How do you calculate the critical value of X^2 at the 5% level of significance in a chi squared? And how do you calculate the degree of freedom?
The textbook wording makes no sense and doesn't show it fully and I've read it over at least 10 times now to try to figure out how they get it.
Thanks for the help!
Calculating the critical value in a chi-squared test requires two steps: determining the degree of freedom and finding the corresponding critical value from a chi-squared distribution table or using statistical software.
1. Degree of Freedom (df):
To calculate the degree of freedom in a chi-squared test, you need to know the number of categories or groups involved. In a contingency table or a chi-squared test of independence, the degree of freedom is equal to the product of the number of categories minus one for each variable. For example, if you have a 2x3 contingency table (2 rows and 3 columns), the degrees of freedom would be (2-1) x (3-1) = 2.
2. Critical Value:
Once you know the degree of freedom, you can find the critical value either from a chi-squared distribution table or by using statistical software.
a) Chi-Squared Distribution Table: The table provides critical values for different levels of significance (e.g., 5%, 1%) and for various degrees of freedom. Locate the row corresponding to your degree of freedom and find the intersection with the column representing the desired significance level (e.g., 0.05 for 5% level). The value at this intersection is your critical value.
b) Statistical Software: Many statistical software packages can calculate the critical value directly. For example, using R, you can use the `qchisq` function with the desired significance level and degrees of freedom to obtain the critical value.
Please note that chi-squared tests are typically right-tailed, so the critical value represents the value beyond which you would reject the null hypothesis.
I hope this explanation clarifies the process of calculating the critical value and degree of freedom in a chi-squared test.