A well-written composition, among other things, makes effective use of vocabulary. This is not necessarily reflected in a rich vocabulary, but a rich vocabulary is very likely to have a positive effect on the reader (Laufer & Nation, 1995: 307). Therefore, it becomes necessary to choose appropriate methods to measure the lexical richness of writing.

1.2    Significance of this research
This paper endeavors to analyze the effects of frequency on lexical richness. According to related theories, a high repetition rate and an extensive contact of a language are the key to learning it well. Ellis once said, “Language learning is the associative learning of representations that reflect the possibilities of occurrence of form-function mappings ” (Ellis, 2002: 178), and “The knowledge underlying fluent use of language is not grammar in the sense of abstract rules or structure but a huge collection of memories of previously experienced utterances” (Ellis, 2002: 178). Plus, researchers have considered that lexical richness is only one of a variety of factors that affects the overall quality of a piece of writing (Engber, 1995; Laufer & Nation, 1995). Thus, this paper attempts to investigate whether the frequency of writing would affect the lexical richness of compositions.

2    Literature Review
2.1 Ellis’s View of Frequency Effects
“Frequency Effects in Language Processing and Acquisition”, written by Ellis in 2002, illustrated his main ideas about frequency. This article first introduced various studies on frequency in relation to psycholinguistic and cognitive linguistic theories, and then gave some examples of frequency effects in the processing of phonology, phonotactics, reading, spelling, lexis, morphosyntax, formulaic language, language comprehension, grammaticality, sentence production, and syntax (Ellis, 2002: 143). It is found that frequency is a key determinant of acquisition because “rules” of language, at all level of analysis (from phonology, through syntax, to discourse), are structural regularities that emerge from learners’ lifetime analysis of the distributional characteristics of the language input (Ellis, 2002: 178). He proposed a set of L2 acquisition theories based on frequency effects. Wen Qiufang (2003) reduced his theory into three hypotheses:

(1)    Language learning is based on exemplar.
According to Ellis (2002), learning language is a process of accumulating exemplars. These exemplars are linked, related to each other, and form a network, in which the linguistic regularities emerge as central tendencies. For language learners, to be accurate and fluent in their generalizations, they need to process sufficient exemplars.

(2)    Grammar learning is to grasp the constructions.
Ellis (2002) said that when learning some certain language, the learners should keep hold of those grammatical constructions gradually instead of the rules, and abstract the frequency-oriented linguistic regularities. “A construction is a conventional linguistic unit—that is, part of the linguistic system, accepted as a convention in the speech community, and entrenched as grammatical knowledge in the speaker’s mind (Ellis, 2002: 167).”

(3)    Frequency is the key to language acquisition.
The language representations stored in mind reflect the probabilities of occurrence of form-function mappings. Learning language is the associative learning of representations. The representational strength is determined by the power law of practice and type frequency. At all levels of analysis, the “rules” of language are structural regularities that emerge from learners’ life analysis of the distributional characteristics of the language input (Ellis, 2002: 144). Thus, frequency is a key determinant of L2 acquisition.  

2.2 Previous Research of Frequency Effects on L2 Writing 练习频次对写作词汇丰富性的影响(2):http://www.youerw.com/yingyu/lunwen_5174.html