2018
DOI: 10.2134/agronj2017.10.0580
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Letters in Mean Comparisons: What They Do and Don’t Mean

Abstract: Letter displays are often used to report results of all pairwise comparisons among treatment means in comparative experiments. In captions to tables and charts using such letter displays, it is crucial to explain properly what the letters mean. In this paper I explain what the letters mean and how this meaning can be succinctly conveyed in a single sentence without ambiguity. This is contrasted to counterexamples commonly found in publications.

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Cited by 65 publications
(32 citation statements)
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“…The BLUPs for the untested locations are the predictions obtained from the observed locations, and these values are reported to growers. However, these BLUPs do not equal Table 10 The letter representation of all-pairwise differences by the insert-and-absorb algorithm (Piepho 2004) *Means not sharing any letter are significantly different at the 5% level of significance with Bonferroni adjustment (Piepho, 2018) the yield that the growers will get in practice. Furthermore, the standard errors of the predictions based on the observed locations cannot be applied to the grower's fields since the trials hardly ever coincide with these.…”
Section: Discussionmentioning
confidence: 99%
“…The BLUPs for the untested locations are the predictions obtained from the observed locations, and these values are reported to growers. However, these BLUPs do not equal Table 10 The letter representation of all-pairwise differences by the insert-and-absorb algorithm (Piepho 2004) *Means not sharing any letter are significantly different at the 5% level of significance with Bonferroni adjustment (Piepho, 2018) the yield that the growers will get in practice. Furthermore, the standard errors of the predictions based on the observed locations cannot be applied to the grower's fields since the trials hardly ever coincide with these.…”
Section: Discussionmentioning
confidence: 99%
“…Significances are illustrated in the figures by * ( p < 0.05), ** ( p < 0.01) or *** ( p < 0,001), for a paired Student’s t -test ( Figure 1 ). To indicate all significant differences between the different data sets as calculated by one-way ANOVA ( p < 0.05), we chose the letters A–D (for a detailed explanation, see [ 49 ]). Significantly different datasets do not share the same letters ( Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6 ).…”
Section: Methodsmentioning
confidence: 99%
“…All data analyses were conducted via the SAS 9.1.3 software package (SAS Institute, 2005). To avoid any misunderstanding regarding the LSD test, we followed the suggestions in Piepho (2018).…”
Section: Discussionmentioning
confidence: 99%