Resent-Date: Sun, 4 May 1997 04:33:35 +1000
Resent-From: anzstat-error@melia.qut.edu.au
Date: Sat, 03 May 1997 09:51:52 +0800
From: lloyd@hkustasc.hku.hk
Subject: Re: Correlation - storks and babies
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I have just had a consulting project that is very relevent.
A Professor of Medicine came to me some with measurements
(x1,x2,age) on 23 babies. He had found a significant
correlation between x1 and x2, and had a paper accepted
by the Journal of Gerontology on the amazing discovery
of this correlation.

Luckily a dissenting referee had pointed out that the
correlation was likely spurious because both x1 and x2
tend to increase with age. No doubt x1 and x2 are also
highly correlated with penis length of the baby (at least
for the males!).

However, the editor had accepted the paper and only asked
that the correlation coefficients should also be computed
separately for young, medium and older babies and these
packed into an appendix. Even if these were not at all
significant there was no suggestion that the paper be
rejected.

Below are the data. Find a significant association if you
can! The list might like to ponder the following questions.

(1) What should we do about journals that accept papers 
    with wrong statistics?
(2) How widespread is the publication of papers with
    wrong statistics?
(3) How can we find out how widespread it is? Should say
    the Biometrics Society fund people to scrutinise sundry
    journals for statistical validity?
(4) What should a consultant do when faced with a wrongly
    accepted paper like this? In my case I agreed to perform
    an adhoc analysis suggested by the dissenting referee,
    so long as my name did not appear on the paper. This
    analysis showed no association.

 x1       x2  age in months
0.729	280.1    3
0.785	402.2    3
0.625	351.4    3
0.604	315.5    3
0.701	306.0    3
0.957	315.0    3
0.664	220.2    3
0.640	223.6   12
0.464	214.3   12
0.684	224.5   12
0.517	256.0   12
0.581	285.4   12 
0.814	215.1   12
0.636	231.0   12
1.051	269.6   12
0.410	222.5   24
0.701	221.1   24
0.650	208.9   24
0.234	170.1   24
0.674	254.5   24 
0.545	263.9   24
0.429	249.1   24
0.358	210.8   24

Spurious correlation of x1 and x2 is 0.45, spurious P=0.031. Notice
that there are only 3 distinct ages. You guessed it! 3 months means
0-6, 12 months means 6-18 and 24 means 18-30. Thus even the three
separate correlations probably contain a large spurious element.

C.J.Lloyd