Demonstration app I
Small samples can mislead correlations
This teaching app shows how a small sample from a desired population can distort the observed range, skewness, outliers, correlation, confidence interval, and Type I / Type II error risk.
Controls
Teaching scenarios
Grey dots = desired population. Blue dots = one observed sample. The dashed line is the sample regression line.
Observed sample r
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95% CI for r
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Fisher z approximation
p-value
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Current error label
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Given the true ρ setting
Repeated-sampling view
Run many small samples from the same population. Each dot below is one sample correlation. Red vertical lines mark r = 0 and the true population ρ.
Significant samples
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p < α
Type I error rate
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Only meaningful when true ρ = 0
Type II error rate
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Only meaningful when true ρ ≠ 0
Mean sampled r
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Across repeated samples