Final answer:
In creating a Frequency Distribution Table, categories must be set such that values don't overlap, and every possible outcome is represented once. This enables accurate statistical analysis, particularly for tests of independence and when distinguishing between marginal and conditional distributions in bivariate data.
Step-by-step explanation:
When setting up the categories for a Frequency Distribution Table, one must make sure that values cannot overlap between categories. This is crucial for ensuring that each datum is accounted for properly and that the resulting frequency distribution accurately reflects the collected data. The process of creating categories in a frequency distribution table involves deciding how to group data so that similar values are counted together, and different values are counted separately. To conduct a test of independence or analyze marginal distributions, it is essential to have non-overlapping categories and usually, to combine categories so that each cell has an expected value of at least five. This helps satisfy the requirement in statistical tests like chi-square that each category has a sufficient count to maintain the validity of the test results.
Additionally, categories must be comprehensive and mutually exclusive, ensuring that all possible outcomes or measurements are covered and that no data point can belong to more than one category. When one works with bivariate data and sets up a two-way table, understanding the difference between marginal and conditional distributions becomes relevant. Marginal frequencies or distributions are found in the margins of the frequency distribution table and often are the totals by row or column. In contrast, conditional distributions focus on subpopulations.