What is the chi-square goodness-of-fit test used for?

What is the chi-square goodness-of-fit test used for?

• A. To test whether two categorical variables are independent.
• B. To test whether means of two groups are equal.
• C. To assess if two samples come from the same continuous distribution using a Kolmogorov-Smirnov test.
• D. To test whether observed categorical frequencies match expected frequencies under a specified distribution.

Answer: (D)

The chi-square goodness-of-fit test checks whether the observed frequencies in categorical data match what you would expect under a specified distribution. You start with expected counts for each category based on a theoretical or hypothesized distribution, then compute the test statistic by summing (observed − expected)² / expected across all categories. A large value suggests the observed data do not fit the specified distribution, and you assess significance with the chi-square distribution (using appropriate degrees of freedom, typically number of categories minus one minus any parameters estimated from the data). This test also requires sufficiently large expected counts (generally at least five per category) for the approximation to be reliable. Other tests describe different situations: testing independence between two categorical variables, comparing means between groups, and comparing a sample to a continuous distribution with a Kolmogorov-Smirnov test. The goodness-of-fit test specifically targets whether categorical frequencies align with a predefined distribution, matching the described scenario.

The chi-square goodness-of-fit test checks whether the observed frequencies in categorical data match what you would expect under a specified distribution. You start with expected counts for each category based on a theoretical or hypothesized distribution, then compute the test statistic by summing (observed − expected)² / expected across all categories. A large value suggests the observed data do not fit the specified distribution, and you assess significance with the chi-square distribution (using appropriate degrees of freedom, typically number of categories minus one minus any parameters estimated from the data). This test also requires sufficiently large expected counts (generally at least five per category) for the approximation to be reliable.

Other tests describe different situations: testing independence between two categorical variables, comparing means between groups, and comparing a sample to a continuous distribution with a Kolmogorov-Smirnov test. The goodness-of-fit test specifically targets whether categorical frequencies align with a predefined distribution, matching the described scenario.