Final answer:
In a chi-square test, an increase in the chi-square value suggests a larger discrepancy between observed and expected values, often leading to the rejection of the null hypothesis, indicating a statistically significant result.
Step-by-step explanation:
When the value of χ2 (chi-square) increases, it suggests a greater divergence between the observed values and the expected values under the null hypothesis. The chi-square test is often used to determine the likelihood that the observed distribution of data diverges significantly from the expected distribution. If the chi-square value increases past a certain critical value, which is determined by the degrees of freedom and the significance level (usually 0.05), we would reject the null hypothesis. This is because a high chi-square value indicates that the differences between observed and expected values are too large to be due to chance alone, implying that the variables being tested are likely not independent.
An increase in the chi-square statistic indicates a lower probability of the null hypothesis being true, and thus a higher chance of finding a statistically significant result. However, it's also important to check the degrees of freedom and ensure that the expected frequency in each category is at least five to validate the test results.