Which of the following is true about cross-tabulation?

Question

BlackTom AI · Accepted Answer

A cross-tabulation (contingency table) displays how cases are distributed across combinations of categorical variable levels, so the categories are defined to be mutually exclusive and collectively exhaustive.

1) Relevant concepts
- Contingency / cross-tabulation table: a matrix showing frequency counts (or proportions) of observations for combinations of categorical variable levels (e.g., rows = gender, columns = age group).
- Mutually exclusive: each observation belongs to only one category within a variable.
- Collectively exhaustive: the set of all categories covers the entire sample so every observation falls into some category.

2) Step-by-step reasoning
- Step 1: A cross-tabulation tallies observations by category combinations. If you have two categorical variables, each observation contributes one count to exactly one cell (row × column).
- Step 2: Because every observation must be counted somewhere, the sum of all cell frequencies equals the total sample size. That implies the subcategories together make up the entire dataset.
- Step 3: Therefore, a correct statement about cross-tabulation is that all subcategories together constitute the complete data set.

3) Intermediate logic steps (no numeric calculation)
- Let n be total observations. Let cells cij be counts in each cell. Then sum over all i,j of cij = n. This equality expresses that the subcategories collectively exhaust the data.

4) Why the correct answer is correct
- "All subcategories together must constitute the complete data set." directly expresses the collectively exhaustive property of the table and the requirement that cell counts sum to the total sample. This is a defining feature of cross-tabulations.

5) Why other options are incorrect
- "Each observation can be classified into many subcategories." contradicts mutual exclusivity; standard cross-tabs assign each observation to exactly one level per variable (unless special multiple-response coding is used, which is not the default).
- "The table displays the number of categorical variables between two observations." is incorrect phrasing: it displays counts of observations across levels of categorical variables, not “between two observations.”
- "A cross-tabulation table is often called a latent class model." is false: latent class models are statistical models for unobserved (latent) group membership, not simply a frequency table.

Conclusion: The correct answer is "All subcategories together must constitute the complete data set." This matches the provided answer.

Which of the following is true about cross-tabulation?单项选择题

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