While it is common practice for researchers in psychology and other social sciences to use inferential statistical methods such as t-test, F-test, and chi-square test, it is only the beginning for linguists and investigators of language acquisition to get acquainted with the full power of inferential statistics. As the linguistic science becomes more quantitative, there have been admirable efforts to introduce statistics into the field, with the publications of several statistics books specifically designed for linguists (Anshen, 1978; Butler, 1985; Hatch & Farhady, 1982; Woods, Fletcher, & Hughes, 1986; see Grotjahn, 1988, for a review). However, none of these books has discussed a very important statistical method for the analysis of categorical data, the loglinear analysis — a method that has nevertheless been applied widely in sociology and other social sciences. In this paper, I will first examine a problem that many researchers in language acquisition may have encountered, i.e., the limited power of the analysis of categorical data by the use of chi-square. I will then discuss how loglinear analysis overcomes the problem. Although descriptions about loglinear analysis are available in many statistics books, they are in general not easily accessible to language acquisition researchers because of their technicality and mathematical flavor. For this reason, I will deliberately avoid very technical descriptions here, but will instead present the rationale behind the method, the basic procedures involved in the analysis, and a real example that makes use of this method to illustrate the significance of loglinear analysis for language acquisition data..