Basic Statistical Concepts

The Prerequisites Checklist page on the Department of Statistics website lists a number of courses that require a foundation of basic statistical concepts as a prerequisite.  All of the graduate courses in the Master of Applied Statistics program heavily rely on these concepts and procedures. Therefore, it is imperative — after you study and work through this lesson — that you thoroughly understand all the material presented here. Students that do not possess a firm understanding of these basic concepts will struggle to participate successfully in any of the graduate-level courses above STAT 500. Courses such as STAT 501 - Regression Methods or STAT 502 - Analysis of Variance and Design of Experiments require and build from this foundation.

Review Materials

These review materials are intended to provide a review of key statistical concepts and procedures. Specifically, the lesson reviews:

  • populations and parameters and how they differ from samples and statistics,
  • confidence intervals and their interpretation,
  • hypothesis testing procedures, including the critical value approach and the P-value approach,
  • chi-square analysis,
  • tests of proportion, and
  • power analysis.

For instance, with regards to hypothesis testing, some of you may have learned only one approach — some the P-value approach, and some the critical value approach. It is important that you understand both approaches. If the P-value approach is new to you, you might have to spend a little more time on this lesson than if not.

Learning Objectives & Outcomes

Upon completion of this review of basic statistical concepts, you should be able to do the following:

  • Distinguish between a population and a sample.
  • Distinguish between a parameter and a statistic.
  • Understand the basic concept and the interpretation of a confidence interval.
  • Know the general form of most confidence intervals.
  • Be able to calculate a confidence interval for a population mean µ.
  • Understand how different factors affect the length of the t-interval for the population mean µ.
  • Understand the general idea of hypothesis testing -- especially how the basic procedure is similar to that followed for criminal trials conducted in the United States.
  • Be able to distinguish between the two types of errors that can occur whenever a hypothesis test is conducted.
  • Understand the basic procedures for the critical value approach to hypothesis testing. Specifically, be able to conduct a hypothesis test for the population mean µ using the critical value approach.
  • Understand the basic procedures for the P-value approach to hypothesis testing. Specifically, be able to conduct a hypothesis test for the population mean µ using the P-value approach.
  • Understand the basic procedures for testing the independence of two categorical variables using a Chi-square test of independence.
  • Be able to determine if a test contains enough power to make a reasonable conclusion using power analysis.
  • Be able to use power analysis to calculate the number of samples required to achieve a specified level of power.
  • Understand how a test of proportion can be used to assess whether a sample from a population represents the true proportion of the entire population.

Self-Assessment Procedure

  1. Review the concepts and methods on the pages in this section of this website.  
  2. Download and complete the Self-Assessment Exam at the end of this section.
  3. Review the Self-Assessment Exam Solutions and determine your score.

A score below 70% suggests that the concepts and procedures that are covered in STAT 500 have not been mastered adequately. Students are strongly encouraged to take STAT 500, thoroughly review the materials that are covered in the sections above or take additional coursework that focuses on these foundations.

If you have struggled with the concepts and methods that are presented here, you will indeed struggle in any of the graduate-level courses included in the Master of Applied Statistics program above STAT 500 that expect and build on this foundation.