统计与概率
已验证计算器，公式透明
Coefficient of Alienation Calculator.
Calculates the coefficient of alienation (1 - r²) from a Pearson correlation coefficient, indicating the proportion of variance not shared between two variables.
您的输入
工作原理
- 1
Enter the Pearson correlation coefficient (r) between -1 and 1.
- 2
Square the correlation coefficient to get r².
- 3
Subtract r² from 1 to obtain the coefficient of alienation.
- 4
The result represents the proportion of variance not shared between the variables.
1 - r^2常见问题
What does the coefficient of alienation mean?
It measures the proportion of variance in one variable not explained by the other variable. A higher value indicates less shared variance.
How is it related to the coefficient of determination?
The coefficient of determination (r²) is the proportion of shared variance, and the coefficient of alienation is 1 - r². They sum to 1.
Can the coefficient of alienation be negative?
No, because r² is always between 0 and 1, so 1 - r² is always between 0 and 1.
结果
公式已检查估算仅供参考——重要决策请咨询专业人士。
工作原理
Calculates the coefficient of alienation (1 - r²) from a Pearson correlation coefficient, indicating the proportion of variance not shared between two variables.
- Enter the Pearson correlation coefficient (r) between -1 and 1.
- Square the correlation coefficient to get r².
- Subtract r² from 1 to obtain the coefficient of alienation.
- The result represents the proportion of variance not shared between the variables.
公式
此计算器背后的数学公式，供您核对结果。
Coefficient of Alienation
KA quantifies the lack of association between two variables. It is the complement of the coefficient of determination.
Example:
Input: r = 0.5
Calculation: 1 - 0.5² = 1 - 0.25
Result: 0.75
实际应用场景
此计算在日常生活中的应用。
Assessing prediction accuracy
In regression, a high coefficient of alienation indicates poor predictive power of the model.
Example: r = 0.3 gives KA = 0.91, meaning 91% of variance is unexplained.
Comparing variable relationships
Use KA to compare how strongly different pairs of variables are related.
Example: Compare r = 0.6 (KA=0.64) vs r = 0.8 (KA=0.36).
Educational statistics
Helps students understand the concept of variance explained in correlation.
Example: Illustrate with r = 0.7, KA = 0.51.
提示与常见错误
Tips
- Remember that r must be between -1 and 1.
- A coefficient of alienation close to 0 indicates a strong relationship.
- Use the secondary result r² to see the proportion of shared variance.
- This calculator is for educational purposes; always consider context.
Common Mistakes to Avoid
- Forgetting to square r before subtracting from 1.
- Using the absolute value of r instead of squaring.
- Interpreting the coefficient of alienation as a percentage without multiplying by 100.
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.