统计与概率
已验证计算器，公式透明
Chi-Square Statistic Calculator.
Calculates the chi-square statistic for a contingency table or goodness-of-fit test based on observed and expected frequencies.
您的输入
工作原理
- 1
Enter the observed frequency for a category.
- 2
Enter the expected frequency for that category.
- 3
The calculator computes (observed - expected) squared divided by expected.
- 4
The result is the chi-square contribution for that cell.
((observed - expected)^2) / expected常见问题
What does the chi-square statistic measure?
It measures the discrepancy between observed and expected frequencies. A larger value indicates a bigger difference.
Can I use this for multiple categories?
This calculator handles one cell at a time. For a full test, sum the contributions from all cells.
What if the expected frequency is zero?
Expected frequencies should be greater than zero. The calculator uses a minimum of 0.0001 to avoid division by zero.
工作原理
Calculates the chi-square statistic for a contingency table or goodness-of-fit test based on observed and expected frequencies.
- Enter the observed frequency for a category.
- Enter the expected frequency for that category.
- The calculator computes (observed - expected) squared divided by expected.
- The result is the chi-square contribution for that cell.
公式
此计算器背后的数学公式，供您核对结果。
Chi-square contribution
For each category, subtract the expected frequency from the observed, square the difference, and divide by the expected frequency.
Example:
Input: O = 50, E = 40
Calculation: (50 - 40)² / 40 = 100 / 40
Result: 2.5
实际应用场景
此计算在日常生活中的应用。
Goodness-of-fit test
Compare observed counts to expected counts from a theoretical distribution.
Example: Testing if a die is fair.
Test of independence
Assess whether two categorical variables are related in a contingency table.
Example: Checking if gender affects product preference.
Homogeneity test
Compare the distribution of a categorical variable across different populations.
Example: Comparing survey responses across age groups.
提示与常见错误
Tips
- Ensure expected frequencies are at least 5 for validity in many tests.
- Sum the contributions from all cells to get the total chi-square statistic.
- Use the degrees of freedom to determine the p-value from a chi-square distribution table.
Common Mistakes to Avoid
- Using percentages instead of raw frequencies.
- Forgetting to square the difference between observed and expected.
- Dividing by observed instead of expected.
假设与限制
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.