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For First Responders · Meta-Analysis

Meta-Analysis for a lottery-odds check

Built for first responders planning or training for real incidents. Run fast what-if scenarios for response planning and training — no software to install in the field. Simulate a lottery-odds check live below — adjust the inputs and watch it respond, right in your browser.

Confidence Interval

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Confidence IntervalsLive

what 95% really means

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Sample size n

A confidence interval is often misread. It does not mean the true value has a 95% chance of being in one interval — it means that if you repeated the experiment many times, about 95% of the intervals would contain the true mean. The red intervals here are the unlucky ones that miss it.

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Data Inspector

Confidence level95%

Observed coverage0%

Intervals shown50

Governing equation

\overset{x}{ˉ} \pm z \frac{σ}{n} = 50 \pm 1.96 \cdot \frac{10}{30}

Reading this result: About 0% of these 50 intervals captured the true mean — close to the 95% you asked for. Raising n from 30 tightens each interval (SE = σ/√n) but does not change that hit rate: the confidence level, not the sample size, sets how often you are right.

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Bootstrap

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Bootstrap ResamplingLive

confidence without formulas

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Original sample size

Bootstrap resamples B

The bootstrap estimates uncertainty by resampling your data with replacement thousands of times and recomputing the statistic each time. The spread of those bootstrap means gives a confidence interval — no formula or normality assumption required. Powerful when the math is intractable.

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Data Inspector

Sample mean0.00

95% CI low0.00

95% CI high0.00

CI width0.00

Governing equation

\hat{θ}^{*} = \frac{1}{25} i = 1 \sum 25 x_{i}^{*}, CI_{95%} = [\hat{θ}_{(2.5%)}^{*}, \hat{θ}_{(97.5%)}^{*}] = [0.00, 0.00]

Reading this result: The spread of the resampled means is the confidence interval — no normality assumption needed. Sample size sets its width; more resamples only sharpen its edges.

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Frequently asked questions

Is this good for first responders?: Yes — this version of "Meta-Analysis for a lottery-odds check" is framed for first responders planning or training for real incidents. Run fast what-if scenarios for response planning and training — no software to install in the field.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.