Final answer:
A statistically significant chi-square statistic obtained from a two-variable analysis signifies independence between variables.
Step-by-step explanation:
A statistically significant chi-square statistic obtained from a two-variable analysis signifies independence between variables.
When conducting a test of independence using the chi-square distribution, the null hypothesis states that the two factors are independent. A statistically significant chi-square statistic indicates that there is evidence to reject the null hypothesis and conclude that the variables are not independent.
For example, if we conduct a chi-square test to analyze the relationship between gender and voting preference, and obtain a statistically significant chi-square statistic, we can conclude that there is a relationship between gender and voting preference, and they are not independent of each other.