# Tagged Questions

The term "degrees of freedom" is used to describe the number of values in the final calculation of a statistic that are free to vary.

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### Intuition or explanation of “rule of thumb” for loss of degrees of freedom in chi-square for model selection/knot placement?

A document I read many years ago (to do with actuarial education; sorry I can't link to a copy) used chi-square tests to assess lack of fit of various models to mortality rates which were treated ...
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### Examples of degrees of freedom [duplicate]

The idea of degrees of freedom is pretty well sunk into my head, but I was wondering could someone perhaps give me few easy examples on how one would determine the number of degrees of freedom? For ...
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### Degrees of freedom in theoretical sample variance (for use in F-distribution)

My question is essentially simple: suppose we have a sequence of heads and tails with an apparent chance of getting heads $\hat{p} = 0.5$. h h t h t t t h t t h ... How do we tell if this ...
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### Implication of difference in degrees of freedom on t-test results

I'm trying to figure out the practical meaning of less degrees of freedom regarding the results of t-test results. For example: If I have two dependent samples and would like to compare their means ...
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### Correct degrees of Freedom for Variance estimator in Ridge Regression

When I run a ridge regression on the following data using the Hoerl, Kennard and Baldwin estimator I only get the correct value of k when I use (n-p) where n is the number of observations and p the ...
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### Nonnegativity of model optimism

The following sounds like a very basic question in learning theory to me, so I am hoping someone can point out the obvious. Efron's "expected optimism" is the expected difference between the ...
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### degrees of freedom of covariance estimator

Several papers, such as this one have given the notion of, and a formula for the "degrees of freedom" of a regularized estimator. Roughly, the Zou et. al. paper suggests using SURE, and cites a result ...
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### Temporal autocorrelation in perMANOVA?

I have a data set where samples are collected once per year for 15 years at a number of sites. I am worried that these data are temporally autocorrelated and was trying to figure out if I need to ...
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### How to determine degree of freedom for a certain test of interaction?

The scenario is like this: I have a cohort with 2000 people, half of them taking DRUG, the other half not taking it. I would like to check interactions between DRUG and the other variables in the ...
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### Degrees of freedom for a weighted average

And yet another for the long list of degrees-of-freedom questions! Given an i.i.d. sample $x_1,..., x_n$ from an arbitrary real-valued distribution with expectation $\mu$, the sample mean can be ...
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### Should I use Welch's (1947) approximate degrees of freedom or Satterthwaite's (1946)?

I'm confused as to the correct formula for approximate degrees of freedom to use for Welch's t-test. Satterthwaite's (1946) formula is the most commonly cited formula, but Welch gave an alternative in ...
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### How to calculate the degree of freedom for Williams' Test

Williams' test is a multiple comparison test. My question is, when compare the Williams' test statistic with the tabulated critical values, which degree of freedom should I look for. In the SAS ...
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### HUGE number of degrees of freedom in MLM mixed model - is this correct?

We are doing a mixed multilevel modeling analysis, using SAS PROC MIXED with 145 subjects, and 255 observations per subjects. We used subjects as a random factor and had three continuous variables ...
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### Degrees of freedom in a simultaneous confirmatory factor analysis

I am performing a simultaneous confirmatory factor analysis to check whether the items of a survey refer to intended separate underlying concepts without cross loading on the concepts. Since I am ...
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### Fieller's Theorem Degrees of Freedom

In a previous question I was trying to figure out how to compute the confidence interval of a ratio. Having come to the conclusion that the correct way to do this is Fieller's Theorem, I realize I'm ...
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### Degrees of freedom due to treatment

let $a$ be the number of treatments. In Randomized Complete Block Design(RCBD), degrees of freedom due to treatment is $(a-1)$ . let $k$ be the number of treatments exactly in each block in a ...
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### Standard deviation and n-1 : degrees of freedom or unbiased? [duplicate]

I am trying to understand if the division for n-1 in the calculation of standard deviation related to degrees of freedom, unbiasing of the estimator, or both. I understand what is a degree of ...
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I'm running mixed design ANOVA using R. Somehow, I got incorrect values for the Df. There are two factors: time (within subjects), and ...
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### DF for regression SS in multiple linear regression when sigma is known

In the typical environment for multiple linear regression, we have that $Y = \mathbf{X}\beta + \epsilon$ where $\epsilon$ is iid $\mathcal{N}(0, \sigma^2I)$ where $\sigma^2$ is unknown. In this case, ...
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### Prediction error and covariance penalty

I am studying the paper by Efron: The Estimation of Prediction Error: Covariance Penalties and Cross-Validation. To estimate prediction error in the Gaussian case by Mallows' $C_p$ or other methods ...
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### Degrees of freedom of a linear function of four independent random variables

This is basically a modified version of a previously unanswered question I posed here, as I'm starting to have second thoughts about my methodology. In summary, I have four random variables: Xideal, ...
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### What do I use for degrees of freedom in ANOVA?

Just figuring out statistics on my own after doing a psycholinguistics study for my undergrad thesis (never taken a statistics class). Basically, the experiment recorded subjects' reaction times to ...
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### Increasing degrees of freedom with mixed models

I used the glmulti package in R to generate a linear model with interactions. The response variable has 21 observations, set against 5 input variables, one of which is a binary factor while the rest ...
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### Degrees of freedom ANOVA table for regression

I've calculated the following ANOVA table for a linear regression in R: ...
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### SAS and T-Tests - Degrees of Freedom

Why is it that in a normal t-test we have n-2 degrees of freedom while in the SAS output, and consequently the confidence interval constructed from this output, we end up using our 'error' degrees of ...
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### Bayesian inference and degrees of freedom

While learning frequentist linear regressions, one thing the professors always talked about was about the number of degrees of freedom, I never saw this expression in a bayesian book though. Perhaps ...
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### Degrees of freedom for standard deviation of sample

would someone please explain why the degrees of freedom for a random sample is n-1 instead of n ? I'm looking for an explanation that is intuitive and easily understood by a high school student.
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### How is the Df computed in a mixed model?

The following is the output for a mixed model example. The only difference between fm1 and fm2 is the random factor "URBAN", why the df for fm2 is 5 but not 4? Any help would be great. ...
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### Which are the correct sum of squares for repeated measures ? (balanced example)

Below are three ways to fit a MANOVA model in R and to extract ANOVA tables from the fitted model. The design is balanced. All methods give different results. The data are 5 groups of 4 individuals ...
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### How to compute df for ARIMA models?

Running this example from Hyndman's textbook in Chapter 9.1: ...
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### Generalized Linear Model in SPSS with common values among predictors treated as subpopulations. Why?

I am teaching a class on logistic regression with SPSS. The textbook supplies a sample data set with a binary predictor and two numeric covariates. The sample contains 1000 rows and a number of these ...
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### Markov chain model likelihood ratio test

Suppose I am using two Markov Chain Models, one with order $k=1$ and a second one with order $k=2$. I am "reducing" the higher order model to a $k=1$ model in order to have easier calculation ...
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### How to assign degrees of freedom for two-way ANOVA with two within-subjects factors?

I have an experiment with 44 subjects and two within-subject factors, condition (3 levels) and round (6 levels). It is fully crossed such that each person completes one of each task condition in each ...
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### Likelihood ratio test for sex ratio

I am trying to solve this problem: Assume that each child is male with probability $p$ independently of all other children. We observed 19711 male births out of a total of 38562 births in American ...
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### Include Type B in effective degrees of freedom for expanded uncertainty?

This post has sat unanswered for a couple days in the TalkStats forum so I'm hoping somebody here can help me out. I'm looking for assistance in clarifying how Type B uncertainty is incorporated into ...
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### Why is it valid to account for k-1 intercepts w/ only 1 random intercept parameter?

I possess a basic understanding of random vs. fixed effects, and how to code random effects models in SAS. However, I'm having trouble wrapping my head around the derivation of random effects terms, ...
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### What are the degrees of freedom of a distribution?

I am dealing right now with a lot of distributions, e.g., $F$, $t$, $\chi^2$. I was wondering why do these degrees of freedom signify for distributions such as the $F(m,n)$ distribution?
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### How to calculate minF' with corrected degrees of freedom?

If you're working with crossed random effects (a sample of words and a sample of people), you should report a minF' rather than just your F1 and F2 values according to Clark (1973), Raaijmakers et al. ...
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### Weird denominator degrees of freedom in SAS glimmix

I´m trying to learn generalized mixed models in SAS and I have now bumbed into a situation that I cannot figure out by myself. So I was thinking that maybe some of you could help me forward. I´m ...
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### Degrees of freedom in quadratic regression simultaneous confidence bands

I have been working on an inverse regression addon for SPSS and using this paper heavily: I. Lavagnini, F. Magno, A statistical overview on univariate calibration, inverse regression, and detection ...
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### Differences between PROC Mixed and lme / lmer in R - degrees of freedom

Note : this question is a repost, as my previous question had to be deleted for legal reasons. While comparing PROC MIXED from SAS with the function lme from the ...
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### How many degrees of freedom with many subjects and many tests?

Lets say I run an experiment testing accuracy of hitting targets of two different sizes. I have 10 participants and 40 targets, 15 small and 25 large. I then have the number of misses for each target ...
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### Interpreting group level coefficents/degrees of freedom in mixed effects model

I was hoping you could provide some information on how one should interpret and present group level coefficients and degrees of freedom in a mixed effects (in my case: logistic) model. I'm fully ...
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### Likelihood Ratio Testing in Multinomial logistic regression using SPSS

I am doing multinomial logistic regression. Dependent variable is categorical with 6 categories. 6 Independent variables are measured on an interval scale (included as covariates in SPSS) Now I am ...
I know that distribution of sample variance $$\sum\frac{(X_i-\bar{X})^2}{\sigma^2}\sim \chi^2_{(n-1)}$$ $$\sum\frac{(X_i-\bar{X})^2}{n-1}\sim \frac{\sigma^2}{n-1}\chi^2_{(n-1)}$$ It's from the ...