I don’t know what constitutes the popular use of correlation, but the (1980) Steele and Torrie quote is more of an opinion or view than a definition – I’m not saying it’s wrong, but the mathematical definitions of correlation are less subjective or mushy.
Anyway, based on the responses to the quote I threw out there, I am guessing that none of the critics have actually read the book I recommended (from which the “correlation implies causation” quote was taken – my apologies for quoting it out of context – I assumed ecologists were familiar with some literature surrounding path analysis) and probably haven’t read another work that I enthusiastically recommend - Sewell Wright’s “Correlation and Causation,” which is available for free as a PDF if you search for it. I will not defend the quote myself, I’ll just recommend those published works, which certainly take into account all of the comments that it elicited and elegantly explore the questions about correlation and causation. Of course it is easy to criticize poorly procured correlations and it is a ton of fun to come up with spurious correlations that were calculated for the sole purpose of showing that unrelated variables can be correlated. But, like it or not, research in Ecology and Evolutionary Biology has long depended on good correlational data, and it seems like a fair idea to pay attention to great thinkers like Sewell Wright when they come up with methods for testing causal hypotheses using correlational data (i.e. path analysis). I definitely agree that experiments are awesome (read the first sentence of Sewell Wright’s Correlation and Causation, he agrees too). I adore well-designed, relevant experiments, and I don’t know anybody who would argue that experiments are not one of the best ways to (try to) test for causal relationships. However, causality is really a slippery concept – experiments can also fail to appropriately test causality, as discussed in the broad literature on this topic. Furthermore, experiments are only one of our many tools as ecologists, and I have seen countless irrelevant, horribly conceived ecological experiments where the investigators appear to have never made a useful observation in the field, nor considered interesting correlations in the systems they study, nor actually measured a useful variable in a real ecosystem. Yes, correlational data have been abused frequently and some investigators unwittingly assume proximal causal relationships from field data or from inappropriately applied regressions. But it is troubling when ecologists refuse to acknowledge that you can test causal hypotheses using approaches such as structural equation modeling (or they simply dismiss such approaches as elaborate models), or when they feel that an experiment proves some proximal causal relationship between two variables (i.e. they ignore latent variables or causal webs). Arguments about which approach is better or more legitimate are not very helpful, when in fact the best scientists start with their question and attempt to utilize all available tools for generating and testing good hypotheses related to that question. Those tools include analytical models, simulation models, lab experiments, field experiments, mensurative experiments, observational data, and statistical models. If you want to know the answer to questions such as what causes higher diversity in the tropics (a latitudinal correlation noted many years ago by Darwin, Wallace, and others, who generated some nice causal hypotheses about the relationship), I would recommend using all of these tools to test your favorite causal hypotheses – and make sure that a heavy dose of observational data are included. ******************************************************* Lee Dyer Biology Dept. 0314 UNR 1664 N Virginia St Reno, NV 89557 OR 585 Robin St Reno, NV 89509 Email: [email protected] Web: www.caterpillars.org phone: 504-220-9391 (cell) 775-784-1360 (office) > Date: Wed, 10 Oct 2012 16:11:49 +0000 > From: [email protected] > Subject: Re: [ECOLOG-L] correlation v. causation > To: [email protected] > > Seems relevant at this time to remind ourselves of the statistical meaning > of correlation vs its popular use and perhaps more importantly why Ecology > and Evolutionary Biology became and continue to be experimental sciences > whenever possible. > > >From the classic stats text Steele and Torrie (1980 p 277). > > "Correlation measures a co-relation, a joint property of two variables. > Where variables are jointly affected because of external influences, > correlation may offer the most logical approach to that analysis of the > data. Regression deals primarily with the means of one variable and how > their location changes with another variable. Š. Correlation is > associated with descriptive techniques: regression has to do with a > relation between population means and the values of a concomitant > variable. Thus, whereas a correlation coefficient tells us something abut > a joint relationship between variables, a regression coefficient tells us > that if we alter the value of the independent variable then we can expect > the dependent variable to alter by a certain amount on the average, > sampling variation making it unlikely that precisely the stated amount of > change will be observed." > > Thus, in Tom's example the correlation between churches and drunks implies > not that either drives variation in the other, but simply that they > covary, which may be a result of simple coincidence or that the are both > responding to a common external driver. So, when most lay people talk > about correlation, especially in looking for causal drivers, they are > really implying regression and have a priori chosen one variable as the > putative independent variable. Both approaches may IMPLY causation, > regression by one of a pair of variables and correlation by some external > driver affecting both variables, but neither can establish causation. > > Only well-designed experiments actually establish causation. These may > identify causal factors phenomenologically (without necessarily > identifying mechanism) or mechanistically, but either way are the only > method for definitively establishing causal relationships. When used as > the ultimate analysis (rather than for hypothesis generation) The > elaborate and increasing sophisticated statistical methods of regression > and elaborate models are quite simply a substitute for situations where > experiments are infeasible. Good to never lose sight of that. > > > William J. Resetarits, Jr > Professor > Department of Biological Sciences > Texas Tech University > Lubbock, Texas 79409-3131 > Phone: (806) 742-2710, ext.300 > Fax (806) 742-2963 > > > > > On 10/9/12 8:01 PM, "Thomas J. Givnish" <[email protected]> wrote: > > >The number of drunks per city is very strongly correlated with the number > >of churches per city. > > > >On 10/09/12, Lee Dyer wrote: > >> My favorite *introduction* to this vast topic can be found in the first > >>few chapters of Bill Shipley's short book, Cause and Correlation in > >>Biology (2000). A quote from his book: > >> "In fact, with few exceptions, correlation does imply > >> causation. If we observe a systematic relationship between two > >>variables, and > >> we have ruled out the likelihood that this is simply due to a random > >>coincidence, then something > >> must be causing this relationship." > >> > >> ******************************************************* > >> Lee Dyer > >> Biology Dept. 0314 > >> UNR 1664 N Virginia St > >> Reno, NV 89557 > >> > >> > >> > >> OR > >> > >> > >> > >> 585 Robin St > >> Reno, NV 89509 > >> > >> > >> > >> Email: [email protected] > >> Web: www.caterpillars.org > >> phone: 504-220-9391 (cell) > >> 775-784-1360 (office) > >> > >> > >> > >> > >> > Date: Tue, 9 Oct 2012 10:57:34 -0500 > >> > From: [email protected] > >> > Subject: Re: [ECOLOG-L] correlation v. causation > >> > To: [email protected] > >> > > >> > Hi Shelley, others, > >> > > >> > Slate recently had a great article on correlation and causation with a > >> > historical perspective. > >> > > >> > My favorite line: "'No, correlation does not imply causation, but it > >> > sure as hell provides a hint." > >> > > >> > > >>http://www.slate.com/articles/health_and_science/science/2012/10/correlat > >>ion_does_not_imply_causation_how_the_internet_fell_in_love_with_a_stats_c > >>lass_clich_.html > >> > > >> > > >> > > >> > > >> > > >> > > >> > > >> > "Having nothing better to do, I set fire to the prairie." > >> > -- Francis Chadron, 1839, Fort Clark, North Dakota > >> > > >> > http://www.devanmcgranahan.info > > > >-- > > Thomas J. Givnish > > Henry Allan Gleason Professor of Botany > > University of Wisconsin > > > > [email protected] > > http://botany.wisc.edu/givnish/Givnish/Welcome.html
