# [R] correlation and causality examples

Jean lobry lobry at biomserv.univ-lyon1.fr
Sat Nov 15 15:49:29 CET 2003

```Dear All,

I'am looking for examples showing that correlation does not imply
causality, the targeted audience consists of undergraduate students
(their first year at the university but in the BioMathStat track).
All practicals are under R.

I was able to extract this from R datasets:

### begin
data(sunspots)
data(lynx)
spots <- window(sunspots, freq = 1, start = 1880, end = 1900)
lnx <- window(lynx, start = 1880, end = 1900)
ratio <- max(lnx)/max(spots)
par(mai = rep(1, 4))
plot(lnx, main = "Sun spots intensity\nand lynx population density",
t = "b", ylab = "")
lines(ratio*spots, col = "red", t = "b")
axis(side = 4, col = "red", col.axis = "red", at = ratio*pretty(spots),
lab = pretty(spots))
legend(1887, 4500, col = c("red", "black"), c("spots", "lynx"), pch = 21)
### end

Shouldn't I try to publish this in Nature or Science with a title
that goes "Solar activity increase libido in lynx populations" ?
Note the nice shift between the two curves corresponding to the
gestation time!

A brief look at the whole dataset demonstates that this is
definitively wrong:

### begin
spots <- window(sunspots, freq = 1, start = 1821, end = 1934)
ratio <- max(lynx)/max(spots)
plot(lynx, main = "Sun spots intensity\nand lynx population density",
ylab = "")
lines(ratio*spots, col = "red")
axis(side = 4, col = "red", col.axis = "red", at = ratio*pretty(spots),
lab = pretty(spots))
legend(1870, 6000, col = c("red", "black"), c("spots", "lynx"), lty = 1)
### end

So, I'am looking for similar examples, any hint would be greatly
appreciated. Basically, I'am looking for correlations between
completely deconnected phenomena so that the overinterpreted
causality relationships look stupid at first glance (and the more

BTW, does someone know where to find the data of this example
of a high correlation between beer drinking in the US and children
mortality in japan (or something like that, I'm unsure, I have
googled around with these keywords but found nothing) ?

All the best, and many thanks to the whole R team for providing
us such a nice tool.

Jean
--
Jean R. Lobry            (lobry at biomserv.univ-lyon1.fr)
Laboratoire BBE-CNRS-UMR-5558, Univ. C. Bernard - LYON I,
43 Bd 11/11/1918, F-69622 VILLEURBANNE CEDEX, FRANCE
allo  : +33 472 43 12 87     fax    : +33 472 43 13 88
http://pbil.univ-lyon1.fr/members/lobry/

```