TEST STATISTIC
Categories ($k$)6
Total $\chi^2$0.00
p-value0.05
$\chi^2$ Distribution ($df = k-1$)
■ Test Statistic:
$\chi^2 = \sum \frac{(\text{Observed} - \text{Expected})^2}{\text{Expected}}$
■ Goodness of Fit:
Measures how far the observed sample counts (red) deviate from the expected theoretical counts (blue) under the Null Hypothesis.
If the dice is fair ($H_0$ is true), $\chi^2$ will be small, landing in the bulk of the distribution curve. If it's loaded, large deviations get squared, blowing up $\chi^2$ into the far right tail (Rejection Region, $p < \alpha$).
$\chi^2 = \sum \frac{(\text{Observed} - \text{Expected})^2}{\text{Expected}}$
■ Goodness of Fit:
Measures how far the observed sample counts (red) deviate from the expected theoretical counts (blue) under the Null Hypothesis.
If the dice is fair ($H_0$ is true), $\chi^2$ will be small, landing in the bulk of the distribution curve. If it's loaded, large deviations get squared, blowing up $\chi^2$ into the far right tail (Rejection Region, $p < \alpha$).