Multiple-Range Test

Comparisons between data sets (r test, multiple range test, F test, simple ANOVA),... 

Question 3. Which of the m groups is significantly different from the rest Do the multiple-range test (Section 1.5.4) to find sets of means that are indistinguishable among themselves it may occur that a given mean belongs to more than one such set of similar means. 

A setting that turns up quite often is the following A series of m batches of a given product have been produced, and a certain parameter, such as the content of a particular compound, was measured n, times for each batch. The largest and the smallest means, x iean,max resp. Xmean.min. appear to differ significantly. Which of the two is aberrant A simple /-test cannot answer this question. The multiple-range test combines several /-tests into one simultaneous test. ... 

Table 4.2. Confirmed Hypotheses (MRT Multiple Range Test)...

The multiple range test was used to decide which means could be grouped together. First, the means were sorted and all possible differences were printed, as in Table 4.9. 

The six data sets do not differ in variance (Bartlett test) or in means (ANOVA), so there is no way to group them using the multiple range test. This being so, the data were pooled for compounds A and B, yielding the two columns at right (data in CU-Assay2.dat). 

Multiple Range Test) yields a triangular matrix of differences Axmean.y... 

QRED-TBL.dat Table 1.7 Reduced critical -values (division of -values for p = 0.05 by the appropriate Student s f-factor and SQR(2)), as used with the multiple range test in MULTI. 

Harter, H. L., Critical Values for Duncan s New Multiple Range Test, Biometrics, December 1960, 671-685. 

Difference significant at p<0.05 by ANOVA and Duncan s multiple range test. 

Means followed by the same letter are not different according to Duncan s Multiple Range Test. 

The dry weights (104 C, 48 hr) of ten plants from each treatment group were taken at the termination of each experiment in order to compare growth effects with plant water status. Dry weight data were analyzed using analysis of variance (ANOVA) and Duncan s multiple-range test. Diffusive resistance and water potential were evaluated using the t-test. Each of these and subsequent experiments was replicated. 

Note Values in a row not followed by the same letter are significantly different, P<0.05, ANOVA and Duncan s multiple-range test. Kochia data adapted with permission from Einhelliq and Schon (29), Copyright 1982, the National Research Council of Canada. 

Values are the means of 15 plants harvested 7 days after treatment. Means In each column followed by the same letter are not significantly different at the 5% level of probability using Duncan s Multiple Range test. 

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