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📊honors statistics review

key term - Association

Citation:

Definition

Association is a statistical concept that describes the relationship between two or more variables, indicating the degree to which they are related or connected. It is a fundamental principle in the analysis of contingency tables, which examine the interdependence between categorical variables.

5 Must Know Facts For Your Next Test

  1. Association between variables in a contingency table can range from complete independence to a strong, positive or negative relationship.
  2. The strength of the association is determined by the magnitude of the difference between the observed and expected frequencies in the contingency table.
  3. A statistically significant association indicates that the observed relationship between the variables is unlikely to have occurred by chance alone.
  4. The chi-square test is commonly used to assess the statistical significance of the association in a contingency table.
  5. Odds ratios provide a measure of the strength of the association between two binary variables, with values greater than 1 indicating a positive association and values less than 1 indicating a negative association.

Review Questions

  • Explain the concept of association in the context of contingency tables.
    • Association in the context of contingency tables refers to the relationship or interdependence between two or more categorical variables. It describes the degree to which the variables are related, indicating whether they tend to occur together or independently. The strength of the association is determined by the magnitude of the difference between the observed and expected frequencies in the contingency table. A statistically significant association suggests that the observed relationship between the variables is unlikely to have occurred by chance alone.
  • Describe how the chi-square test is used to assess the statistical significance of the association in a contingency table.
    • The chi-square test is a statistical method used to determine whether there is a significant association between two categorical variables in a contingency table. The test compares the observed frequencies in the table to the expected frequencies under the assumption of no association. If the difference between the observed and expected frequencies is sufficiently large, the test will indicate that the association is statistically significant, meaning the relationship is unlikely to have occurred by chance. The chi-square test provides a p-value that represents the probability of observing the given pattern of frequencies if the variables are truly independent.
  • Analyze how the odds ratio can be used to quantify the strength of the association between two binary variables in a contingency table.
    • The odds ratio is a measure of the strength of the association between two binary variables in a contingency table. It represents the odds of an outcome occurring in one group compared to the odds in another group. An odds ratio greater than 1 indicates a positive association, where the outcome is more likely to occur in one group than the other. An odds ratio less than 1 indicates a negative association, where the outcome is less likely to occur in one group than the other. The magnitude of the odds ratio reflects the strength of the association, with values farther from 1 indicating a stronger relationship. Analyzing the odds ratio can provide valuable insights into the nature and strength of the association between the two binary variables in the contingency table.