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Статистика и вероятность

Проверенный калькулятор с прозрачной формулой

Статистика и вероятность

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.

Результаты обновляются в реальном времени по мере ввода.
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Ваши данные

Как это работает

  1. 1

    Enter the Pearson correlation coefficient (r) between -1 and 1.

  2. 2

    Square the correlation coefficient to get r².

  3. 3

    Subtract r² from 1 to obtain the coefficient of alienation.

  4. 4

    The result represents the proportion of variance not shared between the variables.

1 - r^2

Часто задаваемые вопросы

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.

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Результаты

Формула проверена

Coefficient of Alienation

0,75

Coefficient of Determination (r²)0,2500
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Как это работает

Calculates the coefficient of alienation (1 - r²) from a Pearson correlation coefficient, indicating the proportion of variance not shared between two variables.

  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.

Формулы

Математика, лежащая в основе этого калькулятора, изложена так, чтобы вы могли проверить результат.

Coefficient of Alienation

KA = 1 - r²

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

Примеры из реальной жизни

Где этот расчет встречается в повседневной жизни.

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.

Советы и частые ошибки

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.

Допущения и ограничения

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.