Similarly, neither "number of independent scores that go into the estimate" nor "the number of parameters used as intermediate steps" are well-defined. Because "final calculation of a statistic" is not well-defined (it apparently depends on what algorithm one uses for the calculation), it can be no more than a vague suggestion and is worth no further criticism. We can dispose right away of some of the claims in the question. This is of especial interest because it is the first hint that DF is not any of the things claimed of it. An interesting aspect of some of these is the appearance of non-integral "degrees of freedom" (the Welch/Satterthwaite tests and, as we will see, the Chi-squared test). In spirit, these tests run a gamut from being exact (the Student t-test and F-test for Normal variates) to being good approximations (the Student t-test and the Welch/Satterthwaite tests for not-too-badly-skewed data) to being based on asymptotic approximations (the Chi-squared test). The Chi-squared test, comprising its uses in (a) testing for independence in contingency tables and (b) testing for goodness of fit of distributional estimates. The F-test (of ratios of estimated variances). The Chi-squared distribution (defined as a sum of squares of independent standard Normals), which is implicated in the sampling distribution of the variance. The Student t-test and its variants such as the Welch or Satterthwaite solutions to the Behrens-Fisher problem (where two populations have different variances). Where does the concept of degrees of freedom (DF) arise? The contexts in which it's found in elementary treatments are: I haven't the time (and there isn't the space here) to give a full exposition, but I would like to share one approach and an insight that it suggests. It takes a thoughtful person not to understand those quotations! Although they are suggestive, it turns out that none of them is exactly or generally correct. If possible, some mathematical formulations will help clarify the concept.Īlso do the three interpretations agree with each other? The bold words are what I don't quite understand. Many components need to be known before the vector is fully Random vector, or essentially the number of 'free' components: how Mathematically, degrees of freedom is the dimension of the domain of a In sample variance, is one, since the sample mean is the only Intermediate steps in the estimation of the parameter itself (which, That go into the estimate minus the number of parameters used as In general, the degrees of freedom of anĮstimate of a parameter is equal to the number of independent scores Information that go into the estimate of a parameter is called theĭegrees of freedom (df). Values in the final calculation of a statistic that are free to vary.Įstimates of statistical parameters can be based upon differentĪmounts of information or data. In statistics, the number of degrees of freedom is the number of That December, slavery in America was formally abolished with the adoption of the 13th Amendment.From Wikipedia, there are three interpretations of the degrees of freedom of a statistic: Although emancipation didn’t happen overnight for everyone-in some cases, enslavers withheld the information until after harvest season-celebrations broke out among newly freed Black people, and Juneteenth was born. Many enslavers from outside the Lone Star State had moved there, as they viewed it as a safe haven for slavery.Īfter the war came to a close in the spring of 1865, General Granger’s arrival in Galveston that June signaled freedom for Texas’s 250,000 enslaved people. In Texas, slavery had continued as the state experienced no large-scale fighting or significant presence of Union troops. However, as Northern troops advanced into the Confederate South, many enslaved people fled behind Union lines. The proclamation only applied to places under Confederate control and not to slave-holding border states or rebel areas already under Union control. But in reality, the Emancipation Proclamation didn’t instantly free any enslaved people.
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