The choice between the chi-square test and the point-biserial correlation depends on the nature of your data and the specific research question you're trying to address. These tests are used for different types of relationships and data scenarios:
Chi-Square Test: Type of Data: The chi-square test is used when you have categorical data, often organized into contingency tables. Research Question: It's used to assess the association or independence between two categorical variables. Examples: You might use the chi-square test to analyze the relationship between gender (categorical) and voting preference (categorical). Strength: It's a powerful tool for identifying if there's a statistically significant association between two categorical variables.
Point-Biserial Correlation: Type of Data: The point-biserial correlation is used when you have one categorical variable and one continuous variable (which can be dichotomously coded as 0 and 1). Research Question: It's used to assess the strength and direction of the relationship between a continuous variable and a binary categorical variable. Examples: You might use the point-biserial correlation to analyze the relationship between height (continuous) and basketball player status (binary: plays or doesn't play basketball). Strength: It provides information about the strength of the linear relationship between a continuous and a binary variable.
In summary, if you're looking to assess the relationship between two categorical variables, the chi-square test is appropriate. If you're interested in understanding the strength and direction of the relationship between a continuous variable and a binary categorical variable, the point-biserial correlation is more suitable.
Remember that the choice of statistical test should align with your research question and the type of data you have. Additionally, it's always a good practice to consider the assumptions of the chosen test and to interpret the results in the context of your research hypothesis.
Neither is better or worse-- it all depends on which is most appropriate to answer the research question. Correlations look at the relationship between two variables, with point biserial used when 1 of those variables is continuous and the other is dichotomous (categorial, with only two options). Chi-square looks at the relationship/differences across two categorical variables without restricting the number of response options. Technically, correlation focuses on the shared pattern of change (connection in trends/similarities/relationship), while chi-square tries to determine the differences in the distributions.