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What are the differences between statistical significance and practical significance?
Statistical Significance: A result is statistically significant if the p-value is below the significance level. | Practical Significance: Considers whether the magnitude of the effect is meaningful in the real world, regardless of statistical significance.
What are the differences between a Chi-Square Goodness-of-Fit test and a Chi-Square Test for Independence?
Goodness-of-Fit: Tests if the distribution of a categorical variable matches a claimed distribution. | Test for Independence: Tests if there is an association between two categorical variables.
What are the differences between the null and alternative hypotheses?
Null Hypothesis: A statement of no effect or no difference. | Alternative Hypothesis: A statement that contradicts the null hypothesis, suggesting there is a significant effect or difference.
What are the differences between Type I and Type II error?
Type I error: Rejecting the null hypothesis when it is true (false positive). | Type II error: Failing to reject the null hypothesis when it is false (false negative).
Define 'p-value'.
The probability of observing results as extreme as, or more extreme than, the observed data if the null hypothesis is true.
What is the null hypothesis?
A statement of no effect or no difference, which we aim to disprove with statistical evidence.
Define 'alternative hypothesis'.
A statement that contradicts the null hypothesis, suggesting there is a significant effect or difference.
What is 'statistical significance'?
A result is statistically significant if the p-value is less than the significance level (alpha), indicating the observed effect is unlikely due to chance.
Define 'degrees of freedom' in a Chi-Square test.
The number of independent pieces of information used to calculate the test statistic. For goodness-of-fit, df = (number of categories - 1).
What is 'power' in a statistical test?
The probability of correctly rejecting the null hypothesis when it is false.
What is the formula for the Chi-Square test statistic?
\$\chi^2 = \sum \frac{(O - E)^2}{E}$, where O is observed frequency and E is expected frequency.
How do you calculate expected counts in a chi-square test for independence?
Expected Count = (Row Total * Column Total) / Grand Total
How do you calculate degrees of freedom (df) for a chi-square goodness-of-fit test?
df = Number of categories - 1
How do you calculate degrees of freedom (df) for a chi-square test for independence?
df = (Number of rows - 1) * (Number of columns - 1)