The article by Hae-Young Kim from the Department of Health Policy and Management at Korea University discusses the chi-squared test and Fisher’s exact test, which are used to compare proportions of categorical outcomes across different independent groups. The chi-squared test is suitable for large samples and assumes independence between variables, while Fisher’s exact test is more accurate for small samples and does not rely on approximations. 1. **Independency Test**: The chi-squared test assesses whether the distribution of a categorical variable is independent of another variable. If the observed frequencies are close to the expected frequencies, the variables are considered independent. The test statistic is calculated as χ² = ∑ (O-E)² / E, where O is the observed frequency and E is the expected frequency. The degrees of freedom are (r-1)(c-1), and the null hypothesis (H₀) is that the variables are independent, while the alternative hypothesis (H₁) is that they are not. 2. **Effect Size**: Measures of effect size for the chi-squared test include Phi (φ), Cramer’s V (V), and odds ratio (OR). φ and V are used for 2x2 tables, while OR can be used for larger tables. For example, φ = √(χ² / n) and V = √(χ² / n·df), where n is the total number of observations and df is the degrees of freedom. 3. **Post-hoc Pairwise Comparison**: When comparing three or more levels of a variable, post-hoc pairwise comparisons are necessary. This involves breaking down the data into multiple 2x2 contingency tables and performing chi-squared tests with a Bonferroni corrected alpha level. Fisher’s exact test is used for small samples and does not rely on approximations. It uses the hypergeometric distribution to assess the null hypothesis of independence. This test is particularly useful when more than 20% of cells have expected frequencies less than 5. Many statistical packages provide Fisher’s exact test for 2x2 tables, but it is available for larger tables through web pages like 'Social Science Statistics'. The article provides a detailed guide on how to perform these tests using IBM SPSS Statistics, including steps for data input, descriptive statistics, Crosstabs, and effect size calculations.The article by Hae-Young Kim from the Department of Health Policy and Management at Korea University discusses the chi-squared test and Fisher’s exact test, which are used to compare proportions of categorical outcomes across different independent groups. The chi-squared test is suitable for large samples and assumes independence between variables, while Fisher’s exact test is more accurate for small samples and does not rely on approximations. 1. **Independency Test**: The chi-squared test assesses whether the distribution of a categorical variable is independent of another variable. If the observed frequencies are close to the expected frequencies, the variables are considered independent. The test statistic is calculated as χ² = ∑ (O-E)² / E, where O is the observed frequency and E is the expected frequency. The degrees of freedom are (r-1)(c-1), and the null hypothesis (H₀) is that the variables are independent, while the alternative hypothesis (H₁) is that they are not. 2. **Effect Size**: Measures of effect size for the chi-squared test include Phi (φ), Cramer’s V (V), and odds ratio (OR). φ and V are used for 2x2 tables, while OR can be used for larger tables. For example, φ = √(χ² / n) and V = √(χ² / n·df), where n is the total number of observations and df is the degrees of freedom. 3. **Post-hoc Pairwise Comparison**: When comparing three or more levels of a variable, post-hoc pairwise comparisons are necessary. This involves breaking down the data into multiple 2x2 contingency tables and performing chi-squared tests with a Bonferroni corrected alpha level. Fisher’s exact test is used for small samples and does not rely on approximations. It uses the hypergeometric distribution to assess the null hypothesis of independence. This test is particularly useful when more than 20% of cells have expected frequencies less than 5. Many statistical packages provide Fisher’s exact test for 2x2 tables, but it is available for larger tables through web pages like 'Social Science Statistics'. The article provides a detailed guide on how to perform these tests using IBM SPSS Statistics, including steps for data input, descriptive statistics, Crosstabs, and effect size calculations.