What are the differences between Observed and Expected frequencies?
Observed: Actual counts in the sample. | Expected: Counts predicted by the null hypothesis.
What are the differences between a small and large Chi-Square statistic?
Small ฯยฒ: Supports Hโ, observed and expected are similar. | Large ฯยฒ: Suggests expected counts are inaccurate, leading to rejection of Hโ.
What are the differences between rejecting and failing to reject the null hypothesis?
Reject Hโ: Concluding there is enough evidence for Hโ. | Fail to reject Hโ: Concluding there is not enough evidence for Hโ.
What is the formula for the Chi-Square statistic (ฯยฒ)?
$\chi^2 = \sum \frac{(Observed - Expected)^2}{Expected}$
How do you calculate expected frequencies?
Expected Frequency = (Probability of category) * (Total number of observations)
How to calculate degrees of freedom (df)?
df = Number of categories - 1
Explain the concept of a p-value in the context of a Chi-Square test.
The probability of observing a ฯยฒ statistic as extreme as the one calculated, assuming Hโ is true. A low p-value leads to rejecting Hโ.
Explain what a large ฯยฒ value suggests.
A large ฯยฒ value suggests that the expected counts are not accurate, leading to rejection of Hโ.
Explain the importance of context in the conclusion of a Chi-Square test.
Always relate your findings back to the original problem to provide a meaningful interpretation of the results.
Explain what failing to reject the null hypothesis means.
It means there is not convincing evidence for the alternative hypothesis. We do not 'accept' the null hypothesis.
Explain what rejecting the null hypothesis means.
It means there is convincing evidence for the alternative hypothesis.
