# Question regarding Pearson correlation and r-squared

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## Question regarding Pearson correlation and r-squared

 I am trying to find out why there is no information regarding the computation of r-squared once you've obtained your pearson r coefficient. It appears to me if I have found a significant correlation between two variables, the next logical question is which one weighs more or has greater strength in the reltaionship. Am I asking the wrong question? Does it stop at significance?   Also, the student I am working with is producing very creative ways to report her findings. I have found (but am not sure which to advise) many ways of reporting correlation coefficients that are significant. For example, she has a .562 coefficient with a significance p <.01. She is looking at the coefficient as low because of it's actual value rather than the statistical significance. The literature shows anything above .7 or .8 to be statistically significant. So, how do I explain to her that this .561 is also significant even though it's below the recommended level?   I apologize if this is remedial, I think I am just mixing thngs up and need help with clarification.   Thank you in advance.                         Sharon D. Voirin, RhD   Survey Design Services   Carbondale, IL 62903   618-559-2507   "Our lives begin to end the day we become silent about things that matter." The Reverend Martin Luther King
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## Re: Question regarding Pearson correlation and r-squared

 The closer the absolute value of r is to 1 the stronger the association between the two variables: you need not square r to determine that. r=.562 is not really "low"; if anything it would indicate a substantial linear association between the two variables. Finally, you can have r=.1 that is significant, if your sample size is large enough. In other words, "statistical significance" (i.e. the correlation between the two variables is unlikely to be due to chance) and "strength" of the correlation are two difference issues. Dominic Lusinchi Statistician Far West Research Statistical Consulting San Francisco, California 415-664-3032 www.farwestresearch.com -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Sharon Sent: Friday, October 13, 2006 9:11 AM To: [hidden email] Subject: Question regarding Pearson correlation and r-squared I am trying to find out why there is no information regarding the computation of r-squared once you've obtained your pearson r coefficient. It appears to me if I have found a significant correlation between two variables, the next logical question is which one weighs more or has greater strength in the reltaionship. Am I asking the wrong question? Does it stop at significance?   Also, the student I am working with is producing very creative ways to report her findings. I have found (but am not sure which to advise) many ways of reporting correlation coefficients that are significant. For example, she has a .562 coefficient with a significance p <.01. She is looking at the coefficient as low because of it's actual value rather than the statistical significance. The literature shows anything above .7 or .8 to be statistically significant. So, how do I explain to her that this .561 is also significant even though it's below the recommended level?   I apologize if this is remedial, I think I am just mixing thngs up and need help with clarification.   Thank you in advance.                         Sharon D. Voirin, RhD   Survey Design Services   Carbondale, IL 62903   618-559-2507   "Our lives begin to end the day we become silent about things that matter." The Reverend Martin Luther King
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## Re: Question regarding Pearson correlation and r-squared

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## Re: Question regarding Pearson correlation and r-squared

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## Re: Question regarding Pearson correlation and r-squared

 In reply to this post by Sharon-10 sharon-- as many responders have mentioned, when interpreting correlations it is important to differentiate between "practical" or "meaningful" and "statistical" significance. it is also important to heed the results of previously-conducted research. while your student's result of r = 0.562 is "statistically" significant, it can be seen to be lower than the results reported in the literature. you can interpret this quite simply to say that there is a positive, moderate, significant relationship between the two variables, however, the strength of this relationship is less than that reported by previous research. the computed correlation isn't necessarily low, only when compared to previous values. at this point, the question is subjective - what does it mean in the context of the current study to have a statistically significant correlation that is lower than previously reported values? did the other studies have larger/smaller sample sizes? was my sample size adequate? is there a floor or ceiling effect in my data which might deflate my correlation? best of luck, --matthew ............................................. matthew m. gushta, m.ed. research associate american institutes for research [hidden email] -- 202.403.5079 -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Sharon Sent: Friday, October 13, 2006 12:11 PM To: [hidden email] Subject: Question regarding Pearson correlation and r-squared I am trying to find out why there is no information regarding the computation of r-squared once you've obtained your pearson r coefficient. It appears to me if I have found a significant correlation between two variables, the next logical question is which one weighs more or has greater strength in the reltaionship. Am I asking the wrong question? Does it stop at significance?   Also, the student I am working with is producing very creative ways to report her findings. I have found (but am not sure which to advise) many ways of reporting correlation coefficients that are significant. For example, she has a .562 coefficient with a significance p <.01. She is looking at the coefficient as low because of it's actual value rather than the statistical significance. The literature shows anything above .7 or .8 to be statistically significant. So, how do I explain to her that this .561 is also significant even though it's below the recommended level?   I apologize if this is remedial, I think I am just mixing thngs up and need help with clarification.   Thank you in advance.                         Sharon D. Voirin, RhD   Survey Design Services   Carbondale, IL 62903   618-559-2507   "Our lives begin to end the day we become silent about things that matter." The Reverend Martin Luther King
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