↔️ Drag Near Cutoff Line: Moves the vertical χ² Bound left or right.
🎛️ Drag Graph Canvas Background: Drag Left/Right to dynamically change the Degrees of Freedom (df).
How to Use the Interactive Chi-Square Distribution Visualizer
This interactive Chi-Square distribution calculator is an advanced pedagogical tool developed to help users visualize probability density functions commonly applied in Chi-Square independence tests and goodness-of-fit assessments.
Modify Degrees of Freedom – Use the manual input box or simply click and drag horizontally across the graph background to alter the degrees of freedom (df). Watch how the distribution shifts from highly skewed to a more symmetrical bell shape as df increases.
Determine Statistical Significance – Grab the red vertical bound line to slide your Chi-Square cutoff score (χ²). The shaded right-tail region instantly calculates the corresponding critical p-value for hypothesis testing.
Native Presentation Export – Right-click to copy or save the image directly. The system hardcodes the active statistical criteria (df value, χ² bound, and exact area percentages) cleanly over the canvas element, preserving your full data presentation.