Histogram
Density scale · Fitted normal overlay
Bars = sample density
Fitted N(μ̂,σ̂²)
▶ Bin Controls & Example Datasets
Bin width
auto
Bin start
0.00
Example datasets (illustrate bin sensitivity):
What to look for: Bars should follow the green normal curve. Asymmetry → skewness. Multiple peaks → mixture. Adjust bin width to see how it reveals or hides structure — narrow bins are noisy, wide bins over-smooth. Use "Old Faithful" to see a bimodal dataset that looks unimodal with wide bins.
Box Plot
Quartiles · 1.5×IQR whiskers
What to look for: Centered median line → symmetry. Equal whisker lengths → symmetric distribution. Many outlier dots → heavy tails. Unequal box widths (IQR) across groups → heteroscedasticity. The x-axis is synchronized with the CI chart.
▶ What are Groups B and C?
Group B — Normal(0, 1): A control group drawn from a standard normal distribution. It serves as the baseline for comparison — same mean and variance as a "perfect" normal.
Group C — Normal(0, 2.2): Also drawn from a normal distribution but with more than double the standard deviation (σ = 2.2 vs σ = 1). This deliberately introduces heteroscedasticity (unequal variance), making it easy to see how wider spread shows up as a wider IQR box and longer whiskers. Comparing B and C illustrates the equal-variance assumption that many parametric tests rely on.
Group C — Normal(0, 2.2): Also drawn from a normal distribution but with more than double the standard deviation (σ = 2.2 vs σ = 1). This deliberately introduces heteroscedasticity (unequal variance), making it easy to see how wider spread shows up as a wider IQR box and longer whiskers. Comparing B and C illustrates the equal-variance assumption that many parametric tests rely on.
Kernel Density Estimate
Gaussian kernel · Silverman bandwidth
KDE
Fitted normal
●Brushed point
Bandwidth
1.00×
What to look for: Smooth bell = normal. Adjust bandwidth: too small → jagged/overfit; too large → masks modes. Rug marks show individual observations. The brushed point (hover on CI chart) appears as a pink line.
Confidence Intervals with Error Bars
Mean ± 95% CI · Jittered individual points · Hover to brush KDE & QQ
What to look for: CI width = spread. Equal CI widths across groups supports homoscedasticity. Group C has 2× SD of Group B to illustrate heteroscedasticity. Hover Group A dots to highlight the same observation in KDE and QQ plot.
▶ Axis zoom
Horizontal axis:
▶ What are Groups B and C?
Group B — Normal(0, 1): Drawn from a standard normal distribution (σ = 1). This group mirrors Group A's sample size but always uses a known normal distribution, providing a visual reference for what "normal spread" looks like in a CI chart.
Group C — Normal(0, 2.2): Drawn from a normal with σ = 2.2. Because the standard deviation is more than double that of Group B, Group C's CI bar will be noticeably wider. This contrast demonstrates heteroscedasticity — unequal variances across groups — which is important to check before running ANOVA or pooled t-tests that assume equal variance.
Group C — Normal(0, 2.2): Drawn from a normal with σ = 2.2. Because the standard deviation is more than double that of Group B, Group C's CI bar will be noticeably wider. This contrast demonstrates heteroscedasticity — unequal variances across groups — which is important to check before running ANOVA or pooled t-tests that assume equal variance.
Normal Q–Q Plot
Sample vs Theoretical quantiles · Brushing enabled
What to look for: Points on the diagonal → normal. S-curve → skewness. Points curling above at both ends → heavy tails. Points curling below → light tails (uniform). Brushed point (from CI chart hover) highlighted in pink.
CI of the Difference
Group 1 vs Custom Normal(μ,σ) · Within- or Between-subjects
Group 2 — Custom Normal
μ
0.00
σ
1.00
What to look for (top panel): Individual group CIs with μ₂ population indicator. Bottom panel: CI of the difference (Group 1 − Group 2). The zero line is aligned with Group 1's mean above. If the CI includes 0, the difference is not significant at α=0.05. Adjust Group 2's μ and σ sliders to explore how effect size and variance influence significance. Within-subjects (paired) designs reduce variance by removing between-subject variability.