Re: [tips] Spurious Correlations
Thanks! I am just introducing correlational methods...good timing! G.L. (Gary) Peterson,Ph.D Psychology@SVSU On Oct 9, 2014, at 9:23 PM, Carol DeVolder devoldercar...@gmail.com wrote: Perhaps others are familiar with this site, but I wasn't. It's a fun collection of spurious correlations. Good for examples in class. http://tylervigen.com/ Carol -- Carol DeVolder, Ph.D. Professor of Psychology St. Ambrose University 518 West Locust Street Davenport, Iowa 52803 563-333-6482 --- You are currently subscribed to tips as: peter...@svsu.edu. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13445.e3edca0f6e68bfb76eaf26a8eb6dd94bn=Tl=tipso=39053 (It may be necessary to cut and paste the above URL if the line is broken) or send a blank email to leave-39053-13445.e3edca0f6e68bfb76eaf26a8eb6dd...@fsulist.frostburg.edu --- You are currently subscribed to tips as: arch...@mail-archive.com. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5n=Tl=tipso=39059 or send a blank email to leave-39059-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
Re: [tips] Spurious Correlations
And just a reminder, you can find examples of confusing correlation and causation here http://jfmueller.faculty.noctrl.edu/100/correlation_or_causation.htm Jon === Jon Mueller Professor of Psychology North Central College 30 N. Brainard St. Naperville, IL 60540 voice: (630)-637-5329 fax: (630)-637-5121 jfmuel...@noctrl.edu http://jonathan.mueller.faculty.noctrl.edu Gerald Peterson peter...@svsu.edu 10/10/2014 7:28 AM Thanks! I am just introducing correlational methods...good timing! G.L. (Gary) Peterson,Ph.D Psychology@SVSU On Oct 9, 2014, at 9:23 PM, Carol DeVolder devoldercar...@gmail.com wrote: Perhaps others are familiar with this site, but I wasn't. It's a fun collection of spurious correlations. Good for examples in class. http://tylervigen.com/ Carol -- Carol DeVolder, Ph.D. Professor of Psychology St. Ambrose University 518 West Locust Street Davenport, Iowa 52803 563-333-6482 --- You are currently subscribed to tips as: peter...@svsu.edu. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13445.e3edca0f6e68bfb76eaf26a8eb6dd94bn=Tl=tipso=39053 (It may be necessary to cut and paste the above URL if the line is broken) or send a blank email to leave-39053-13445.e3edca0f6e68bfb76eaf26a8eb6dd...@fsulist.frostburg.edu --- You are currently subscribed to tips as: jfmuel...@noctrl.edu. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13269.01f6211e00cc8f00a7b68e8e24b1b4d6n=Tl=tipso=39059 (It may be necessary to cut and paste the above URL if the line is broken) or send a blank email to leave-39059-13269.01f6211e00cc8f00a7b68e8e24b1b...@fsulist.frostburg.edu --- You are currently subscribed to tips as: arch...@mail-archive.com. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5n=Tl=tipso=39060 or send a blank email to leave-39060-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
re: [tips] Spurious Correlations
On Thu, 09 Oct 2014 18:23:19 -0700, Carol DeVolder wrote: Perhaps others are familiar with this site, but I wasn't. It's a fun collection of spurious correlations. Good for examples in class. http://tylervigen.com/ For people interested in such things, I suggest one take a look at some of Brian Haig's writing on spurious correlations which provides a more nuanced perspective on them (one can classify spurious correlation between those that are truly spurious versus those that are not). Here's the reference for one of his articles: Haig, B. D. (2003). What is a spurious correlation?. Understanding Statistics: Statistical Issues in Psychology, Education, and the Social Sciences, 2(2), 125-132. http://www.tandfonline.com/doi/abs/10.1207/S15328031US0202_03#preview: or http://psycnet.apa.org/psycinfo/2004-12710-003 A key point is whether a correlation represents a direct effect or relationship (which is typically assumed in a correlational analysis) or an indirect effect or relationship exists between two or more variables. If we have three variables X, Y, and Z, and (1) there is no direct relationship between X and Z but (2) there is an indirect relationship X - Z - Y This raises thorny questions of mediation and moderation which I will leave to Karl Wuensch to elaborate (or to provide access to his notes on the these topics ;-). Haig would probably call the correlations provided on the Tyler Vigen website nonsense correlations but, for fans of the belief of everything is connected to everything else, one might refer to the butterfly effect. The butterfly effect refers to two conceptually unrelated events (apparently nonsensical) but which are connected by a complex nonlinear relationship. Simple correlational analysis that (a) do not have the necessary intermediate variables, and/or (b) do not have the necessary nonlinear terms, will not accurately represent the relationship or, more correctly, the process that connects two variables. Just something to think about. ;-) -Mike Palij New York University m...@nyu.edu --- You are currently subscribed to tips as: arch...@mail-archive.com. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5n=Tl=tipso=39061 or send a blank email to leave-39061-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
RE: [tips] Spurious Correlations
One thing I have found helpful in teaching the concept of spurious correlations is to have students populate a number of columns in a spreadsheet with random numbers and then calculate correlations between all the columns of random numbers. Since they are random, the correlation in the population from which all of these samples are drawn is 0. For every 100 correlations calculated in this circumstance, using a .05 alpha level, students will find about five spurious correlations that are statistically significant but are clearly spurious (mind blown) :) Rick Dr. Rick Froman Professor of Psychology Box 3519 John Brown University 2000 W. University Siloam Springs, AR 72761 rfro...@jbu.edumailto:rfro...@jbu.edu (479) 524-7295 http://bit.ly/DrFroman The LORD detests both Type I and Type II errors. Proverbs 17:15http://www.biblegateway.com/passage/?search=proverbs%2017:15version=NIV -Original Message- From: Mike Palij [mailto:m...@nyu.edu] Sent: Friday, October 10, 2014 8:17 AM To: Teaching in the Psychological Sciences (TIPS) Cc: Michael Palij Subject: re: [tips] Spurious Correlations On Thu, 09 Oct 2014 18:23:19 -0700, Carol DeVolder wrote: Perhaps others are familiar with this site, but I wasn't. It's a fun collection of spurious correlations. Good for examples in class. http://tylervigen.com/ For people interested in such things, I suggest one take a look at some of Brian Haig's writing on spurious correlations which provides a more nuanced perspective on them (one can classify spurious correlation between those that are truly spurious versus those that are not). Here's the reference for one of his articles: Haig, B. D. (2003). What is a spurious correlation?. Understanding Statistics: Statistical Issues in Psychology, Education, and the Social Sciences, 2(2), 125-132. http://www.tandfonline.com/doi/abs/10.1207/S15328031US0202_03#preview: or http://psycnet.apa.org/psycinfo/2004-12710-003 A key point is whether a correlation represents a direct effect or relationship (which is typically assumed in a correlational analysis) or an indirect effect or relationship exists between two or more variables. If we have three variables X, Y, and Z, and (1) there is no direct relationship between X and Z but (2) there is an indirect relationship X - Z - Y This raises thorny questions of mediation and moderation which I will leave to Karl Wuensch to elaborate (or to provide access to his notes on the these topics ;-). Haig would probably call the correlations provided on the Tyler Vigen website nonsense correlations but, for fans of the belief of everything is connected to everything else, one might refer to the butterfly effect. The butterfly effect refers to two conceptually unrelated events (apparently nonsensical) but which are connected by a complex nonlinear relationship. Simple correlational analysis that (a) do not have the necessary intermediate variables, and/or (b) do not have the necessary nonlinear terms, will not accurately represent the relationship or, more correctly, the process that connects two variables. Just something to think about. ;-) -Mike Palij New York University m...@nyu.edumailto:m...@nyu.edu --- You are currently subscribed to tips as: rfro...@jbu.edumailto:rfro...@jbu.edu. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13039.37a56d458b5e856d05bcfb3322db5f8an=Tl=tipso=39061 or send a blank email to leave-39061-13039.37a56d458b5e856d05bcfb3322db5...@fsulist.frostburg.edumailto:leave-39061-13039.37a56d458b5e856d05bcfb3322db5...@fsulist.frostburg.edu --- You are currently subscribed to tips as: arch...@mail-archive.com. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5n=Tl=tipso=39063 or send a blank email to leave-39063-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
RE: [tips] Spurious Correlations
On Fri, 10 Oct 2014 06:41:38 -0700, Rick Froman wrote: One thing I have found helpful in teaching the concept of spurious correlations is to have students populate a number of columns in a spreadsheet with random numbers and then calculate correlations between all the columns of random numbers. Since they are random, the correlation in the population from which all of these samples are drawn is 0. For every 100 correlations calculated in this circumstance, using a .05 alpha level, students will find about five spurious correlations that are statistically significant but are clearly spurious (mind blown) :) I like this but it works primarily as a mathematical exercise. The real issue is how to translate what one learns from such exercises to real life research situations where one is calculating correlations between variables. Unless one knows the real-life situation/phenomenon really well one won't know when a statistically significant correlation is real or a Type I error. A minor point: technically the example you provide above is not an example of a spurious correlation, rather, it is an example of making Type I errors. Consider the following distinctions, partly based on Haig's writing (ref below) (1) Nonsense Correlations: we have two variables X and Y and they are correlated X -- Y but there is no reasonable or plausible explanation for why such a correlation exist. Haig uses the example of the high positive correlation between human birth rate and the number of storks in Great Britain during period of time (see Haig p127). Haig notes that Kendall Buckland (1982) in their dictionary of statistical terms defines such a result an illusory correlation. The correlation appears to be real, possibly due to a butterfly effect (see below) but is not easily explainable. (2) Traditional Spurious Correlations: we have three variables X, Y, and Z and X and Y are not correlated at all but both are dependent upon Z or X -- Z -- Y. One example I use is If you look take all of the cities in the U.S. with population over 100,000 and make Y = number of crimes committed and X = number of churches in each city, you will probably find a positive correlation between number of crimes and number of churches. The simple mined solution to eliminating this relationship would be get rid of the churches (Just Say No!) and crime should disappear. However, smaller cities should have both fewer crimes and churches and larger cities should have both more crimes and churches. But this is probably due to population size: control or partial out the relationship of population size to the number of crimes and churches and you'll probably find that the correlation disappears. If it doesn't, then consider closing the churches. ;-) (3) Haig's Spurious Correlations: We have three variables X, Y, and Z and X is related to Y but is mediated by Z, that is, X -- Z --- Y. This is an indirect correlation (in contrast to a direct correlation X --- Y which is not dependent upon a third variable) and is of interest in its own right. Indeed, mediation and moderation analysis is a popular method analysis especially in for correlational and quasi-experimental designs. So, spurious correlations can be tricky things especially when dealing with correlations from uncontrolled situations and/or one has limited knowledge of the phenomenon being studied. -Mike Palij New York University m...@nyu.edu -Original Message- On Friday, October 10, 2014 8:17 AM, Mike Palij wrote: On Thu, 09 Oct 2014 18:23:19 -0700, Carol DeVolder wrote: Perhaps others are familiar with this site, but I wasn't. It's a fun collection of spurious correlations. Good for examples in class. http://tylervigen.com/ For people interested in such things, I suggest one take a look at some of Brian Haig's writing on spurious correlations which provides a more nuanced perspective on them (one can classify spurious correlation between those that are truly spurious versus those that are not). Here's the reference for one of his articles: Haig, B. D. (2003). What is a spurious correlation?. Understanding Statistics: Statistical Issues in Psychology, Education, and the Social Sciences, 2(2), 125-132. http://www.tandfonline.com/doi/abs/10.1207/S15328031US0202_03#preview: or http://psycnet.apa.org/psycinfo/2004-12710-003 A key point is whether a correlation represents a direct effect or relationship (which is typically assumed in a correlational analysis) or an indirect effect or relationship exists between two or more variables. If we have three variables X, Y, and Z, and (1) there is no direct relationship between X and Z but (2) there is an indirect relationship X - Z - Y This raises thorny questions of mediation and moderation which I will leave to Karl Wuensch to elaborate (or to provide access to his notes on the these topics ;-). Haig would probably call the correlations provided on the Tyler Vigen website nonsense correlations but, for
RE: [tips] Spurious Correlations
Hi A lot of the discussion of how to interpret correlations involves the presence of a simple correlation, as in the spurious correlation examples. It is equally important to emphasize to students that the absence of correlation is subject to all the same concerns. That is, absence of correlation does not imply absence of relationship between X and Y because of all the same mechanisms. For example, Z might be positively related to X and negatively related to Y, masking a direct positive association between X and Y. Take care Jim Jim Clark Professor Chair of Psychology 204-786-9757 4L41A -Original Message- From: Mike Palij [mailto:m...@nyu.edu] Sent: Friday, October 10, 2014 10:10 AM To: Teaching in the Psychological Sciences (TIPS) Cc: Michael Palij Subject: RE: [tips] Spurious Correlations On Fri, 10 Oct 2014 06:41:38 -0700, Rick Froman wrote: One thing I have found helpful in teaching the concept of spurious correlations is to have students populate a number of columns in a spreadsheet with random numbers and then calculate correlations between all the columns of random numbers. Since they are random, the correlation in the population from which all of these samples are drawn is 0. For every 100 correlations calculated in this circumstance, using a .05 alpha level, students will find about five spurious correlations that are statistically significant but are clearly spurious (mind blown) :) I like this but it works primarily as a mathematical exercise. The real issue is how to translate what one learns from such exercises to real life research situations where one is calculating correlations between variables. Unless one knows the real-life situation/phenomenon really well one won't know when a statistically significant correlation is real or a Type I error. A minor point: technically the example you provide above is not an example of a spurious correlation, rather, it is an example of making Type I errors. Consider the following distinctions, partly based on Haig's writing (ref below) (1) Nonsense Correlations: we have two variables X and Y and they are correlated X -- Y but there is no reasonable or plausible explanation for why such a correlation exist. Haig uses the example of the high positive correlation between human birth rate and the number of storks in Great Britain during period of time (see Haig p127). Haig notes that Kendall Buckland (1982) in their dictionary of statistical terms defines such a result an illusory correlation. The correlation appears to be real, possibly due to a butterfly effect (see below) but is not easily explainable. (2) Traditional Spurious Correlations: we have three variables X, Y, and Z and X and Y are not correlated at all but both are dependent upon Z or X -- Z -- Y. One example I use is If you look take all of the cities in the U.S. with population over 100,000 and make Y = number of crimes committed and X = number of churches in each city, you will probably find a positive correlation between number of crimes and number of churches. The simple mined solution to eliminating this relationship would be get rid of the churches (Just Say No!) and crime should disappear. However, smaller cities should have both fewer crimes and churches and larger cities should have both more crimes and churches. But this is probably due to population size: control or partial out the relationship of population size to the number of crimes and churches and you'll probably find that the correlation disappears. If it doesn't, then consider closing the churches. ;-) (3) Haig's Spurious Correlations: We have three variables X, Y, and Z and X is related to Y but is mediated by Z, that is, X -- Z --- Y. This is an indirect correlation (in contrast to a direct correlation X --- Y which is not dependent upon a third variable) and is of interest in its own right. Indeed, mediation and moderation analysis is a popular method analysis especially in for correlational and quasi-experimental designs. So, spurious correlations can be tricky things especially when dealing with correlations from uncontrolled situations and/or one has limited knowledge of the phenomenon being studied. -Mike Palij New York University m...@nyu.edu -Original Message- On Friday, October 10, 2014 8:17 AM, Mike Palij wrote: On Thu, 09 Oct 2014 18:23:19 -0700, Carol DeVolder wrote: Perhaps others are familiar with this site, but I wasn't. It's a fun collection of spurious correlations. Good for examples in class. http://tylervigen.com/ For people interested in such things, I suggest one take a look at some of Brian Haig's writing on spurious correlations which provides a more nuanced perspective on them (one can classify spurious correlation between those that are truly spurious versus those that are not). Here's the reference for one of his articles: Haig, B. D. (2003). What is a spurious correlation?. Understanding Statistics
RE: [tips] Spurious Correlations
On Fri, 10 Oct 2014 08:20:18 -0700, Jim Clark wrote: Hi A lot of the discussion of how to interpret correlations involves the presence of a simple correlation, as in the spurious correlation examples. It is equally important to emphasize to students that the absence of correlation is subject to all the same concerns. That is, absence of correlation does not imply absence of relationship between X and Y because of all the same mechanisms. For example, Z might be positively related to X and negatively related to Y, masking a direct positive association between X and Y. I admit to not completely understanding everything that is said above. A few points: (1) In the simplest case, a correlation may not be statistically significant for two reasons: (a) The null hypothesis (population rho = 0) is true or (b) There is insufficient power to achieve significance in the sample. (2) The first idea that popped into my mind when I read the example above was Jim is talking about suppression effects but it did not quite sound right to me. I went over to David Howell's website to look at his stat notes on suppression but could not find a situation described by Jim; see: https://www.uvm.edu/~dhowell/gradstat/psych341/lectures/MultipleRegression/multreg3.html Howell describes three suppression situations (which he borrows from Cohen Cohen; I don't have the latest edition handy to check): Since this is in the context of multiple regression, allow me to restate the variables Y (criterion), X1, and X2 (predictors). These are the situations (about half way down the webpage) (a) Classical suppression: r(Y, X1) is significant but r(Y, X2) is not. r(X1,X2) is significant which means that including it in a regression of Y on X1 and X2 will provide the best model because the variance in X1 that is related to X2 but not Y, will provide a stronger effect because what was error variance in X1 is now removed because it is recognized as systematic variance between X1 and X2. Howell provides an example. (b) Net suppression: all r's are positive, that is r(Y,X1), r(Y,X2), and r(X1,X2). As in (a) above, r(X1,X2) reduces the error variance in X1 but now the error variance in Y is also reduced by partialing out the variance due to r(Y,X2), assuming that the correlation of interest is r(Y,X1). One problem with this is that the Ballantine or Venn-Euler diagrams are misleading if there is variance that is common to Y, X1, and X2 (i.e., the intersection of Y, X1, and X2 in set theory terms). I believe Darlington goes into more detail about this in his textbook on regression. (c) Cooperative suppression: the situation most similar to Jim's example above is cooperative suppression where r(X1,X2) 0.00, that is. there is a negative correlation.between X1 and X2. There is no situation where X1 or X2 is negative related to Y. Perhaps Jim is referring to something other than suppression? Summarizing Howell on suppression effects from his website: |To paraphrase Cohen and Cohen (1983), if Xi has a (near) |zero correlation with Y, we are talking about possible classical |suppression. If its bi is opposite in sign to its correlation with Y, |we are looking at net suppression. And if its bi exceeds rYi |and is of the same sign, we are looking at cooperative suppression. NOTE: Post #3 for me today. -Mike Palij New York University m...@nyu.edu --- You are currently subscribed to tips as: arch...@mail-archive.com. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5n=Tl=tipso=39069 or send a blank email to leave-39069-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
RE: [tips] Spurious Correlations
Yes, X might have a zero correlation with Y despite being causally related to Y. One way this can happen is when there is no direct effect but two indirect effects, one indirect effect being positive, the other negative, and their magnitudes being similar. Alternatively, with only one mediator, the direct effect of X on Y and the indirect effect of X through M on Y might be of similar magnitudes but opposite signs. And yes, this can also be conceived as suppression. See http://core.ecu.edu/psyc/wuenschk/SimData/XD-Mediate.htm . For more on suppressor effects, see http://core.ecu.edu/psyc/wuenschk/MV/multReg/Suppress.docx (with thanks to Jake Cohen). Cheers, Karl L. Wuensch -Original Message- From: Mike Palij [mailto:m...@nyu.edu] Sent: Friday, October 10, 2014 12:48 PM To: Teaching in the Psychological Sciences (TIPS) Cc: Michael Palij Subject: RE: [tips] Spurious Correlations On Fri, 10 Oct 2014 08:20:18 -0700, Jim Clark wrote: Hi A lot of the discussion of how to interpret correlations involves the presence of a simple correlation, as in the spurious correlation examples. It is equally important to emphasize to students that the absence of correlation is subject to all the same concerns. That is, absence of correlation does not imply absence of relationship between X and Y because of all the same mechanisms. For example, Z might be positively related to X and negatively related to Y, masking a direct positive association between X and Y. I admit to not completely understanding everything that is said above. A few points: (1) In the simplest case, a correlation may not be statistically significant for two reasons: (a) The null hypothesis (population rho = 0) is true or (b) There is insufficient power to achieve significance in the sample. (2) The first idea that popped into my mind when I read the example above was Jim is talking about suppression effects but it did not quite sound right to me. I went over to David Howell's website to look at his stat notes on suppression but could not find a situation described by Jim; see: https://www.uvm.edu/~dhowell/gradstat/psych341/lectures/MultipleRegression/multreg3.html Howell describes three suppression situations (which he borrows from Cohen Cohen; I don't have the latest edition handy to check): Since this is in the context of multiple regression, allow me to restate the variables Y (criterion), X1, and X2 (predictors). These are the situations (about half way down the webpage) (a) Classical suppression: r(Y, X1) is significant but r(Y, X2) is not. r(X1,X2) is significant which means that including it in a regression of Y on X1 and X2 will provide the best model because the variance in X1 that is related to X2 but not Y, will provide a stronger effect because what was error variance in X1 is now removed because it is recognized as systematic variance between X1 and X2. Howell provides an example. (b) Net suppression: all r's are positive, that is r(Y,X1), r(Y,X2), and r(X1,X2). As in (a) above, r(X1,X2) reduces the error variance in X1 but now the error variance in Y is also reduced by partialing out the variance due to r(Y,X2), assuming that the correlation of interest is r(Y,X1). One problem with this is that the Ballantine or Venn-Euler diagrams are misleading if there is variance that is common to Y, X1, and X2 (i.e., the intersection of Y, X1, and X2 in set theory terms). I believe Darlington goes into more detail about this in his textbook on regression. (c) Cooperative suppression: the situation most similar to Jim's example above is cooperative suppression where r(X1,X2) 0.00, that is. there is a negative correlation.between X1 and X2. There is no situation where X1 or X2 is negative related to Y. Perhaps Jim is referring to something other than suppression? Summarizing Howell on suppression effects from his website: |To paraphrase Cohen and Cohen (1983), if Xi has a (near) zero |correlation with Y, we are talking about possible classical |suppression. If its bi is opposite in sign to its correlation with Y, |we are looking at net suppression. And if its bi exceeds rYi and is of |the same sign, we are looking at cooperative suppression. NOTE: Post #3 for me today. -Mike Palij New York University m...@nyu.edu --- You are currently subscribed to tips as: wuens...@ecu.edu. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13060.c78b93d4d09ef6235e9d494b3534420en=Tl=tipso=39069 or send a blank email to leave-39069-13060.c78b93d4d09ef6235e9d494b35344...@fsulist.frostburg.edu --- You are currently subscribed to tips as: arch...@mail-archive.com. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5n=Tl=tipso=39071 or send a blank email to leave-39071-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
RE: [tips] Spurious Correlations
Hi Here's one example of what I have in mind. A few decades ago I came across a newspaper heading Want to get good grades? Don't study! It was based on a survey of high school students finding no significant correlation between amount of studying and grades. The research literature shows that there is a negative correlation between intelligence and study time, which tends to dampen (suppress, mask) the simple rs between each predictor and grades. The negative correlation makes sense, since brighter students don't need to study as much to learn the material. Multiple regression reveals the strong, positive association between each predictor and grades. Thinking about the formula for a regression coefficient in a two predictor equation shows that all kinds of changes can happen, with predictors having significant simple rs becoming non-significant or reversing sign, and predictors having non-significant simple rs becoming significant in either direction. Here's the critical part of the formula ry1 - ry2 * r12 Depending on the sign and magnitude of the rs, a lot can happen, including the effect I referred to as a non-significant r being due to some masking or suppression by other variable(s). Here's a small SPSS simulation that illustrates the effect. SET SEED = 27395137. INPUT PROGRAM. LOOP SUBJ = 1 TO 16. COMP #z1 = RV.NORMAL(0,1). COMP #z2 = RV.NORMAL(0,1). END CASE. END LOOP. END FILE. END INPUT PROGRAM. COMP abil = RND(100 + 15*#z1). COMP stdy = RND( 20 + 5*(#z1*-.5 + #z2*SQRT(1-.5**2))). COMP grde = RND(65+10*(#z1*.4+#z2*.4 + RV.NORMAL(0,1)*SQRT(1-.68**2))). LIST. REGRE /DESCR /DEP = grde /ENTER abil /ENTER stdy. The regression shows abil by itself is not significant (model 1), whereas it becomes significant when stdy is entered (model 2). Happy Canadian Thanksgiving to all. Take care Jim Jim Clark Professor Chair of Psychology 204-786-9757 4L41A -Original Message- From: Wuensch, Karl L [mailto:wuens...@ecu.edu] Sent: Friday, October 10, 2014 12:04 PM To: Teaching in the Psychological Sciences (TIPS) Subject: RE: [tips] Spurious Correlations Yes, X might have a zero correlation with Y despite being causally related to Y. One way this can happen is when there is no direct effect but two indirect effects, one indirect effect being positive, the other negative, and their magnitudes being similar. Alternatively, with only one mediator, the direct effect of X on Y and the indirect effect of X through M on Y might be of similar magnitudes but opposite signs. And yes, this can also be conceived as suppression. See http://core.ecu.edu/psyc/wuenschk/SimData/XD-Mediate.htm . For more on suppressor effects, see http://core.ecu.edu/psyc/wuenschk/MV/multReg/Suppress.docx (with thanks to Jake Cohen). Cheers, Karl L. Wuensch -Original Message- From: Mike Palij [mailto:m...@nyu.edu] Sent: Friday, October 10, 2014 12:48 PM To: Teaching in the Psychological Sciences (TIPS) Cc: Michael Palij Subject: RE: [tips] Spurious Correlations On Fri, 10 Oct 2014 08:20:18 -0700, Jim Clark wrote: Hi A lot of the discussion of how to interpret correlations involves the presence of a simple correlation, as in the spurious correlation examples. It is equally important to emphasize to students that the absence of correlation is subject to all the same concerns. That is, absence of correlation does not imply absence of relationship between X and Y because of all the same mechanisms. For example, Z might be positively related to X and negatively related to Y, masking a direct positive association between X and Y. I admit to not completely understanding everything that is said above. A few points: (1) In the simplest case, a correlation may not be statistically significant for two reasons: (a) The null hypothesis (population rho = 0) is true or (b) There is insufficient power to achieve significance in the sample. (2) The first idea that popped into my mind when I read the example above was Jim is talking about suppression effects but it did not quite sound right to me. I went over to David Howell's website to look at his stat notes on suppression but could not find a situation described by Jim; see: https://www.uvm.edu/~dhowell/gradstat/psych341/lectures/MultipleRegression/multreg3.html Howell describes three suppression situations (which he borrows from Cohen Cohen; I don't have the latest edition handy to check): Since this is in the context of multiple regression, allow me to restate the variables Y (criterion), X1, and X2 (predictors). These are the situations (about half way down the webpage) (a) Classical suppression: r(Y, X1) is significant but r(Y, X2) is not. r(X1,X2) is significant which means that including it in a regression of Y on X1 and X2 will provide the best model because the variance in X1 that is related to X2 but not Y, will provide a stronger effect because what was error variance in X1 is now
[tips] Spurious Correlations
Perhaps others are familiar with this site, but I wasn't. It's a fun collection of spurious correlations. Good for examples in class. http://tylervigen.com/ Carol -- Carol DeVolder, Ph.D. Professor of Psychology St. Ambrose University 518 West Locust Street Davenport, Iowa 52803 563-333-6482 --- You are currently subscribed to tips as: arch...@mail-archive.com. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5n=Tl=tipso=39053 or send a blank email to leave-39053-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
Re: [tips] Spurious Correlations
wonderful...thank you! Nancy Melucci LBCC -Original Message- From: Carol DeVolder devoldercar...@gmail.com To: Teaching in the Psychological Sciences (TIPS) tips@fsulist.frostburg.edu Sent: Thu, Oct 9, 2014 6:23 pm Subject: [tips] Spurious Correlations Perhaps others are familiar with this site, but I wasn't. It's a fun collection of spurious correlations. Good for examples in class. http://tylervigen.com/ Carol -- Carol DeVolder, Ph.D. Professor of Psychology St. Ambrose University 518 West Locust Street Davenport, Iowa 52803 563-333-6482 --- You are currently subscribed to tips as: drna...@aol.com. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=12993.aba36cc3760e0b1c6a655f019a68b878n=Tl=tipso=39053 (It may be necessary to cut and paste the above URL if the line is broken) or send a blank email to leave-39053-12993.aba36cc3760e0b1c6a655f019a68b...@fsulist.frostburg.edu --- You are currently subscribed to tips as: arch...@mail-archive.com. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5n=Tl=tipso=39054 or send a blank email to leave-39054-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
