What is the formula for degrees of freedom in the chi-squared goodness-of-fit test?

What is the formula for degrees of freedom in the chi-squared goodness-of-fit test?

• A. n - 1
• B. n + 1
• C. 2n
• D. n

Answer: (A)

In the context of the chi-squared goodness-of-fit test, the degrees of freedom are calculated using the formula n - 1, where n represents the number of categories or groups in the data set being analyzed. This formula arises from the fact that when estimating a distribution based on sample data, each additional category reduces the degrees of freedom by one due to the requirement that the sum of the observed proportions (or counts) must equal the total number of observations. Using this formula allows statisticians to accurately determine the appropriate chi-squared distribution to reference when calculating the p-value, which ultimately informs decisions about the null hypothesis. Each category contributes to the overall chi-square statistic, but since one parameter (the total count) is fixed once the other counts are determined, one degree of freedom is lost. In summary, n - 1 accurately reflects the degrees of freedom for the chi-squared goodness-of-fit test, allowing for proper statistical analysis and inference.

In the context of the chi-squared goodness-of-fit test, the degrees of freedom are calculated using the formula n - 1, where n represents the number of categories or groups in the data set being analyzed. This formula arises from the fact that when estimating a distribution based on sample data, each additional category reduces the degrees of freedom by one due to the requirement that the sum of the observed proportions (or counts) must equal the total number of observations.

Using this formula allows statisticians to accurately determine the appropriate chi-squared distribution to reference when calculating the p-value, which ultimately informs decisions about the null hypothesis. Each category contributes to the overall chi-square statistic, but since one parameter (the total count) is fixed once the other counts are determined, one degree of freedom is lost.

In summary, n - 1 accurately reflects the degrees of freedom for the chi-squared goodness-of-fit test, allowing for proper statistical analysis and inference.