# In teachingApps: Apps for Teaching Statistics, R Programming, and Shiny App Development

### Confidence Intervals

Confidence intervals (CI) are useful tools for quantifying the uncertainty associated with a point estimate. The amount of uncertainty depends on a associated with du

• What does it mean to say "...the $100\times(1-\alpha)\%$ CI for $\theta =(\underline{\widehat{\theta}},\overline{\widehat{\theta}})$..."

• For $\alpha=0.05,$ a $95\%$ CI on $\theta$ this means

• If an experiment were run $i$ times (each run producing a distinct data set)

• The true (but unknown) value of $\theta$ would be in the interval $(\underline {\widehat {\theta_{i}}},\overline{\widehat{\theta_{i}}})$ in $95\%$ of those runs.

• A $95\%$ CI on $\theta$ does not mean $P(\underline{\widehat{\theta_{i}}} <\theta<\overline{\widehat{\theta_{i}}})=0.95$

• For each experiment the probability $P(\underline{\widehat{\theta_{i}}} <\theta<\overline{\widehat{\theta_{i}}})$ is either $1$ or $0$

• This is because $\theta$ is either in the interval, or it isn't

• The Examples tab

• Walks through a 'not-so-real-world' example showing how ML Estimation works
• The Details Tab

• Presents an interactive simulation showing how likelihood values are computed for different distributions

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teachingApps documentation built on July 1, 2020, 5:58 p.m.