# 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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### finding out distributions mathematically

we know that the larger the degree of freedom, the less likely extreme events will occur (e.g., if you throw fair coin once, odds of heads is 50%, if you throw twice, odds of two heads are 25% and so ...
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### LmerTest::lmer degrees of fredom incorret

I had a good search but apologies if this has been answered elsewhere. I am using LmerTest::lmer to estimate a mixed effects model. I have 50 subjects (in three groups) and two measurements per ...
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### Where to find t statistic and degree of freedom in T test in Google Sheets?

I'm using Google sheets to find TTEST scores. Its outcome is a single value, namely, p value. But in addition to this p value I also need to report degree of freedom and a t statistic value: t(degress ...
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### Interaction term alters degrees of freedom for main effects in glmmTMB model

I am using the glmmTMB package to test whether the probability of a seed remaining dormant in the soil (binary variable) depends on the population it comes from (fixed effect, 8 levels of population), ...
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### Analogy between degrees of freedom in simultaneous equations and regression

Background: I went looking for intuitive explanations for degrees of freedom. I found some analogies that used simultaneous equations and constraints, others that cast them as independent data points ...
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### Determining differences between hierarchical clustering groups with ANOVA: Is my method correct?

I have 20 different hybrids of plants (three replications each in a randomized complete block design), and I have taken measurements on subsamples within each of the plot. In order to see if there are ...
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### What does replication mean for a mixed model?

I'm struggling to figure out how to test fixed effects appropriately in a mixed model, because of the concept of pseudoreplication (I have only seen this term in the fields of ecology and psychology). ...
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### Meaning of “Error in contr.treatment(n = 0L) : not enough degrees of freedom to define contrasts” when adding fixed effects to nlme?

We are attempting to model and compare logistic growth over time for 6 different treatments using nlme. So far, we have successfully added random effects of ...
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### Why $\frac{\chi^2}{number\,of\,data\,points - 1} \approx 1$ means good fit?

In my statistics class, I learned that if $\frac{\chi^2}{number\,of\,data\,points - 1} \approx 1$ the fitting of the model to the data points is good. I do not really understand why this statement is ...
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### What does a lower bound do to the degrees of freedom of this random vector?

Consider two procedures to sequentially draw $4$ random numbers $(k_1, k_2, k_3, k_4)$ that add up to $100$: Procedure 1 can pick real numbers $\geq 0$ Procedure 2 can pick real numbers $\geq 20$ ...
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### How are terms in SS (corrected sum of squares) independent?

What does the highlighted test mean? How are the terms not independent? Can someone elaborate in detail?
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### Why no degrees of freedom for Z test

I am reading about hypothesis testing and have encountered Z test and T test. I have understood both the tests and their usage. One part that is not still clear is why does Z test does not depend on ...
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### Is there any concepts for degree of freedom on dynamic system specified by differential equations?

We can fit covid19 data with SIR model (here is a good example). My question is how much data is needed to get a unique fit? Is there any concept for degree of freedom on dynamic system specified by ...
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### Trace of the Hat Matrix in Ridge Regression

Generally, I know that the trace of the hat matrix ($H$) is equal to the rank of H since it is an orthogonal projection. If I wanted to show the trace of $H$ in ridge regression, would I be able to ...
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### F-Distribution: difference between the expected value for a random variable and the expected value of its inverse?

It is known that the expected value of the F-Distribution depends only on the degrees of freedom associated with the Chi-square random variable in the denominator. In other words, E[1/X] does not ...
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### Estimated degrees of freedom close to 1 in a GAM(M) indicate linear term; citeable reference?

I have several generalized additive mixed models that have smooth function terms with estimated degrees of freedom (edf) that are 1 or close to one. I have seen in several places such as blogs that ...
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### What is Degrees of Freedom? [duplicate]

I have gone through tonnes of online resources (other stackexchange postings as well) and textbooks but still have not been able to grasp the concept. Most of them have vague explanations like "if you ...
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### Degrees of freedom with categorical variables

I am constructing a Sequential ANOVA table using categorical variables. Variable $A$ has 2 levels, variable $B$ has 3 levels. I want to find the degrees of freedom for $A, B, A:B$ in the sequential ...
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### How to calculate the ratio of observations to model parameters in a VAR(p) model

In machine learning, it's pretty common to use the general rule of thumb that one should have at least 10X as many observations as there are model parameters to avoid overfitting. As discussed here ...
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### Finding Degrees of Freedom For Chi Squared Test proportions

There's a litany of other questionspreviously posted about finding df during a GOF test but I still struggle to understand it. I know that a way of thinking of df is to do (number of categorical ...
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### Degree of freedom/sample size of a combined quantity calculated from several individual estimates?

Say I have data for CO2, CH4 and N2O emission in my experiment (having different experimental treatments). Each treatment means of either CO2, CH4 & N2O are calculated from 4 replicates (4 pieces ...
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### How do you calculate the degrees of freedom for the chi-squared distribution for Pearson's chi squared test?

I am conducting the Pearson's $\chi^2$ test for three variables under the independence model. The data is in a $2 \times 2 \times 2$ contingency table. How do I find the degrees of freedom for $\chi^2$...
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### Calculation of degrees of freedom for chi-square test

I am not sure how to calculate the df for the following data: The data is for a cross between flies to see if the observed phenotypic ratios are following the predictions of Mendel's laws. The total ...
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### Is p in the formula for adjusted R-square defined for tree models?

Let $R^2$ be the R-squared defined for regression models. Given a vector x, the target, and a vector, y, the prediction of the ...
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### Degrees of Freedom in Trading Moving Average (Open, High, Low, Close)

I have read "The Evaluation and Optimization of Trading Strategies" by Robert Pardo. He gave an example in page 293, of a moving average of CLOSE with 57 DOF. (50 MA + 7 trading rules/MA). He uses ...
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### How do I go about choosing the right degrees of freedom for a simulation study?

How does one go about choosing the right degrees of freedom when sampling from a T-Distribution? I understand n-1 degrees of freedom is the theoretical rule of thumb, but my sample size is quite large ...
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### Why am I seeing 0 degrees of freedom when testing main effects using lme4, but see 1 df when testing interaction?

So sorry if this is a dumb question, but I've been searching around and can't figure out what's going on. I'm running a mixed effect model with 2 fixed effects and random intercepts, as shown below. ...
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### Degree of freedom of different distributions: Chi-Square Goodness of Fit Test

I try to understand why the number of constraints differ for the distributions in the table below, for the Chi-square goodness of fit test. I found the content in the following link. https://www....
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### Why cannot the sandwich standard errors be used together with the Kenward-Roger denominator? [duplicate]

This question is about mixed models, and the use of both the Kenward-Roger correction (K-R) for small sample sizes and robust (sandwich) estimators for standard errors in the same model. Is it ...
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### What is the equivalence of BETWITHIN degrees of freedom in mixed-effect models R?

As in the title. Let's assume I cannot use the Kenward-Roger or Satterthwaite method in mixed-effect models. I was told to use the BETWITHIN method. Now I switched to R. I can use any package I want. ...
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### Why cannot the sandwich SE be used when the Kenward-Roger denominator df are in use?

This question is about mixed models, and the use of both the Kenward-Roger correction (K-R) for small sample sizes and robust (sandwich) estimators for standard errors in the same model. Is it ...
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### Degrees of freedom in matching for calculating p-value of t-score

I am running a matching analysis using the Match function from the Matching R-package. My sample includes 86048 firms, from which 611 have received treatment. After matching on sector(exact), number ...