If two variables, X & Y, are correlated with a third Z, they may be related to each other simply because they are related to the third variable. It may bo of interest to know if there is any correlation between X and Y that is NOT due to their both being correlated with Z. To do this you calculate a partial correlation.

Partial correlation is used for collect many variables in one form to access the collective behaviour of them at once

thank you very much for your valuable reply. As i have read in an article which has given the example of when two variables does not correlate then those two variables can be kept as control to find the correlation among other two random variables.

So what is the rational behind this Mr.Oday Hamadi..?

Actually, partial correlation is when you have several variables that are all correlated. Some of the information in the correlation of two of the variables is ALSO contained in the correlation between OTHER variables. For example, if you measured a person, height, arm length, leg length, weight are all correlated, and some of the correlation between arm length and leg length is also contained in height. So, the partial correlation calculates the correlation between two of the variables CONTROLLING for the correlations between the OTHER variables that are also correlated. In fact, it is often the partial correlation that should be the value of interest.

thank you for your answer James Roper. If partial correlation shows 'r' value less than bivariate correlation 'r' value what does it mean regards to control variables...?

A lower partial r than bivariate r means that much of the correlation was accounted for in the OTHER variables. For example, if you used height, weight and leg length, you would find that once you REMOVED the correlation between height and weight, leg was no longer strongly correlated with weight. That is because leg length and height are so strongly correlated, that once you removed the correlation with height and weight, nothing was left for leg length.

Also, you should not call the other variables "control" variables. They are all just variables.

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Mr.Sathiyaseelan, I don't understand. You say that your 4 variables are corelated with each other, then why do you go for a partial corelation? Also, if you consider 2 groups among the 4 as control groups, obviously the result of the remaining 2 groups is either higher or lower than the 2 control groups.

If two variables, X & Y, are correlated with a third Z, they may be related to each other simply because they are related to the third variable. It may bo of interest to know if there is any correlation between X and Y that is NOT due to their both being correlated with Z. To do this you calculate a partial correlation.

@ Mr.James Roper, as I read the article with an example of partial correlation it mentioned about the control variables also SPSS tool it takes as CONTROL variable.

@ Mr. Sai Kishore. Please read my question properly as I said having four variables correlated each other but not significantly.

@ Mr.Stephen Senn, thank you very much for your valuable answer. should not use the term CONTROL variable, is it so?

If partial correlation shows 'r' value lesser than bivariate correlation 'r' value what does it mean regards to 'control variables'...?

After searching lot in web finally I have found the article about partial correlation. Here it is the article for your kind reference.

If the partial correlation is less than the first order correlation it suggests that some of the relationship between the two variables is explicable in terms of their correlation with other variables.

Here is a system that might show some features of interest. Consider the variables body mass index (BMI), height, sex and weight. In terms of first order correlations I would expect weight to be strongly correlated with sex, height and BMI. However, once height is taken into account I would expect the correlation with sex to be much lower. Men are on average heavier than women because (amongst other things) they are taller but short men are not necessarily much heavier than short women. Once height and BMI are taken into account I would expect the correlation between height and sex to be quite low.

Thank you Mr.Stephen Senn. If partialling out two variables at a time could reduce/ increase the 'r' value. what would be the analysis results..?

I don't understand the question. The results are what they are and depend on the data you have. Do you mean, "if the partial correlation is not the same as the first order correlation what dose this mean?"

Yes, i meant if partial correlation 'r' value is lesser than first order correlation what does the role of control variables..? how we can state that in result..?

Remember, if your original correlations are low, or not significant, then there is NO need to worry about partial correlations. The question about control variables and so on is probably because now it is unclear exactly what your goal is. And, when we do not know that, our answers are more general and may not apply in your case. If you only have 4 variables, then there are a variety of ways to control your analysis so that the partial correlations are resolved. With all these explanations, exactly WHAT a partial correlation is should be clear - what may NOT be clear is what to do next.

My goal is to find correlation among four variables I have (A, B, C & D). I did bivariate correlation analysis which showed A & D not having significant correlation, so I would like to know if partialling out these (A & D) could produce any changes on B & C.

Here my doubt is shall we do partialling out any of other two variables. Hope my question is understandable.

You have 4 variables. What are the Pearson correlation coefficients between them all? If D is NOT correlated with A, they are by definition independent. But, what about B and C? If you only three correlated variables, partials might still be worth looking into. Also, remember, if these variables are correlated with other variables THAT YOU DID NOT MEASURE, the correlations may still be due to other variables, in which case, partials would be more appropriate.

I did Pearson correlation for all variables which showed non-significant correlation b/t A & D but significant correlation each other variables of A, B & D. So I can go for partialling out A & D.

Thank you very much Mr.James Roper.

You still did not explain very clearly. For 4 variables, you have A+B, A+C, A+D, B+C, B+D and C+D correlations (there are 6 possible pairs). So, WHICH of those were significant? If D is NOT significant in any, then you only need to do partials on A, B and C.

As you mentioned out of six, i have got for five except for A+D. so wanna go for partial on A, B, & C. What are variable to be chosen as control in SPSS tool..?

I think I understand. You will have to first use A, then B, then C as your controls to get all the partials. One at a time. If you used R or SAS, or JMP, you could get it to give you all the partials at once.

Hello SATHIYASEELAN GANESAN, if you go to my website and click on favourite links and then search in the electronic textbook using the search term that you are seeking information on there is a definition. Cheers, Debbie

http://sites.google.com/site/deborahhilton/

Thank you Mr.James Roper.

Dear Deborah Hilton..

I am not able to find the link what I require. Could you please give the link here regarding my query.

Is your question not solved? And if not, what remains to be understood?

Dear James thank you very much. I have got solution for my question through your explanation, I did asked in my last answer was to Deborah Hilton.

Sorry if I was wrong.

Hello Sathiyaseelan Ganesan,

http://www.statsoft.com/textbook/multiple-regression/

Unique Prediction and Partial Correlation

Note that in this equation, the regression coefficients (or B coefficients) represent the independent contributions of each independent variable to the prediction of the dependent variable. Another way to express this fact is to say that, for example, variable X1 is correlated with the Y variable, after controlling for all other independent variables. This type of correlation is also referred to as a partial correlation (this term was first used by Yule, 1907). Perhaps the following example will clarify this issue. You would probably find a significant negative correlation between hair length and height in the population (i.e., short people have longer hair). At first this may seem odd; however, if we were to add the variable Gender into the multiple regression equation, this correlation would probably disappear. This is because women, on the average, have longer hair than men; they also are shorter on the average than men. Thus, after we remove this gender difference by entering Gender into the equation, the relationship between hair length and height disappears because hair length does not make any unique contribution to the prediction of height, above and beyond what it shares in the prediction with variable Gender. Put another way, after controlling for the variable Gender, the partial correlation between hair length and height is zero.

Does the link work on your system ? Http://www.statsoft.com/textbook

Very useful links. Thank you very much Deborah Hilton.

Hi I've just tried to view some of the other videos on get stats site, but I get the following message.

Resource Limit Is Reached

The website is temporarily unable to service your request as it exceeded resource limit. Please try again later.

sorry I've put this message on the wrong question, just ignore the question above, sorry abotu that I've just started using this system. Does the link to the statsoft textbook work now ?

yeah Deborah.. its working. thank you.

Considering there is a strong relationship between climate variables, we often use the partial correlation to try to remove that correlation. I used to explore the relationship between daytime-temperature-vegetation and nighttime-temperature-vegetation based on the partial correlation, 

controlling the solar radiation and precipitation simultaneously. As all we know, there is a huge correlation especially between daytime and nighttime,which even could reach about 1 (figure 1).

  However, I encountered a weird problem beyond my knowledge. In my case,  I used two different ways to calculate the partial correlation between vegetation and climate variables. The first one is all variables participate the calculation including day-temperature, night-temperature, precipitation and solar radiation. Then we got the partial correlation coefficient

respectively (figure 2). The second is that we conducted reduced partial correlation analyses in which the dependent variables were correlated twice: once against day-temperature, precipitation and solar radiation, and once against night-temperature, precipitation and solar radiation (figure 3). The weird is the direction of the night coefficients of these two methods is almost opposite andthe night-temperature coefficient is almost contrary to daytime. However, they are nearly similar in the second method. What's more, the direction of the night-temperature is same as thesimple Pearson correlation. 

Now I am traped into these two completely opposite direction. which one is the true answer? So I wonder whether there is some pre-condition or not. For example, two strong correlated variables (r is more than 0.9) can't input into the partial correlation at the same time.

Thanks very much.