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Independence Tests quiz

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  • What does it mean for two variables to be independent in statistics?
    It means that the variables do not affect each other in any way.
  • What is the purpose of a chi-square test of independence?
    It is used to determine whether two categorical variables are independent or related.
  • What is the null hypothesis in a test of independence?
    The null hypothesis states that the two variables are independent.
  • How is the alternative hypothesis stated in an independence test?
    The alternative hypothesis claims that the variables are dependent.
  • What test statistic is used in a chi-square test of independence?
    The chi-square test statistic is used, calculated from observed and expected frequencies.
  • How do you calculate expected frequencies in an independence test?
    Multiply the row total by the column total and divide by the grand total for each cell.
  • What is the formula for degrees of freedom in a chi-square test of independence?
    Degrees of freedom = (number of rows - 1) × (number of columns - 1).
  • What do you compare the p-value to when making a decision in a chi-square test?
    You compare the p-value to the significance level, alpha.
  • What conclusion do you draw if the p-value is greater than alpha in an independence test?
    You fail to reject the null hypothesis, suggesting insufficient evidence of dependence.
  • What does it mean to 'fail to reject' the null hypothesis in this context?
    It means there is not enough evidence to say the variables are dependent.
  • What are the main conditions that must be met to run a chi-square test of independence?
    You need random samples, observed frequencies for all categories, and expected frequencies of at least 5 in each cell.
  • How is a chi-square test of independence similar to a goodness of fit test?
    Both use the chi-square statistic and compare observed to expected frequencies.
  • How is the calculation of expected frequencies different in an independence test compared to a goodness of fit test?
    In an independence test, expected frequencies are based on row and column totals, not just claimed distributions.
  • If you have 2 rows and 3 columns in your data table, what are the degrees of freedom?
    The degrees of freedom are (2-1) × (3-1) = 2.
  • Why is it important to check that all expected frequencies are at least 5 in a chi-square test?
    This ensures the validity of the test results and that the chi-square approximation is appropriate.