Day 17
Introduction to Confidence Intervals



EPSY 5261 : Introductory Statistical Methods

Learning Goals

At the end of this lesson, you should be able to …

  • Identify when to answer a research question with a confidence interval.
  • Explain the need for creating a confidence interval to do statistical inference.
  • Know how to calculate a confidence interval by hand and using R Studio.
  • Interpret a confidence interval.

Confidence Intervals

  • We have uncertainty in our sample estimates because of sampling variability (i.e., samples vary)
  • We need something to quantify the uncertainty in our estimates.

…

→ Confidence Intervals

Terminology

  • Standard Deviation (SD): Average distance from the mean, where each case in the data is an individual value.
  • Standard Error (SE): Standard deviation for a sampling distribution (where each case in the sampling distribution is a statistic).

Terminology (cntd.)

  • 95% Confidence Interval

\[ 95\%~\text{CI} = \text{Sample Statistic} \pm \underbrace{(2 \times SE)}_{\text{Margin of Error}} \] - To get a confidence interval, we add and subtract a specified number of standard errors from the sample statistic. - Margin of error quantifies the amount of uncertainty (sampling error due to variation from sample-to-sample).

Table 19.1 in Textbook

Interpretation

  • When interpreting a CI you need to include:
    • Confidence level
    • Population parameter
    • Interval Estimate

Example: We are 95% confident that the average price of a single-family house near the University of Minnesota is between $348K and $461K.

Introduction to Confidence Intervals Activity

Examine the Intervals on the Board…

What do you notice?

Summary

  • For a research question asking for an estimate, the best way to answer is with a confidence interval.
  • The confidence interval allows us to account for uncertainty by including sampling variability in our estimate of the parameter.