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With a table showing correlations between several variables, one must choose whether to show values in only ~half the cells (and if so, then choose above or below the diagonal) or all the cells. Since correlation is a symmetric measure, the same amount of information is conveyed with both options.

Filling the whole matrix might make it easier for people to find a particular value, because they can think of either one as primary and look for it in either part of the matrix. However, filling the whole matrix might make the presentation more overwhelming to a reader ("wow, that's a lot of numbers") while the half matrix might seem more elegant.

Has there been any work done looking at which is more effective for communication?
Are there widely used style guides in certain fields that answer this question, which might provide a starting point for a field which lacks such a guide?

Related: https://academia.stackexchange.com/q/79256/36320

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    I would only include (i,j) pairs with j<i . I won't expect that potential readers (mostly researchers) have any problem in the undertanding a correlation matrix. – user1420303 Nov 2 '16 at 20:49
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    Strictly speaking, I'm not sure this is off-topic but I think it would make a lot more sense to ask over on stats.stackexchange.com – Ian_Fin Nov 3 '16 at 9:16
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    "Requirements and expectations of academicians" is explicitly on-topic here. Stats.SE is more for questions about actually doing the statistics than formatting their presentation. That's why I asked here. Also @Ian_Fin, when you think something should be migrated, you can flag to request migration instead of close. – WBT Nov 3 '16 at 12:55
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    @WBT I at least would see no obvious reason to flag this as off-topic over at Cross Validated. Indeed, they have a tag for reporting, which, as the name suggestions, is concerned with guidelines for presenting data/results. There's also likely to be a greater number of people over there with related expertise. Of course it's your choice where to ask the question. – Ian_Fin Nov 3 '16 at 13:43
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    Consider whether there is extra information that could be included in the other half of the table e.g. potentially one half could show r^2 and the other could show the p-value. – user2390246 Dec 8 '16 at 16:48
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For what it's worth, the convention in APA format is for the diagonals to be labelled with a dash and for the upper triangle to be left blank. See e.g. Table 1 in this paper.

Personally, I think that including redundant information in the upper triangle is wasteful and only serves to overwhelm the reader. A table formatted like a lower triangle is, at first glance, obviously a correlation matrix, while a fully-filled-in table could be anything. However, I'm not aware of any studies on the effectiveness of either method.

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