Chi-Square Goodness of Fit Test in Statistics
03/01/2024 | By: FDS
The Chi-Square Goodness of Fit test is a statistical method used to assess how well empirical data aligns with expected theoretical distributions. This test is often applied to categories or groups to check whether observed frequencies significantly deviate from expected frequencies.
Process of the Chi-Square Goodness of Fit Test:
- Formulate Hypotheses: State a null hypothesis (\(H_0\)) asserting that observed and expected frequencies are equal and an alternative hypothesis (\(H_A\)) suggesting a significant deviation.
- Calculate Expected Frequencies: Based on an assumed distribution or model, calculate the expected frequencies for each category.
- Compute Chi-Square Value: Calculate the Chi-Square value, representing the sum of squared differences between observed and expected frequencies.
- Determine p-Value: Compare the Chi-Square value to the Chi-Square distribution to determine the p-value.
- Make Decision: Based on the p-value, decide whether to reject the null hypothesis. A low p-value indicates a significant deviation.
Applications of the Chi-Square Goodness of Fit Test:
- Genetics: Checking expected and observed ratios of genetic traits.
- Market Research: Verifying whether the distribution of product preferences deviates from the expected distribution.
- Quality Control: Examining whether the quality of products is consistent across different production batches.
- Medical Research: Assessing the distribution of disease cases in various population groups.
Example:
Suppose we conduct a survey on music preferences and want to check if the observed frequencies of music genres deviate from the expected frequencies. The Chi-Square Goodness of Fit test would be applicable in this scenario.