In the context of a chi-square test for independence, what does the term 'independence' indicate?

In the context of a chi-square test for independence, the term 'independence' refers to the idea that there is no relationship between two nominal variables. When we say that two variables are independent, it means that the occurrence or value of one variable does not affect the occurrence or value of the other variable. Therefore, if you were to examine the distribution of one variable across the categories of another variable, you would expect to see a similar distribution regardless of the category of the second variable if they are truly independent.

The chi-square test evaluates the observed frequencies of data against the expected frequencies under the assumption of independence. If the test yields a significant result, it indicates that there is an association between the variables, which contradicts the notion of independence. This test is particularly useful for categorical data, allowing researchers to understand whether the distributions of these variables are related or not.

In regard to the other options, while they touch on different aspects related to statistical analysis, they do not accurately reflect what 'independence' means in the context of a chi-square test for independence. For instance, stating that there is a significant relationship (the first choice) contradicts the definition of independence, and suggesting that one variable influences the other (the third choice