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  2. Degrees of freedom (statistics) - Wikipedia

    en.wikipedia.org/wiki/Degrees_of_freedom...

    Here, the degrees of freedom arises from the residual sum-of-squares in the numerator, and in turn the n − 1 degrees of freedom of the underlying residual vector {¯}. In the application of these distributions to linear models, the degrees of freedom parameters can take only integer values. The underlying families of distributions allow ...

  3. Welch–Satterthwaite equation - Wikipedia

    en.wikipedia.org/wiki/Welch–Satterthwaite_equation

    In statistics and uncertainty analysis, the Welch–Satterthwaite equation is used to calculate an approximation to the effective degrees of freedom of a linear combination of independent sample variances, also known as the pooled degrees of freedom, [1] [2] corresponding to the pooled variance.

  4. Mixed-design analysis of variance - Wikipedia

    en.wikipedia.org/wiki/Mixed-design_analysis_of...

    In order to calculate the degrees of freedom for between-subjects effects, df BS = R – 1, where R refers to the number of levels of between-subject groups. [ 5 ] [ page needed ] In the case of the degrees of freedom for the between-subject effects error, df BS(Error) = N k – R, where N k is equal to the number of participants (also known as ...

  5. F-test - Wikipedia

    en.wikipedia.org/wiki/F-test

    To locate the critical F value in the F table, one needs to utilize the respective degrees of freedom. This involves identifying the appropriate row and column in the F table that corresponds to the significance level being tested (e.g., 5%). [6] How to use critical F values: If the F statistic < the critical F value Fail to reject null hypothesis

  6. Coefficient of determination - Wikipedia

    en.wikipedia.org/wiki/Coefficient_of_determination

    where df res is the degrees of freedom of the estimate of the population variance around the model, and df tot is the degrees of freedom of the estimate of the population variance around the mean. df res is given in terms of the sample size n and the number of variables p in the model, df res = n − p − 1. df tot is given in the same way ...

  7. Folded-t and half-t distributions - Wikipedia

    en.wikipedia.org/wiki/Folded-t_and_half-t...

    In statistics, the folded-t and half-t distributions are derived from Student's t-distribution by taking the absolute values of variates. This is analogous to the folded-normal and the half-normal statistical distributions being derived from the normal distribution .

  8. Deviance (statistics) - Wikipedia

    en.wikipedia.org/wiki/Deviance_(statistics)

    In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing.It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood.

  9. Studentized range distribution - Wikipedia

    en.wikipedia.org/wiki/Studentized_range_distribution

    Suppose that we take a sample of size n from each of k populations with the same normal distribution N(μ, σ 2) and suppose that ¯ is the smallest of these sample means and ¯ is the largest of these sample means, and suppose s² is the pooled sample variance from these samples. Then the following statistic has a Studentized range distribution.

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