Question

Chi-Square Test in 2x2 Contingency Tables:

In
2
×
2
2×2 contingency tables (i.e., two categorical variables with two categories each), it's essential that no expected cell values fall below a certain threshold to test hypotheses using a chi-square test of independence. What is this threshold value, and why is it important?

Answer 1

For a 2x2 contingency table in a chi-square test of independence, expected cell values must be at least five to ensure the chi-square distribution approximates the test statistic well for accurate results.

Step-by-step explanation:

In the context of a 2×2 contingency table using a chi-square test of independence, the threshold value for expected cell frequencies is at least five. This requirement is vital because the chi-square test assumes that the expected frequencies are large enough so that the approximation of the sampling distribution of the test statistic by the chi-square distribution is reasonable. If expected cell values are below this threshold, the test may not perform well, and the chi-square approximation might not be accurate, which could lead to incorrect conclusions about the independence of the variables.