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Checking the rather comprehensive but somewhat dated 2008 review of Evans on dual-process theories, I didn't see anything about [mis]spelling.

But it seems to me an obvious thing to investigate from a dual-process perspective, because (in theory) the more elaborate rules you have to apply the more mistakes you're likely to make under time pressure.

So has anything like this been attempted?

Note that this is a little more sophisticated than simply asking if writing (never mind typing) faster results in more errors. You'd have to discern what's the likely cause of the errors, i.e. under time pressure, do you make more errors of the kind that require more complex "graphotactic" rules?

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Well, it turns out there is some related research, but there are complications because spelling & writing is harder to investigate (compared to syllogisms, for instance)...

Spelling relies on two sets of processes, depending on word frequency (for a review, see Tainturier and Rapp, 2001; Bonin, 2003). For frequent words, the letter sequence is directly retrieved from the orthographic lexicon via the lexical route. For rare or unknown words, the letter sequence is arrived at indirectly, through a process of phoneme–grapheme conversion (assembled route). The resulting orthographic representation is stored in a graphemic buffer (Caramazza et al., 1987; Hillis and Caramazza, 1989) until its graphomotor execution (i.e., initiation and implementation of motor programs and neuromuscular execution). Although the orthographic representation obviously needs to be retrieved or calculated prior to execution (i.e., during the writing latency; Bonin et al., 2002), Delattre et al. (2006) have shown that the orthographic processing of irregular and infrequent words is still generally incomplete at this stage, and therefore, continues during the graphomotor execution, thus, increasing handwriting duration. According to the authors, these results can be interpreted within the dual-route model. When a conflict arises between the outputs of the lexical and assembled spelling routes, it takes time to resolve, and the central processing of this conflict then cascades onto the graphomotor execution.

So yes, there is a posited "dual-route" model for spelling/writing, and yes, it's based on timing experiments... although these did not involve time pressure (or counting spelling errors by type), but rather is based on timing the writing of well-known vs obscure words. Whether this "dual route" neatly matches more conventional dual-process accounts of cognitions is a bit unclear to me.

The complications come from the fact that spelling and writing form a cascading process:

Three factors seem to determine the temporal course of the central processing of spelling. The first one concerns the word’s lexical characteristics. The less frequent and/or regular the word, the longer the central processing takes and the more likely it is to be cascaded. The second factor concerns time pressure. Until now, the cascading phenomenon has only been observed for the production of successive words under time pressure (Delattre et al., 2006; Lambert et al., 2011; Maggio et al., 2012). Producing a single word without any time constraint should minimize cascading, by allowing the spelling process to be completed during the pause (i.e., latency) preceding execution. Third, according to capacity theory, the ability to cascade processing depends heavily on the writer’s development and expertise (Berninger and Swanson, 1994; Alamargot et al., 2010). Because handwriting is not yet fully automatized in younger writers, especially those still in primary school (Bourdin and Fayol, 2000; Olive et al., 2009), they have to prevent overloading by segmenting and sequentializing the higher processes and are therefore, unable to engage in parallel, or cascaded, processing (see Olive and Kellogg, 2002; Alamargot et al., 2007).

Interestingly Kahaneman was also involved in formulating capacity theory. And it seems related to models of divided attention, which he also was involved with.

Anyway, if this is correct, an interesting conclusion is that if you have produce the spelling under time pressure and in a medium that you have little experience with (say you seldom handwrite, or you seldom type) then you are more likely to make spelling errors in that medium not simply because of mechanical issues, but also because it puts a sort of cognitive/time pressure even on processes that you have trained in (spelling).

The introduction of the Delattre paper also has some more interesting observations related to the complexity of the rules, particularly with respect to the how phonemic the orthography is and some empirical support from of specific forms of dysgraphia:

The dual-route model of spelling production (e.g., Ellis, 1982) proposes that two processing systems operate in parallel: a lexical route that retrieves spellings of known words from a memory store of word-specific knowledge and a nonlexical (or assembled) route that generates spellings using a process of sublexical sound-to spelling conversion. The assembled spelling route would be efficient in languages whose orthographies have predictable or consistent orthographic-to-phonological correspondences (such as Turkish, Italian, and Japanese kana) but would be considerably less effective for English and French, whose orthographies are characterized by highly inconsistent relationships (e.g., the vowel /i:/ is spelled in many different ways in English words, as in eel, tea, theme, thief, Keith, people, me, key, quay, ski, etc.). There are many irregular and some almost arbitrarily spelled words in English (e.g., pint, yacht) and French (e.g., fraise, monsieur). The lexical route would work for all known words (irrespective of regularity) but could not provide spellings for new words or nonwords. The assembled route would work for nonwords but would often produce phonologically plausible errors (PPEs), particularly to irregular words, such as yacht (YOT) and monsieur (MESSIEU).

Evidence consistent with the dual-route model comes primarily from studies of the spelling performance of neuropsychological patients with acquired central dysgraphia (for reviews see Barry, 1994; Tainturier & Rapp, 2000). The separation of the dual routes is supported by the double dissociation between surface dysgraphia (e.g., Beauvois & De´rouesne´, 1981; Hatfield & Patterson, 1983) and phonological dysgraphia (e.g., Shallice, 1981). Surfacedysgraphic people accurately spell more regular than irregular words (for which they make many PPEs) and are interpreted as having an impaired lexical route that forces overreliance on their preserved assembled route. Phonological-dysgraphic people have a marked impairment of nonword spelling but have relatively preserved word spelling and are interpreted as having an impaired assembled route but an intact lexical route.

Although the lexical and assembled spelling routes are proposed to be separate, there are at least two lines of evidence to suggest that they interact at some level in normal spellers. First, observation of spelling errors in free writing (e.g., Ellis, 1979; Hotopf, 1980) suggests that assembled spelling plays some role in writing; people sometimes make PPEs (e.g., Ver-knickers ayfasia) and may produce different alternative spellings on different occasions (which suggests that not all errors reflect inaccurate spelling knowledge). Second, there is experimental evidence showing lexical influence on assembled spelling; there are lexical priming effects on nonword spelling (e.g., Barry & Seymour, 1988; Campbell, 1983; Perry, 2003). For example, the nonword /vi:m/ is more likely to be spelled as VEAM after hearing the word team, as VEEM after the word deem, and as VEME after the word theme.

Dual-route models of spelling have been expressed in symbolic terms (e.g., Barry, 1994) but also as more interactive (Rapp, Epstein, & Tainturier, 2002) and connectionist (Houghton & Zorzi, 2003) models. Although single-route models of spelling have been proposed (e.g., Brown & Loosemore, 1994; Bullinaria, 1997; Olson & Caramazza, 1994), Houghton and Zorzi (2003) have argued that these are currently unable to account for the full range of empirical data.

I quoted all this here because the Wikipedia article on spelling has basically zero psychology or neurology information.

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