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Material and Methods: the Materials and methods section should include full details of the statistical techniques used and authors are advised to refer to the article "Guidance for the use and presentation of statistics" in Weed Research (1988) 28, 139-144. This guide is to be updated shortly.   Preference is given to the presentation of standard errors of differences between means with appropriate degrees of freedom, rather than least significant differences in tables. Standard errors, etc., should be given to one more decimal place than the means to which they apply. Please do not use multiple range tests.

[ Last edited by ljq2008 on 2009-10-11 at 10:22 ]
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Duncan's new multiple range test
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In statistics, Duncan's new multiple range test (MRT) is a multiple comparison procedure developed by David B. Duncan in 1955. Duncan's MRT belongs to the general class of multiple comparison procedures that use the studentized range statistic qr to compare sets of means.

Duncan's new multiple range test (MRT) is a variant of the Student¨CNewman¨CKeuls method that uses increasing alpha levels to calculate the critical values in each step of the Newman¨CKeuls procedure. Duncan's MRT attempts to control family wise error rate (FWE) at ¦Áew = 1 − (1 − ¦Ápc)k−1 when comparing k, where k is the number of groups. This results in higher FWE than unmodified Newman¨CKeuls procedure which has FWE of ¦Áew = 1 − (1 − ¦Ápc)k/2.

David B. Duncan developed this test as a modification of the Student¨CNewman¨CKeuls method that would have greater power. Duncan's MRT is especially protective against false negative (Type II) error at the expense of having a greater risk of making false positive (Type I) errors. Duncan's test is commonly used in agronomy and other agricultural research.

Duncan's test has been criticised as being too liberal by many statisticians including Henry Scheff¨¦, and John W. Tukey. Duncan argued that a more liberal procedure was appropriate because in real world practice the global null hypothesis H0= "All means are equal" is often false and thus traditional statisticians overprotect a probably false null hypothesis against type I errors. Duncan later developed the Duncan¨CWaller test which is based on Bayesian principles. It uses the obtained value of F to estimate the prior probability of the null hypothesis being true.

The main criticisms raised against Duncan's procedure are:

    * Duncan's MRT does not control family wise error rate at the nominal alpha level, a problem it inherits from Student¨CNewman¨CKeuls method.
    * The increased power of Duncan's MRT over Newman¨CKeuls comes from intentionally raising the alpha levels (Type I error rate) in each step of the Newman¨CKeuls procedure and not from any real improvement on the SNK method.

[ Last edited by jhuiuc on 2009-10-11 at 06:52 ]
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