Questions tagged [degrees-of-freedom]
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. Use also for "effective degrees of freedom".
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CFA: chi-square value is 0 but with degrees of freedom
I want to do a SEM analysis with an actor-partner interdependence model in Mplus. I managed to calculate it and everything seems right if I look at the means, SD's, effects, etc. But I have a problem ...
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What are the degrees of freedom to consider for a G-test when some cells have expected values of 0?
Let's say I conduct a survey where people can mention their favorite
color among four options (red, green, blue, yellow).
After collecting the data, I create a contingency table crossing
gender with ...
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Pooled Kurtosis Estimator Using Pooled Cumulant Estimators
I am trying to come up with a statistically sensible pooled kurtosis estimator that is based on pooled cumulant estimators.
Specifically, I have unbiased estimators of the second and fourth cumulant ...
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Very small degrees of freedom when using yuen function in WRS2 package of R
I'm trying to run a number of independent samples t-tests. I'm using the yuen function in the WRS2 package because my data are non-normal and ordinal. My sample ...
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p-value of pearson correlation of correlated samples
I'm not completely sure if this question has been asked before, but I couldn't find one that suit my problem so far.
So basically I am doing single cell analysis, and I have roughly > 100000 cells ...
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Understanding degrees of freedom of F-statistic in Linear Regression
I was reviewing linear regression and I wanted to dig deeper into the F test that many software suites provide. I am aware that many sources comment on the degrees of freedom, but I haven't really ...
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Splines, logistic regression and sample size considerations
I have around 500 observations with a binary outcome at 25% prevalence and will be building an internally validated prediction model. I want to use splines to model non linearity in my continuous ...
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Sample covariance of t distribution and degree of freedom
If $X$ is a P by N size matrix, $X_{ij} \sim N(0,\sigma_i^2)$ if I standardize this X matrix with sample mean and sample variance (assuming I don't have access to the population mean and variance) I ...
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Problem with dfs in multilevel analysis after converting data to long format
I have a bit of an odd problem and would love to get some suggestions of what the cause could be as I am currently at a loss:
Some while ago, I had converted a dataset to long format in R using melt ...
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How do I understand the calculation of degrees of freedom in the context of a 2 x 3 contingency table?
I am currently reading an article, Analysis of sensory ratings data with cumulative link models. In section 2.4 - example 1, the authors describe an experiment from Bi, 2002*:
... 25 subjects each ...
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Degree of freedom (df) in maximum likelihood estimate (MLE) for linear regression
I am reading Bain/Engelhardt's "Introduction to Probability and Math Statistics" about maximum likelihood estimate (MLE) for linear regression (p. 519 - 522).
I first summarize 3 key points ...
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Using one linear model to test multiple hypotheses
Let’s assume the following:
I have data of 100 subjects each performing 100 trials of a reaction time task
At each trial, I measured the reaction time (RT) and a specific brain signal (BS)
The RT and ...
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How to interpret zero degrees of freedom on residual deviance
I'm wondering how to interpret residual deviance from a Poisson regression on 0 degrees of freedom?
I have a dataframe with count data on events and number of people at risk for the disease, with ten ...
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When calculating sample variance around a sample mean can I take degrees of freedom to be a fraction
Normally if you have $N$ samples of a random variable, from which you estimate both the sample mean and sample variance, you need to account for the missing degree of freedom in the sample variance:
$$...
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Help with determining statistical significance of bees’ decisions [closed]
Firstly, my apologies for the basic nature of this question. I am numerate but stats has always befuddled me. I have had a look through earlier questions.
I have installed a red mason bee box. It has ...
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What is the reference edf for generalized additive models?
From the summary of my fitted generalized additve model (gam) I see two edfs. The first edf is the model edf and second is the reference edf.
However, for AIC estimation, the reference edf is used. ...
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Selectivity freedom with overlapping conditions
I'm facing a mathematical challenge related to selectivity freedom under overlapping conditions. To make it more relatable, let's consider an analogy.
Imagine a farmer who has just completed his apple ...
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Optimizing Treatment Group Assignments
When setting out experiments, I want to make sure treatment groups are as balanced as possible. Instead of using randomization, I've started to use the following process. I first collect some ...
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What is the critical value for those df not listed in Critical value table for Pearson correlation?
What is the critical value for pearson correlation df=190? The total number of samples is 192, so df is N-2 = 190. The tables have critical values for df 100, 150, 300, 500, 1000. If the df (N-2) ...
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What would be the sample number if two variables have different number of samples?
While correlating two variables, which have different number of samples in each, how can I find the df?
Eg. Sample-A has 35 observations, Sample-B has 22 observations,
How to calculate df (N)-2?
...
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Clarifying degrees of freedom in fixed effects model
I'm new to econometrics and learning about fixed effects. If I understood it correctly, we are literally including dummy variables for every observations. For example, I have a panel data of firms and ...
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Results from extractAIC() from a mixed model lmer() are confusing
I have some legacy code in larger block of looped code that compares models.
It essentially boils down to this similar example:
...
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Chi square reporting df for 2x1
I conducted a 2x1 chi square and need to report it in APA. There are 280 in the sample. Do I deduct the df from the sample size? e.g. X2 (1, N=279)
Thank you
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How to deal with potentially too few levels of the random effect
I built a linear mixed effect model with nlme with Body length, Habitat and Sex as fixed effects. Body length is added for body size correction while the other two both have two levels. In the random ...
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Intuition behind rank of covariance matrix and testing hypotheses
I am trying to acquire some intuition about testing multivariate hypotheses where the test statistic involves inverse covariance matrix. As an example, suppose we have a $p$-variate random vector that ...
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When fitting a generalised additive model, how to choose how much to smooth?
When fitting a GAM, is there a rule (of thumb) for deciding if $k$ (max number of degrees of freedom for a spline) is large enough or not? How much should edf be below $k'$? And is that an absolute ...
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When transforming a dataset using the square root (or any other procedure), does the standard deviation of the dataset get transformed too?
Taking an introductory statistics course, and I am confused about the impact of a transformation on the df for a two-sample t-test. The df is dependent on n of each sample and SD of each sample, but I'...
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Finding degrees of freedom for multinomial regression with participants repeating questions
To find the degrees of freedom, I need to do N-k-1 where N is the sample size and k is the number of predictor variables.
I have about 200 participants in my sample. However, they each answer a ...
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What should be the degree of freedom in ANOVA table
Consider the area under wheat for a sample of 44 clusters
selected from 11 different villages. Four clusters were selected from each of the
11 villages and each cluster consists of 8 survey numbers(...
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Interpreting 'edf' from random factor smooth in GAM model
I specified a random factor smooth in the following way:
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Implementation of Scheffe's adjustment in software
My understanding of Scheffé's adjustment for multiple comparisons is that it already adjusts for any possible contrast that one could make with the data, where the contrast coefficients sum to 0. ...
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Effect of sample size on Chi-squared distribution
As the degrees of freedom increase, the chi-square curve approaches a normal distribution. But what about increasing the sample size?
If I am using degree of freedom =1, but with different sample ...
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Degrees of freedom in a 2^3 factorial experiment without three-way interaction included
I have an ANOVA model with 3 effects (A, B, C) with (a, b, c) levels each and 3 two-way interactions (AB, AC, BC). Within each cell there are n replicates. How to calculate number of degrees of ...
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Statistics question: Degrees of freedom
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I am trying to calculate the degrees of freedom for a LRT between two models to determine whether two variables should be included as time-dependent variables or not.
Model 1:
Model 2:
How do I ...
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Should I use `select=TRUE` for `mgcv::gam` while comparing df? [closed]
While running a GAM (Generalized Additive Model), I noticed that using select=TRUE inside mgcv:gam I get different ...
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How to calculate degrees of freedom for glmmTMB model with mixed effects?
I'm using glmmTMB model with mixed effects and beta distribution and I'm wondering is there a way to count degrees of freedom of my model variables (they are not in my model output)?
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Where do I make a mistake in the proof of the sample variance for the unbiased estimator?
I am trying to prove that the sample variance formula is unbiased.
Firts, let $\mathbb{E}(X_i) = \mu, \text{Var}(X_i)=\sigma^2=\mathbb{E}(X_i^2)-\mathbb{E}(X_i)^2, \bar{X}=\frac{\sum X_i}{n}$.
$\...
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Weird results from Chi Square test
I'm running a chi square test on some categorical values pertaining to race, and whether different racial groups participated in a clinic. As there's about a dozen different races in this data, I ...
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Which degrees of freedom estimate to use for two-tailed t-test?
I have two samples:
Sample A = businesses that have not received a grant
Sample B = businesses that have received a grant
Ua = population mean of survival rate for businesses in A
Ub = population mean ...
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Why does degrees of freedom = $\frac{\operatorname{Tr}(H'H)^2}{\operatorname{Tr}(H'HH'H)}$?
Wikipedia gives the following expression in "degrees of freedom" section, calling it the "Satterthwaite" approximation:
\begin{equation*}
\text{df}\approx \frac{\operatorname{Tr}(H'...
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How many "effective" observations from sliding window sampling?
I have data on the trajectory of a particle and am interested in the displacement of the particle in a given time period. In particular, I have information on how much a particle has moved in each ...
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Is this a known measure of "effective degrees of freedom" in regression?
Suppose $x,y$ are I.I.D random variables in $d$ dimensions. Consider the following quantity:
$$R=\frac{(E\|x\|^2)^2}{E\langle x, y\rangle^2}$$
equivalently for empirical distribution with data matrix $...
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denominator degrees of freedom changes for each model even though I have the same number of
I hope this doesn't come off as a dumb question. I am just having difficulty wrapping my head around why my denominator degrees of freedom are different for most of my linear mixed-effects models when ...
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Effective degrees of freedom for spline term in glmmTMB
I have fitted a model in glmmTMB that includes an spline function for age using the bs function from the splines package (version 3.6.2) in R. The syntax in glmmTMB looks like this:
glmmTMB(...
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Degrees of freedom in emmeans package
This is my first time uploading, so please bear with me.
I am currently trying to do a post-hoc test with three interaction term (time X support X NFC).
We did a follow-up on participants' well-being ...
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Effective degrees of freedom concrete example of variable distribution with Ridge
I am reading a report where they used Lasso and penalty term $\lambda$. Below is a table presented:
I have a question about the DF. The original model had 16 variables and no intercept, i.e without ...
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How to find effective number of degrees of freedom for time series
I have 10 years time series of daily precipitation and temperature data (3652 records) as given below:
Date
Precipitation(mm)
Temperature (°C)
01.01.2010
20
12
02.01.2010
5
6
03.01.2010
0
9
...
.....
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Degrees of freedom of a coin toss
The probability of a fair coin landing heads is $p(H)=1/2$ and since there is only one other outcome we can deduce that the probability for tails is also $p(T)=1-p(H)=1/2$. Yet if we examine a ...
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Is it better to have more degrees of freedom or less?
The concept of degrees of freedom appears in many places in statistics. Yet I still don't understand what is the role of degrees of freedom. Why can we just use sample size (and we need to decrease it ...
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XGBoost when P>>N
Someone built an XGBoost classification model using each pixel in an image (256*256) as a separate feature, plus a few other features. However they only have 500 data points. The target classes were ...
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