Chi-Square Goodness of Fit – AP Statistics

Chi-Square Formula ($\chi^2$)

$$ \chi^2 = \sum \frac{(O - E)^2}{E} $$

Summing the normalized squared differences between your Observed ($O$) and Expected ($E$) categorical counts.

Degrees of Freedom

$$ df = k - 1 $$

Where $k$ is the number of distinct categories.

Hypotheses

$H_0$: The specified distribution is correct.

$H_A$: The specified distribution is NOT correct.

Tags

chi-squareGOFcategoricalp-value

Frequency Deviation Visualizer (O vs E)

$\chi^2$ Distribution & Right-Tail P-Value

Preset Scenarios

Category	Prob %	Exp (E)	Obs (O)

$\chi^2$ Statistic

0.00

DF ($k-1$)

Right-Tail P-Value

0.0000

Reject Null Hypothesis ($\alpha=0.05$)