Topics, Summer 2008 Day 1. Introduction models and the world (probability & frequency) types of data (nominal, count, interval, ratio) some R basics (read.table, barplot, hist, etc.) Day 2. Central limit theorem, sampling, evaluating differences between samples (& between populations) Day 3. Evaluating relationships – scatterplots, correlation, Principal Components Analysis Day 4. Regression and Analysis of Variance Day 5. Logistic regression – log odds, maximum likelihood, relationship to GoldVarb

Goals Understand and appreciate “four main goals of quantitative analysis” (Johnson, 2008, p. 3): 1.data reduction, summary 2.Inference (generalization to larger population) 3.discovery of (potentially causal) relationships 4.exploration of processes that may have a basis in probability Also see “justification for course” written for grant proposal to the National Science Foundation for support for the mini-Institute Ancillary goal: assuage any fear of tools such as R

What is a model? “a simplified description, especially a mathematical one, of a system or process, to assist calculations and predictions” (Concise Oxford English Dictionary, 11 th edition) “A model is any simplification, substitute or stand-in for what you are actually studying or trying to predict. Models are used because they are convenient substitutes, the way that a recipe is a convenient aid in cooking.” (Craig M. Pease & James J. Bull) Types (Pease & Bull): abstract, physical, sampling Goal: acquire some tools for using sampling models and relating them to abstract models

Data and models Each datum is, at some level, a model Relationship of data to larger model – via sequence of pivotal questions: What is the question that I’m trying to answer? What are the relevant assumptions in the linguistic model(s) that I am adopting that provide the context for this question? What are the simplifying assumptions about the world that provide the observational “instrument”? What are the mathematical models that let me relate the observations to the linguistic model(s)?

Types of variable 1.nominal - unordered, named 2.ordinal - ordered, named 3.interval - measured on a scale without an absolute zero 4.ratio - measured on a scale with an absolute zero

Distributions for nominal variables Counts how many Xs do I have? Proportions how many Xs do I have out of the total number of observations? Example: How many of the clauses tagged in the Switchboard portion of the Bresnan et al. (2007) dataset show the PP realization of the recipient? What proportion of the Switchboard observations …?