Explain the concept of degrees of freedom in a Chi-Squared test.
Degrees of freedom represent the number of independent pieces of information used to calculate the test statistic. It affects the shape of the chi-squared distribution.
Explain the concept of expected counts in a Chi-Squared test.
Expected counts are the frequencies we would expect to see in each cell of a contingency table if the null hypothesis were true (i.e., no association between variables).
Explain the role of p-value in Chi-Squared tests.
The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true. A small p-value suggests evidence against the null hypothesis.
Explain why categorical data is required for Chi-Squared tests.
Chi-squared tests analyze frequencies of categories. Continuous data needs to be grouped into categories to be used.
Explain the importance of checking conditions for Chi-Squared tests.
Conditions like randomness, independence, and large counts ensure the validity of the test results. Violating these conditions can lead to inaccurate conclusions.
What is the formula for the Chi-Squared 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-Squared test?
Expected Count = (Row Total * Column Total) / Grand Total
How do you calculate degrees of freedom for a Chi-Squared test for independence?
df = (number of rows - 1) * (number of columns - 1)
How do you calculate degrees of freedom for a Chi-Squared Goodness of Fit test?
df = (number of categories - 1)
What is the general formula for calculating expected values in a chi-squared test?
E = (Row Total * Column Total) / Grand Total
What are the differences between Chi-Squared Test for Independence and Homogeneity?
Independence: One sample, two variables. | Homogeneity: Two or more samples, one variable.
What are the differences between Chi-Squared Test for Goodness of Fit and Independence?
Goodness of Fit: One sample, one variable compared to a theoretical distribution. | Independence: One sample, two variables looking for association.
What are the differences between the null hypothesis for a test of independence and a test of homogeneity?
Independence: No association between two categorical variables within a single population. | Homogeneity: The distribution of a categorical variable is the same across different populations.
What are the differences between observed and expected counts?
Observed: The actual frequencies in the sample data. | Expected: The frequencies predicted under the null hypothesis.
What are the differences between rejecting and failing to reject the null hypothesis?
Rejecting: Evidence supports the alternative hypothesis. | Failing to reject: Insufficient evidence to support the alternative hypothesis.
