Chi-Squared Test for Independence
To determine if there is a significant association between the sex of patients and their surgical outcomes (yes/no), we perform a chi-squared test for independence.
# Check the independence of variables using Pearson's Chi-squared test
chisq_test <- chisq.test(prop_table)
print(chisq_test)
This will output the results of the chi-squared test, including:
- The chi-squared statistic (X²), which measures the difference between observed and expected frequencies.
- The degrees of freedom (df) associated with the test.
- The p-value, indicating the probability of observing a result as extreme or more extreme than the one observed, assuming that there is no real association between the variables.
Interpretation of Results
If the p-value is less than a predetermined significance level (commonly set at 0.05), we reject the null hypothesis and conclude that there is a statistically significant association between the sex of patients and their surgical outcomes. Otherwise, we fail to reject the null hypothesis and do not find a statistically significant association.
Example:
Suppose we found the following output:
# X^2 N DF P.value
# 0.7727 1 121 0.3803
In this case, the p-value (0.3803) is greater than our chosen significance level of 0.05, indicating that we fail to reject the null hypothesis and do not find a statistically significant association between the sex of patients and their surgical outcomes.
Note:
If you prefer to use the prop_table table directly in your chi-squared test, you can modify the code as follows:
# Check the independence of variables using Pearson's Chi-squared test
chisq_test <- chisq.test(prop_table)
print(chisq_test)
This approach eliminates the need to create a separate data frame prop_table for the chi-squared test.
Last modified on 2023-09-14