If a chi-square test produces a chi-square value of 7.83 with 4 degrees of freedom,

Above what chi-square value would you reject the chance hypothesis for an experiment with 7 degrees of freedom?

Key Concepts

Chi-Square Test

The chi-square test is a statistical method used to determine if there is a significant association between categorical variables. It compares the observed frequencies in each category to the expected frequencies, which are calculated under the null hypothesis. A higher chi-square value indicates a greater discrepancy between observed and expected data, suggesting that the null hypothesis may be rejected.

Degrees of Freedom

Degrees of freedom (df) refer to the number of independent values or quantities that can vary in an analysis without violating any constraints. In the context of the chi-square test, degrees of freedom are calculated as the number of categories minus one. They are crucial for determining the critical value of chi-square needed to assess significance at a given alpha level.

Critical Value

The critical value in a chi-square test is the threshold that the calculated chi-square statistic must exceed to reject the null hypothesis. This value is determined based on the desired significance level (commonly 0.05) and the degrees of freedom. For 7 degrees of freedom, the critical value can be found using chi-square distribution tables or statistical software, guiding researchers in their decision-making.