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Degrees Of Freedom

Ankit0

Definition:

Degrees of freedom (df) is a measure of the number of independent variables that are free to vary in a sample, given the constraints imposed by the sample size and any other statistical assumptions.

Formula:

Degrees of freedom (df) = n – r

where:

  • n is the sample size
  • r is the number of parameters estimated from the sample (e.g., the number of intercepts and slopes in a regression model)

Explanation:

  • Degrees of freedom (df) are used to calculate the degrees of freedom for a t-statistic, chi-square statistic, or F-statistic.
  • The number of degrees of freedom is equal to the sample size minus the number of parameters estimated from the sample.
  • For example, if a sample of 20 observations is used to estimate a mean and a standard deviation, then the degrees of freedom for the t-statistic would be 18.
  • Degrees of freedom are important in statistical inference because they determine the critical values for probability distributions.

Examples:

  • T-statistic: The degrees of freedom for a t-statistic are equal to the sample size minus 1.
  • Chi-square statistic: The degrees of freedom for a chi-square statistic are equal to the number of categories minus 1.
  • F-statistic: The degrees of freedom for an F-statistic are equal to the number of groups minus 1.

Additional Notes:

  • Degrees of freedom can be positive or negative.
  • Negative degrees of freedom are not valid.
  • The degrees of freedom are used to calculate the p-value.
  • The degrees of freedom are a key concept in statistics and are used in a wide variety of statistical tests.

FAQs

  1. What is degrees of freedom?

    Degrees of freedom (DoF) refers to the number of independent values or variables that can vary in a system without violating constraints. It is used in statistics, physics, and engineering to describe how a system can move or change.

  2. What is the degree of freedom of motion?

    The degree of freedom of motion refers to the number of independent movements a body or object can make. For example, in 3D space, a rigid body has six degrees of freedom: three translational (moving along x, y, and z axes) and three rotational (rotating around those axes).

  3. What does “df” mean in statistics?

    In statistics, “df” stands for degrees of freedom. It represents the number of independent values that can vary in the calculation of a statistic, such as in a t-test or ANOVA.

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