Showing 11 results
Binomial Probability Model
Interactive Binomial exact probability mass function visualizing discrete histograms. Demonstrates dynamic skew based on fixed $n, p$ ratios and overlays large-sample normal convergence boundaries visually calculating exact vs cumulative density outcomes.
Sampling Distributions (CLT)
Dual-canvas integration rendering Central Limit Theorem convergence. Draws random Monte Carlo datasets mapping sample size variance crushing ($n \geq 30$ rule) converting arbitrary shapes (skewed/bimodal) into stable Gaussian sample-mean distributions.
Confidence Intervals
Visualization generating multiple dynamic Confidence Interval margin 'nets' drawn from random standard errors. Empirically validates the meaning of 95% confidence by revealing the random capture vs failure rate against an unknown stationary population parameter line.
Hypothesis Testing Rules
Inferential hypothesis engine animating null model rejection thresholds vs interactive sample observed P-Value tails. Illuminates the deterministic binary conclusion states driven by fixed Alpha lines mapping Type I geometric error bounds visually.
Linear Regression (LSRL)
Interactive graphical Least Squares regression engine visually proving the $e^2$ square-area minimization property via manual vs automatic fitting while actively mapping high leverage outlier penalties.
Chi-Square Test (Goodness of Fit)
Goodness of Fit interaction engine assessing categorical skew. Graphically maps individual $(O-E)^2/E$ penalty variance blocks onto nominal bar distributions to visually sum into absolute $\chi^2$ scalar outcomes linking directly to cumulative significance rejection limits.
Student's t-Distribution
Interactive dynamic rendering of Student's T probability density logic modeling $df$ expansion from 1 stabilizing towards normal Z convergence. Highlights fat tail density displacement explicitly revealing structural variance uncertainty for small sample designs.
ANOVA Variance Analysis
Interactive ANOVA interaction plotting $MS_{bet}$ vs $MS_{wit}$ signal-to-noise calculations natively. Combines adjustable uniform variance blocks mathematically linking structural layout changes actively to precise numerical F-Distribution test thresholds.
Scatterplots & Correlation (r)
Interactive scatterplot geometry demonstrating Pearson's correlation coefficient mapping bounds ($|r| \to 1$). Employs bivariate normal Box-Muller transformations to visually generate dynamic density clouds calculating $R^2$ determination variances overlaid mathematically on LSRL projection planes natively.
Two-Way Independence
Probability matrices displaying Two-Way intersections visualizing Marginal row sums vs Joint cell probabilities dynamically tracking conditional shrinking denominators highlighting Independence verifications mathematically.
Type I & II Errors & Power
Interactive structural dual-distribution rendering plotting absolute hypothesis decision bounds. Animates the zero-sum mathematical see-saw between Alpha (Type I) restrictions severely punishing statistical Power translating into elevated Type II failures explicitly under sample size constrictions.