Spoiler alert, real data are seldom normally distributed. How does the population distribution influence the estimate of the population mean and its confidence interval?
To figure this out, we randomly draw 100 observations 100 times from three distinct populations and plot the mean and corresponding 95% confidence interval of each sample.
What is a Confidence Interval?
Any sample-based findings used to generalize a population are subject to sampling error. In other words, sample statistics won’t exactly match the population parameters they estimate.
Any time you report estimates of parameters in a statistical analysis, it’s important to include their confidence intervals.
How confident are you that you can explain what they mean? Even those of us who have a solid understand of confidence intervals get tripped up by the wording.
The Wording for Describing Confidence Intervals
Let’s look at an example. (more…)
One issue with using tests of significance is that black and white cut-off points such as 5 percent or 1 percent may be difficult to justify.
Significance tests on their own do not provide much light about the nature or magnitude of any effect to which they apply.
One way of shedding more light on those issues is to use confidence intervals. Confidence intervals can be used in univariate, bivariate and multivariate analyses and meta-analytic studies.
A Science News article from July 2014 was titled “Scientists’ grasp of confidence intervals doesn’t inspire confidence.” Perhaps that is why only 11% of the articles in the 10 leading psychology journals in 2006 reported confidence intervals in their statistical analysis.
How important is it to be able to create and interpret confidence intervals?
The American Psychological Association Publication Manual, which sets the editorial standards for over 1,000 journals in the behavioral, life, and social sciences, has begun emphasizing parameter estimation and de-emphasizing Null Hypothesis Significance Testing (NHST).
Its most recent edition, the sixth, published in 2009, states “estimates of appropriate effect sizes and confidence intervals are the minimum expectations” for published research.
In this webinar, we’ll clear up the ambiguity as to what exactly is a confidence interval and how to interpret them in a table and graph format. We will also explore how they are calculated for continuous and dichotomous outcome variables in various types of samples and understand the impact sample size has on the width of the band. We’ll discuss related concepts like equivalence testing.
By the end of the webinar, we anticipate your grasp of confidence intervals will inspire confidence.
Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.