Chi-Square Test Assumptions Explained

The Chi-square test of significance is used to analyze categorical data. For the test results to be valid, certain assumptions about the data must be met. Let's examine the provided assumptions:

Assumption Analysis

• a. Data should be continuous: This is incorrect. The Chi-square test is designed for categorical data, analyzed in terms of frequencies or counts, not continuous measurements.
• b. Data has to be in frequencies: This is a core assumption. The Chi-square test analyzes observed frequencies (counts) of cases falling into different categories.
• c. All observations should be independent: This is a critical assumption. Each observation must be independent of all other observations; one case should not influence another.
• d. Obtained frequencies are equal in all cells: This is incorrect. While observed frequencies are compared to expected frequencies, there's no requirement for observed frequencies to be equal across all categories. A related assumption concerns minimum *expected* frequencies (typically >= 5).
• e. Data has to be in ratio scale: This is incorrect. The Chi-square test works with nominal (categorical) data presented as frequencies, not necessarily data measured on a ratio scale.

Conclusion on Assumptions

Based on the analysis, the necessary assumptions for the Chi-square test from the given options are:

• b. Data has to be in frequencies.
• c. All observations should be independent.

Therefore, the correct code representing these assumptions is 'b and c'.