Statistical notes for clinical researchers: Chi-squared test and Fisher's exact test

Statistical notes for clinical researchers: Chi-squared test and Fisher's exact test

2017 | Hae-Young Kim
This article provides an overview of the chi-squared test and Fisher's exact test for clinical researchers. Both tests are used to assess the independence between two categorical variables. The chi-squared test is an approximation method suitable for large samples, while Fisher's exact test is an exact method used for small samples. The chi-squared test compares the distribution of a categorical variable across different groups. It tests the null hypothesis of independence between the variables. The test statistic is calculated as the sum of (O-E)^2/E, where O is the observed frequency and E is the expected frequency. The expected frequency is calculated based on the marginal proportions of the contingency table. The test statistic follows a chi-squared distribution, and the degrees of freedom are (r-1)(c-1), where r and c are the number of rows and columns in the contingency table. If the calculated chi-squared statistic is greater than the critical value, the null hypothesis of independence is rejected. The chi-squared test requires a sufficiently large sample size. If more than 20% of cells have expected frequencies less than 5, the test may not be appropriate. Effect size measures such as Phi, Cramer's V, and odds ratio can be used to quantify the magnitude of the association. Fisher's exact test is used when the chi-squared test is not appropriate, especially when more than 20% of cells have expected frequencies less than 5. It uses the hypergeometric distribution to calculate the exact probability of the observed data. Fisher's exact test is particularly useful for 2x2 contingency tables but can also be applied to larger tables using online tools. Both tests are used in clinical research to determine if there is a significant association between two categorical variables. The choice between the two tests depends on the sample size and the expected frequencies in the contingency table.This article provides an overview of the chi-squared test and Fisher's exact test for clinical researchers. Both tests are used to assess the independence between two categorical variables. The chi-squared test is an approximation method suitable for large samples, while Fisher's exact test is an exact method used for small samples. The chi-squared test compares the distribution of a categorical variable across different groups. It tests the null hypothesis of independence between the variables. The test statistic is calculated as the sum of (O-E)^2/E, where O is the observed frequency and E is the expected frequency. The expected frequency is calculated based on the marginal proportions of the contingency table. The test statistic follows a chi-squared distribution, and the degrees of freedom are (r-1)(c-1), where r and c are the number of rows and columns in the contingency table. If the calculated chi-squared statistic is greater than the critical value, the null hypothesis of independence is rejected. The chi-squared test requires a sufficiently large sample size. If more than 20% of cells have expected frequencies less than 5, the test may not be appropriate. Effect size measures such as Phi, Cramer's V, and odds ratio can be used to quantify the magnitude of the association. Fisher's exact test is used when the chi-squared test is not appropriate, especially when more than 20% of cells have expected frequencies less than 5. It uses the hypergeometric distribution to calculate the exact probability of the observed data. Fisher's exact test is particularly useful for 2x2 contingency tables but can also be applied to larger tables using online tools. Both tests are used in clinical research to determine if there is a significant association between two categorical variables. The choice between the two tests depends on the sample size and the expected frequencies in the contingency table.
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[slides and audio] Statistical notes for clinical researchers%3A Chi-squared test and Fisher's exact test