain that, because I do not see the relevance.

 

In answer to your question, advise not to tri-chotomize continuous measures. Instead, use partial correlation, making the language proficiency as the partialled variable. Then compare the zero-order correlation of the two foreign lang prof measures with their partialled correlation. This will inform whether the third variable plays a moderator role.

 

Joe Burleson

 

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From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Humphrey Paulie
Sent: Friday, May 01, 2009 10:37 AM
To: [hidden email]
Subject: Correlation and variablity

 

Dear folks,
In a corralational research with a hypothesis of "There is a positive relationship between X and Y ( X and Y both being some foreing language proficiency

variables) the researcher wants to introduce language proficiency as a moderator variable. That is, the researcher hypothesises that the correlation between

X and Y changes for different language ability groups. She wants to divide the sample into 3 homogeneous language ability groups and study the correlations

separately for each group. My apprehension is that since correlation is a highly population-dependdent statistic, the correlations get depressed as a result

of homogenization of the subjects on the variable of interest. Is it common to introduce such moderator variables in correlational stuides?
Isn't it better to have more variability in the data to get better results?
Your comments are appreciated.
Regards
Humphrey

 

 

[Swank, Paul R]

First of all, I would say a regression model including the moderator and the moderator interactions would be better than looking at individual correlations. However, if the moderator is based on the correlates, then the within group variability will be automatically small and I’m not sure what the benefit if such an analysis would be.

 

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Humphrey Paulie
Sent: Friday, May 01, 2009 9:37 AM
To: [hidden email]
Subject: Correlation and variablity

 

Dear folks,
In a corralational research with a hypothesis of "There is a positive relationship between X and Y ( X and Y both being some foreing language proficiency

variables) the researcher wants to introduce language proficiency as a moderator variable. That is, the researcher hypothesises that the correlation between

X and Y changes for different language ability groups. She wants to divide the sample into 3 homogeneous language ability groups and study the correlations

separately for each group. My apprehension is that since correlation is a highly population-dependdent statistic, the correlations get depressed as a result

of homogenization of the subjects on the variable of interest. Is it common to introduce such moderator variables in correlational stuides?
Isn't it better to have more variability in the data to get better results?
Your comments are appreciated.
Regards
Humphrey

 

 

[Art Kendall]

Instead of conceptualizing the covariate as groups I would leave it as continuous.

I would then start with a 3 way scatterplot and drag the handles back and forth to look at the cloud from different perspectives.
I might even try ordinary regression  and loess fits.

Then I would create the interaction term and familiarize my self with correlation of the 4 variables  (y,x, z, and x*z).
(remember to center x and z before multiplying to get the interaction term.

Then to test the H using a continuous variable I would try regression with one entry step being x.
Then I would see if Z on the next step and the the interaction term on a third step, improved the fit statistically and substantively.

If you are determined to use groups, if the the scatterplot works a lot better with loess than with linear fit, use the picture to guess a number of groups.
redo the scatter plot as a 2 way one with different symbols for the groups, fit regression lines for the groups, do they look way out of parallel?
With small numbers the lines can appear to be quite far out of parallel and still have apparent differences be due to randomness.

You could then redo the regression using groups-1 dummy variables as z and appropriate interaction terms.

Note the steps here are hierarchical steps not to be confused with stepwise approaches.

The question is is there 1) a statistical and 2) a meaningful policy, practice, or theory improvement in the fit of Y from X Z and x*z over X alone.


Art Kendall
Social Research Consultants

Humphrey Paulie wrote:

Dear folks,
In a corralational research with a hypothesis of "There is a positive relationship between X and Y ( X and Y both being some foreing language proficiency

variables) the researcher wants to introduce language proficiency as a moderator variable. That is, the researcher hypothesises that the correlation between

X and Y changes for different language ability groups. She wants to divide the sample into 3 homogeneous language ability groups and study the correlations

separately for each group. My apprehension is that since correlation is a highly population-dependdent statistic, the correlations get depressed as a result

of homogenization of the subjects on the variable of interest. Is it common to introduce such moderator variables in correlational stuides?
Isn't it better to have more variability in the data to get better results?
Your comments are appreciated.
Regards
Humphrey

 

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