The chi-square test is right-tailed because the statistic can only be:

1. The statistic is built from squared differences divided by expected counts. 2. Squaring removes any sign, so no term can be negative. 3. The statistic therefore starts at zero and grows as disagreement grows. 4. Large disagreement puts it way out in the right tail of the chi-square curve. 5. With no left tail available, the goodness-of-fit test is almost always right-tailed. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 11 'The Chi-Square Distribution', sections 11.1-11.5_