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Statistics & Probability

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Statistics & Probability

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.

Results update live as you type.
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Your inputs

How it works

  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

Frequently asked questions

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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Results

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Coefficient of Alienation

0.75

Coefficient of Determination (r²)0.2500
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How it works

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.

Formulas

The math behind this calculator, written out so you can verify the result.

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

Real-world use cases

Where this calculation shows up in everyday life.

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.

Tips and common mistakes

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.

Assumptions and limitations

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