Confidence Intervals, Clearly
Build, read and explain confidence intervals without the usual misunderstandings
A taste of a lesson
My report says 'average wait 42 minutes, 95% CI 38 to 46'. Can I say there's a 95 percent chance the true mean is in there?
That phrasing is very common, but under the usual frequentist method it is not quite right. The method produces intervals that capture the true mean in about 95 percent of repeated samples; any single interval either contains it or not. A safe sentence: 'We estimate the average wait at 42 minutes; plausible values range from about 38 to 46.' Also, the interval covers only sampling noise, not bias. Try this: how would the interval width change if you had four times as many observations?
Written by the teacher as an example. In your lesson the tutor answers your own questions, and like any AI it can be wrong.
What you will be able to do
- Calculate standard errors for means and proportions
- Build and explain a 95 percent confidence interval correctly
- Predict how sample size and variability change interval width
- Use the bootstrap for statistics without simple formulas
- Compare two groups using an interval for the difference
Lesson plan
- 1 Estimates vary Understand sampling variation and standard error. Start
- 2 Building an interval Construct a 95 percent interval for a mean and a proportion. Start
- 3 What 95 percent means Interpret intervals correctly and phrase them well. Start
- 4 Width and sample size Plan sample sizes to reach a useful precision. Start
- 5 The bootstrap Estimate intervals by resampling when formulas do not fit. Start
- 6 Comparing groups honestly Compare two estimates with an interval for their difference. Start
Try asking
About this tutor
An intermediate tutor for learners who know basic statistics and want to report uncertainty properly. You will understand standard error, build confidence intervals for means and proportions, see how sample size and variability change their width, and use the bootstrap when formulas do not fit. A full lesson is devoted to what a 95 percent interval does and does not mean, and another to comparing groups without the overlap fallacy. You finish able to put an honest range on a number and explain it to someone who has never taken a statistics class.
Reviews
4.3
3 ratingsSample
- Zainab A.Sample
The repeated survey thought experiment finally made intervals make sense. I rewrote three slides in our quarterly report.
- Matteo C.Sample
Very clear on the overlap fallacy. The bootstrap lesson was useful for our median based metrics.
- Hye-jin P.Sample
Precise without being dry. I wanted a little more on proportions with small samples.
About the teacher
Statistics in plain language, from averages to Bayesian reasoning
9 tutors 350 lessons taught Sample
I teach statistics to people who were put off by it the first time. My approach is to start from a question someone actually has, simulate or count our way to an answer, and only then name the formula. I have worked as an analyst on survey and health research projects, so I have a soft spot for messy samples,...
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