Introductory Statistics

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IS: Module Four, Introductory Inference

[Module 4]
Module 4: Introductory Inference

This learning module continues our exploration of the relationships between the sample and the population. Here, we will learn how to take sample data and draw inferences about the population parameters.

These statistical procedures have assumptions supporting them. As such, testing that the data meet these requirements is extremely important. This means there will be several tests introduced that check the requirements (assumption tests).

If the data do not meet the requirements, we will “drop down” a level on our allowed procedures. We will continue doing that until the requirements are met. Thus, for estimating a single population mean, the trail is

z-procedure → t-procedure → Wilcoxon → bootstrap

Each step down relaxes an assumption.

[objectives] Module Objectives

By the end of this module, the student will

  • understand the importance of the Central Limit Theorem in statistics
  • explain bias and mean square error and how they are used in selecting appropriate estimators of population parameters
  • be able to calculate confidence intervals for population means, proportions, variances, and differences in population means, differences in population proportions, and ratios of population variances
  • evaluate several competing statistical procedures
  • defend choices in statistical analyses

[procedure] Procedure Flowchart

To help you with learning the appropriate procedures for analyzing data (with respect to the research), I am including a sample flowchart for estimating the population mean, μ. If it is helpful, make sure you create these for each of the analysis procedures covered in this course. Actually, since this is such an important skill, I would expect such a question to find its way on the next examination.

This page was last modified on 2 January 2024.
All rights reserved by Ole J. Forsberg, PhD, ©2008–2024. No reproduction of any of this material is allowed without explicit written permission of the copyright holder.