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For PhD programs in educational sciences/studies, which is a better writing sample? A critical position paper which applies a theory to other researchers' published data and comes up with an alternative interpretation as well as suggestions for how future researchers could test this alternative view or a quantitative study using structural equation modeling (SEM) on data that I have collected myself, which is proposing and testing new links among variables?

The position paper, I believe, is very critical but does not have its own data and analysis. The SEM paper, on the other hand, is a full empirical paper that fills a gap in the literature and is also critical but maybe not as critical as the former.

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If your critical position paper would be considered controversial by anyone (anyone!) it might be a mistake to use that. You don't want to be upsetting people you don't know, but have some influence over your future, at this point.

A research paper is more pertinent to the evaluation of a doctoral application.

But, it may be that one of them is much more "readable" and accessible and even better written than the other. If there are no red flags for the position paper, then either should if they are otherwise of equal writing quality.

The purpose of the sample is to evaluate your language ability primarily and your ability to express ideas. Keep that in mind.

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