inference

Examples of inference in the following topics:

• Introduction to inference for numerical data

  • Chapter 4 introduced a framework for statistical inference based on confidence intervals and hypotheses.
  • In each case, the inference ideas remain the same:

• Foundations for inference

  • Statistical inference is concerned primarily with understanding the quality of parameter estimates.
  • " While the equations and details change depending on the setting, the foundations for inference are the same throughout all of statistics.
  • We introduce these common themes in Sections 4.1-4.4 by discussing inference about the population mean, µ, and set the stage for other parameters and scenarios in Section 4.5.
  • This is the practice of statistical inference in the broadest sense.

• Single-Population Inferences

  • Two notable nonparametric methods of making inferences about single populations are bootstrapping and the Anderson–Darling test.
  • It is often used as an alternative to inference based on parametric assumptions when those assumptions are in doubt, or where parametric inference is impossible or requires very complicated formulas for the calculation of standard errors.
  • The bootstrap works by treating inference of the true probability distribution $J$, given the original data, as being analogous to inference of the empirical distribution of $\hat{J}$, given the resampled data.
  • If $\hat{J}$ is a reasonable approximation to $J$, then the quality of inference on $J$ can, in turn, be inferred.
  • Contrast bootstrapping and the Anderson–Darling test for making inferences about single populations

• Introduction to inference for a single proportion

  • Chapter 6 introduces inference in the setting of categorical data.

• The Role of the Model

  • Any statistical inference requires assumptions.
  • Descriptions of statistical models usually emphasize the role of population quantities of interest, about which we wish to draw inference.
  • Descriptive statistics are typically used as a preliminary step before more formal inferences are drawn.
  • Incorrect assumptions of simple random sampling can invalidate statistical inference.
  • For example, incorrect "Assumptions of Normality" in the population invalidate some forms of regression-based inference.

• Inferential Statistics

  • In statistics, statistical inference is the process of drawing conclusions from data that is subject to random variation--for example, observational errors or sampling variation.
  • The outcome of statistical inference may be an answer to the question "what should be done next?
  • Instead, we query a relatively small number of Americans, and draw inferences about the entire country from their responses.
  • If the sample held only Floridians, it could not be used to infer the attitudes of other Americans.
  • This graph shows a linear regression model, which is a tool used to make inferences in statistics.

• Expert Systems

  • An expert system consists of both an inference engine and a knowledge base and has decision-making abilities.
  • It is divided into two parts: One fixed and independent of the expert system—the inference (reasoning) engine, and one variable—the knowledge base.
  • Break down expert systems to the inference engine, the knowledge base, and conversational

• Summary for inference of the difference of two means

  • When applying the normal model to the point estimate $\bar{x}_1-\bar{x}_2$ (corresponding to unpaired data), it is important to verify conditions before applying the inference framework using the normal model.
  • When these conditions are satisfied, the general inference tools of Chapter 4 may be applied.

• Basic Inferential Statistics

  • Statistical inference makes claims about a population of individuals or things, using data drawn from a smaller subset of the population known as a sample.
  • When psychologists want to test a research hypothesis, they will usually need to use statistical inference.
  • Statistical inference makes propositions about a population by using a sample, which is data drawn from that population.
  • Statistical inference therefore literally helps us make inferences about the characteristics of populations (their parameters) from characteristics of our sample (statistics).
  • Because it is typically impossible to study an entire population, a sample gets us as close as possible, and statistical inference enables us to infer the characteristics of our population.

• Introduction

  • And what can we infer from the analysis?
  • However, many of these investigations can be addressed with a small number of data collection techniques, analytic tools, and fundamental concepts in statistical inference.