Quantitative Methods

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Quantitative Methods
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Introduction

• Experimental Data
• Non-Experimental Data Inference
• Probabilistic versus Deterministic Models
• Political Methodology

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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 factorand that the
  phenomenon does not occur in the absence of that
  causal factor.

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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.

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Introduction

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

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Introduction

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

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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.

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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.

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Introduction

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

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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.

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Introduction

• A Few Other Items
• As noted, in descriptive statistics, we may be
  interested in presenting information about the
  datasuch 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)

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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. Yi is a random variable (that is, we dont
  know the value) we know the particular value for
  lower case yi.