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Answer :
The chi-squared (χ²) test is a statistical test used to determine whether there is a significant association between categorical variables. For the chi-squared test to be valid, certain conditions regarding the sample size and expected frequencies must be met.
The correct condition for the validity of the chi-squared test is: B. n must be large enough so that for every cell the expected cell count will be equal to 5 or more.
Let's break this down further:
Expected Cell Count: The expected cell count is calculated under the assumption that the null hypothesis is true. It represents the expected frequency of observations in each category of the contingency table based on the marginal totals and the overall total.
Large Enough Sample Size: The sample size (n) must be large enough so that each expected count in the contingency table is at least 5. This ensures the approximation to the chi-squared distribution is adequate.
Why 5 is the Threshold: If expected counts are less than 5, the approximation to the chi-squared distribution may not be accurate, potentially leading to incorrect conclusions.
Applications: This guideline applies to various types of chi-squared tests, such as the chi-squared test for independence or the goodness-of-fit test.
In summary, to make the chi-squared test valid, you must have a sample size large enough that each expected frequency in your contingency table is at least 5. This helps ensure the test's statistical assumptions are met, allowing for reliable and meaningful results.
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