A Measure for Contextual Var iability and its Independent Effect on Recognition Memory

CONTEXTUAL VARIABILITY 3 A Measure for Context Var iability and its Independent Effect on Recognition Memory The rather daunting task of a college student participating in a typical study-test list-learning experiment is to remember only one of perhaps a huge number of prior experiences with a studied stimulus, usually a word. Hence, a critical issue for any theory of memory is how memories of past events are accessed given that so many are stored (cf. Maddox & Estes, 1997; Shiffrin, 1970). Many theories of memory address this issue by making a distinction between item and context information (e.g. Bower, 1972; Dennis & Humphreys, 2001; Humphreys, Bain, & Pike, 1989; Mensink & Raaijmakers, 1988; Raaijmakers & Shiffrin, 1984; Shiffrin & Steyvers, 1997): Item information represents a stimulus, and context information represents the environment in which the stimulus was encountered. For our typical college student, her task is to remember an occurrence of a word in the context of the experimental setting. Thus, context plays a critical role in our theories of memory: It allows memory access to focus on those memories that we are trying to remember. While context plays a central role in our theories of memory, it has usually not been well described (but see Brown, 200? ). In stimulus fluctuation theories of memory (Estes, 1955), context is modeled as a set of active elements that change randomly as time progresses (e.g., Bower, 1972; Mensink & Raaijmakers, 1988). While these theories have explained an impressive array of results regarding interference and forgetting, they merely state that context changes randomly over time thereby ignoring some potentially non-random patterns in context changes. In his rational analysis of memory, John CONTEXTUAL VARIABILITY 4 Anderson (1990) showed how the cognitive system might be attuned to the history of use of an item and contextual associations between items in order to predict the need for the item to available to the system. Anderson and Schooler (1991) and Schooler and Anderson (1997) have shown how to concretely define the history and context factor in their theory. They have also shown how specific predictions can be made in free and cued recall experiments based on estimates of these two factors derived from environmental analyses of large word usage databases. In this article, we will also apply an environmental analysis on word usage in a large corpus of text to define and measure a new facto: contextual variability. Some words tend to appear in relatively few different contexts, whereas other words are distributed more evenly among contexts. The contextual variability factor reflects the tendency of words to spread out over multiple contexts as opposed to cluster in a single context. We will distinguish this factor of contextual variability from another contextual factor: the number of contexts that a word has appeared in. As we will show, the number of contexts is strongly related to word frequency, whereas our measure for contextual variability is relatively independent of word frequency. Our present goals are twofold. First, we will show how we define contextual variability and measure it for over 90,000 words. Second, we will empirically test the separate contributions of contextual variability and word frequency in recognition memory. CONTEXTUAL VARIABILITY 5 Defining and Measuring Contextual variability Applying a simple probabilistic analysis on a large corpus of text developed our measure of contextual variability. Our analyses were performed on the Touchstone Applied Science Associates (TASA) corpus (Landauer, Foltz, & Laham, 1998) that contains a large collection of samples of text containing information to which 3 to 12 graders might be exposed (e.g., language and arts, social studies, science, health, business, etc.). Because each sample formed a semantically coherent piece of text, we assumed that different samples could be interpreted as different contexts. Because the texts correspond to the type of information to which school children are exposed, it is likely that adults will have learned much of the same information in similar contexts. We will now introduce some constants and variables that will allow us to introduce the measure for contextual variability. Let N refer to the total number of words in the TASA corpus (N=10,710,325) and D refer to the total number of samples of texts (i.e., contexts) that the corpus contains (D=37,652). Our proposed measure for contextual variability is based on a combination of the number of contexts and word frequency count. It reflects the extent to which words are evenly distributed over multiple contexts as opposed to clustered within few contexts given that the number of occurences of the word in the corpus. To calculate contextual variability, we need to calculate two statistics. First, we measure word frequency by counting how many times words appear in the whole corpus. Next, we count the number of different contexts in which a given word appears. Let di equal the number of different text samples in which the word i occurred, and let f i equal the total number occurrences of word i in the corpus (regardless of which sample of text it occurs in). CONTEXTUAL VARIABILITY 6 Let ci be our measure for the contextual variability of word i: random i actual i i P P c = (1) where the numerator is the probability that a word will be found in a sample of text based on the actual context frequency counts: D d P i actual i = (2) and the denominator is the probability that a word will be found in a sample of text based on the word frequency counts assuming that words are randomly spread over the different samples of text: