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<br />768 STS\TISTICAL $ICNIF[CA~CE TES'i'1\G • ~Olrnson
<br />to scientific understanding (Quinn and Dunham
<br />I9S3). This concept is related to Popperian in-
<br />ference, which seeks to develop and test hy-
<br />potheses that. can cleazly be falsified (Popper
<br />1959), because a falsified hypothesis provides
<br />greater advance in understanding than does a
<br />hypothesis that is supported. Also similar is
<br />Platt's (1960 notion of strong inference, .which
<br />emphasizes developing alternative hypotheses
<br />that lead to different predictions. In such a case,
<br />results inconsistent- with predictions from a hy-
<br />pothesis cast doubt of its validity:
<br />Examples of scientific hypotheses, which
<br />were considered credible, include Copernicus'
<br />notion H.j: the Earth revolves around the sun,
<br />verstls the conventional wisdom of the time, Ht,:
<br />the sun revolves around the Earth. Another ex-
<br />ample is Fermat's last theorem, which states
<br />that for integers n, X, 1; and Z, X" + 2'" = Z"
<br />implies n <_ 2. Alternatively, a 'physicist may
<br />Inake specific predictions about a parameter
<br />based on a theory-. and the theon• is proyision-
<br />alh- accepted onh• if the outcomes are within
<br />measurement error of the predicted value, and
<br />na other theories make predictions that also fall
<br />within that ran_e l ~Iulaik et al. 1997). Contrast
<br />these hypotheses. w~hie~iJrtsol`'e phenomena in
<br />nahrre, with the statistical hypotliese"s presented
<br />iu Thy Jortntal of ~4'ilttlife ~fanaovntent, which
<br />.sere mentioned above, and which invol-e prop-
<br />erties of populations.
<br />R~(r_ctiou of a statistical hypothesis would con-
<br />~stitutc apiece of ryicleuce to he considered its
<br />decidim_ whether ur not to reject a scientific hy-
<br />pothesis c,SintherlafC 1990). Fur example, a sci-
<br />entific hypothesis nti.~,ht it:tte that clutch sizes of
<br />bircLs incrratie yyith the :r`e o[~ the bird. up to
<br />some plateau. That idea w~orild ~,enerate a hy-
<br />patltesis that could hr tested statistically within
<br />a particul:u• pc,pnlatiun of birds. A single such
<br />test. re~,ardless of its P-y;tlue, would little afFect
<br />the,credibiiih al~ the scientific hypothesis. which
<br />is far more ~,eneral.:\ related distiuctiott is that
<br />scientific ltyputltesrs are «luhal. icpphiug to all oC
<br />nuhtre, while statistical hypotheses are l~cah ap-
<br />plin~ to particular ststents (Sirnherloff 1990).
<br />ll'hy do use ailcllite ecologists r;trel• test sci-
<br />entific hypotheses' My view is that we are de:tl-
<br />iu~ with systems more complex than those faced
<br />by physicists. ,-~ casing iu eculo~~ is that even•-
<br />thing is connected to everything else. (In psy-
<br />chah~~, "eyenthing correlates with eve)ything,"
<br />~Jiyin4~ rise to w•hut David Lykl:en caIled the
<br />"curd factor'' fi)r such ambient correlation noise
<br />J. bVildl. i~[mtage. 63(3):1999
<br />[)Vleehl 1997]). This saying implies that all vari-
<br />ables in an ecological system are intercorrelated,
<br />and that any null hypothesis postulating no effect
<br />of a variable on another will in fact be false; a
<br />statistical test of that hypothesis will be rejected,
<br />as long as the sample is sufficiently, la be. This
<br />line of reasoning does not denigrate the value of
<br />experimentation in real systems; ecologists
<br />should seek situations in which variables thought
<br />to be influential can be manipulated and the re-
<br />sults carefully monitored (linderwood 1997).
<br />Too often, however, experimentation in natural
<br />systems is very difficult if not impossible.
<br />REPLICATION
<br />Replication is a cornerstone of science. If re-
<br />sults from a study cannot be reproduced, they
<br />have no credibility. Scale is important here.
<br />Conducting the same study at the same time
<br />but •at. several different sites and vetting com-
<br />parable-results is reassuring, but not nearly so
<br />convincing as haying different investigators
<br />achieve similar results using different methods
<br />in different areal at different times. R. A. Fish-
<br />er's idea of solid knowledge was not a single
<br />extremel\• significant result but rather the abil-
<br />ih~ of repeatedly getting results significant at 59c
<br />lTukey 1969). Sharer (1993:011 absen-ed that
<br />'~T!te question of interest is yyhether un effect
<br />size of a ma_nittule jud~ecl to he important h:>s
<br />been consistently ohtaiued across ~~alicl replica-
<br />tion`. \l'hether arty ar all of the results are sta-
<br />tistiaill~ significant is irrelevant." Replicutecl re-
<br />sults :urtanrtticalh snake statistical sr~~nthe:uu•e
<br />testing, !utnecessan ~. Barternleind 19FiS).
<br />lndiyidu:tl sttulies rarely cunt;un sufficient in-
<br />tinnuttiun to support a final conclusion about the
<br />tntth ur yaine of a hypothesis iSclunidt :utd
<br />f-Iunter 1971. Studies di(l~er in design, measure-
<br />ment devices. samples included, yyNather concli-
<br />tions. and many other ways. TFtis vaRabihh'
<br />an~on~_ shtdies is more penasiye in ec•olusical sit-
<br />natians than iu, (or esautple, the phvsic:tl scieno-
<br />es ! I;llisun 19961. Ta have ,eneralih~, results
<br />should be consistent under a wide varieh~ of cir-
<br />cumstances. V1eta-analysis provides same tools
<br />for combining iuforntation from repeated sh)dies
<br />(e.g.. Hedges and Olkzn 19S~i and cart reduce
<br />clependeuce on si;rtificartce testier} by examining
<br />replicated studies (Schmidt and Hunter 199 ~ ).
<br />v[eta-analysis can be dangerously misleading,
<br />however, if nonsi~mificant results or results that
<br />did not canfortn to the conventional wisdom
<br />were less likely to have been published.
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