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What is a Chi-Square Test?
A statistical test used to determine if observed data significantly differs from expected data, especially with categorical variables.
What is observed frequency?
The actual frequencies you see in your data.
What is expected frequency?
The frequencies you'd expect if there was no relationship between variables.
What is a two-way table?
A table that organizes categorical data, making it easier to calculate expected counts and perform the chi-square test.
What is a frequency table distribution?
A table showing the distribution of categorical data, used to calculate expected counts and perform the chi-square test.
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?
Expected Count = (Row Total * Column Total) / Grand Total
How do you calculate degrees of freedom for a Chi-Square test for independence?
df = (number of rows - 1) * (number of columns - 1)
What is the formula to calculate the Chi-Square statistic?
$\chi^2 = \sum \frac{(Observed - Expected)^2}{Expected}$
What is the formula for calculating expected frequency in a goodness-of-fit test?
Expected Frequency = Total Number of Observations * Hypothesized Proportion
Explain the concept of the Chi-Square Test for Goodness of Fit.
It examines if a sample distribution matches a hypothesized distribution. It tests if your data "fits" a particular model.
Explain the concept of the Chi-Square Test for Independence.
It determines if two categorical variables are independent of each other. It assesses whether they are related or if the observed relationship is due to chance.
Explain the concept of the Chi-Square Test for Homogeneity.
It compares distributions of a categorical variable across different populations or treatments to determine if the groups are similar or different.
Explain the 'Large Counts' condition in Chi-Square tests.
All expected counts must be at least 5. This ensures the sampling distribution of the test statistic is approximately chi-square.
Explain the meaning of a low p-value in a Chi-Square test.
A low p-value means we have evidence to reject the null hypothesis, suggesting a significant association or difference.