Quantitative Methods

Introduction Experimental Data Non-Experimental Data & Inference Probabilistic versus Deterministic Models Political Methodology

Introduction Experimental Data Experiments are a set of observations performed to support or falsify a hypothesis. In order to demonstrate causality, one generally must show that a phenomenon occurs only in the presence of a particular causal factor—and that the phenomenon does not occur in the absence of that causal factor.

Introduction Experimental Data An controlled experiment involves the comparison of results obtained from an experimental group to those obtained under the control group. The control group is exactly like the experimental group except for the manipulation of one method.

Introduction Observational Data A natural experiment or quasi-experiment does not involve manipulation or a controlled environment.

Introduction Observational Data In observational studies, data are gathered and the association between predictors (independent variables) and the response phenomenon (dependent variable) are assessed.

Introduction Observational Data Descriptive statistics involve summarizing a collection of data. In inferential statistics, we are generally using a sample. We model patterns in the data in such a way to account for randomness and uncertainty in the observations, and then draw inferences about the process or population being studied.

Introduction In Inferential Statistics… In inferential statistics, we may be interested in predicting Y with X, or with the casual effect of X on Y. We call the population measure (in these examples, either the mean or the effect of X on Y) the “parameter”, and the sample measure the “parameter estimate”.

Introduction What is a model? A model is a representation or an abstraction of reality.

Introduction Deterministic & Probabilistic Models In deterministic models, if certain conditions are met, the outcome is certain to happen. There is no “error”. In probabilistic or stochastic models, if certain conditions are met, the outcome is more or less likely to happen. When we are modeling, we are essentially fitting a deterministic model to actual data. Click here for a paper by Gelman et al on the two types of models.Gelman

Introduction A Few Other Items… As noted, in descriptive statistics, we may be interested in presenting information about the data—such as measures of central tendency (i.e., means, etc.) We may also want to take a sample and estimate the effect of one variable (or a set of variables) on another. In this case, we are generally using inferential statistics (but contemplate the difference between a population and a sample, and the meaning of “inference”)

Introduction A Few Other Items… Explanatory variables (or independent variables, or “left hand side” or “LHS” variables, or “covariates” ) are often signified by X. Dependent variables (or “outcome” or “right hand side” or “RHS” variables) are generally signified by Y. Y i is a random variable (that is, we don’t know the value); we know the particular value for lower case y i.