All Flashcards
Explain the concept of a p-value in the context of a Chi-Square test.
The probability of observing a χ² statistic as extreme as the one calculated, assuming H₀ is true. A low p-value leads to rejecting H₀.
Explain what a large χ² value suggests.
A large χ² value suggests that the expected counts are not accurate, leading to rejection of H₀.
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.
What is the formula for the Chi-Square statistic (χ²)?
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
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 χ²: Supports H₀, observed and expected are similar. | Large χ²: Suggests expected counts are inaccurate, leading to rejection of H₀.
What are the differences between rejecting and failing to reject the null hypothesis?
Reject H₀: Concluding there is enough evidence for Hₐ. | Fail to reject H₀: Concluding there is not enough evidence for Hₐ.