Ten native Chinese-speaking children and adolescents who immigrated to the United States between ages 5 and 16 were studied for 3 years. The changes in their language preferences, language environments, and proficiency in English, their second language (L2), as well as Chinese, their first language (L1), were measured quantitatively and qualitatively. Participants with arrival ages of 9 or younger switched their language preference from L1 to L2 within the first year, were exposed to a significantly richer L2 than L1 environment, and became more proficient in L2 than in L1. The older participants maintained their preference for L1 across the 3 years, were exposed to a significantly richer L1 than L2 environment, and maintained L1 as the more proficient language. Interactions among L1 proficiency, peer interactions, social abilities, and cultural preferences jointly influenced the dominant language switch or maintenance processes.

This study examined the variables related to US immigrants' long-term attainment in English, their second language (L2), and their native language (L1). For 44 Mandarin-English bilinguals, with increasing age of arrival (AOA) in the United States, their accuracy in L2 grammaticality judgment tasks decreased and accuracy in an L1 grammaticality judgment task increased. Moreover, both AOA in the United States and mothers' English proficiency uniquely predicted a significant proportion of the variance for bilinguals' L2 proficiency. Finally, as a group, 72 speakers of three Asian languages showed lower levels of L2 proficiency and stronger AOA effects on the task performance than 32 speakers of six European languages. These differences in language proficiency were associated with differences in language use, language learning motivation, and cultural identification between the two groups. These findings suggest that L2 acquisition in the immigration setting is a complicated process involving the dynamic interactions of multiple variables. Most immigrants face the task of learning the language of their host country as a second language (L2). Understanding the factors influencing the speed at which they acquire their L2 and the level of L2 proficiency they obtain carries both practical and theoretical significance. One major factor that has been the focus of research is the impact of age of arrival (AOA) in the L2-speaking country on L2 acquisition. Although adults typically have been found to be faster than younger children in the initial stage of learning (e.g., Olson & Sam- 2002 Cambridge University Press 0142-7164/02 $9.50

Patterns of word-by-word reading times differ for subjects who must later recall a sentence and subjects who must simply comprehend it. The data suggest that these two retrieval tasks induce different perceptual coding strategies. The recall subjects have slower reading times and smaller practice effects than the comprehension subjects. Their reading times reflect the syntactic structure of, the sentence, with prolonged pauses at phrase boundaries and bowed reading-time curves within phrases. The data for comprehension subjects, on the other hand, reflect the semantic content. Prolonged reading times occur at important content words, reading times decrease as contextual redundancy increases, and more coding time is used at the ends of causal than noncausal sentences. Hence, the performance data are determined by both the linguistic structure of the stimulus and the cognitive demands of the task.Recent psycholinguistic research deals with "the psychological reality of grammar" (Aaronson, 1974(Aaronson, , 1976. Much of this research concerns the psychological correlates of structure specified by linguistic theories. For example, theoretical questions arise, such as: Is the unit of speech perception the syllable, the word, or the phrase ? Is speech perception determined by the deep or the surface structure? The recent literature reveals conflicting evidence in such attempts to infer the nature of linguistic competence. Our current research attempts to illustrate at least one reason for these conflicts. Conflicts may arise because different experimental tasks are used in order to index the subject's underlying linguistic abilities.

Oner's (1971) computing expressions for nonparametric indices of sensitivity and bias are briefly reviewed, and shown to be incorrect when performance is below chance levels. Modifications of Grier's expressions, for cases when false alarms exceed hits, are presented, Pollack and Norman (1964) suggested general procedures for developing a nonparametric index of sensitivity, A', for recognition and detection experiments in which only a single data point is obtained in the unit square probability space representing hits and false alarms. Later Hodos (1970) suggested a nonparametric index of response bias, B", also based on the geometry of the square probability space. Finally, Grier (1971) derived explicit functional expressions for computing both of these indices. Grier's formulas have been widely used during the past 15 years, and have proved to be useful when the normal-distribution assumptions underlying traditional signal detection procedures fail, or when the assumptions are not testable.The application of Grier's (1971) formulas to detection data from individual subjects, some of whom perform below chance, can yield bizarre numbers. Some values of A', which should represent the area under an "averaged" ROC curve, can be negative rather than positive, and they can also be greater than 1.0 in absolute value. Further, values of B" for points to the left of the equal-bias diagonal can be negative rather than positive as they should be. The magnitudes of such erroneous A' and B" values can be large even when performance is only slightly below the chance diagonal. Discussions with colleagues suggested that some were unaware of the below-chance problem with Grier's formulas, and had reported values of A' and B* averaged over groups, without examining the individual subjects' data. If only a few subjects in a subset of conditions perform even slightly below chance, the averages would be distorted, but in ways that the researcher might not notice. Thus, we felt that it would be useful to provide a brief note on modifications of Grier's formulas that are appropriate for below-chance performance. Grier's FormulasSensitivity index. First, let us briefly review Grier's (1971) computing expressions. In Figure 1 -left, let y denote the proba-

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