Questions tagged [permutation]
The permutation tag has no usage guidance.
59 questions
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How to permute p-values?
Recently, my colleague encountered a problem while working with a dataset, df_a, which contains gene data. Each row represents a ...
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Can my solution to a counting problem be corrected?
There was an interesting question in my stats class:
There are 5 scientists, 2 of which are Statisticians ($N_{a}$) and 3 are Biologists ($N_{b}$). How many ways can we choose 3 scientists, such that ...
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Permutation test in multiple linear regression, which way is correct?
I am fitting a linear regression model $$Y = \beta_0+ \beta_1 Z + \beta_2 X+\epsilon$$ Response $Y$ and covariate $X$ are continuous variables and $Z$ is a 0/1 dichotomous treatment group indicator, ...
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Diaconis' argument for 3 shuffles in a deck
I remember hearing that the great probabilist Persi Diaconis had said that three shuffles of a deck suffice to give an adequately shuffled deck. I wonder if there is an original reference to this ...
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using ranksum test within permutation test scipy
I am a bit confused with the definition of the permutation_test function provided by scipy. the following is what I wrote to calculate the p and null distribution
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100 prisoners problem with n < 50
In the 100 prisoners problem, I understand that when $l \geq 51$, the number of permutations is $100!/l$.
However how to calculate the exact number of permutations when $l < 51$?
When $l = 1$, the ...
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Probability of chain of events over a finite set of event with no repetition
I'm trying to tackle a problem that I suspect resembles others I'm unfamiliar with. I would love pointers for further reading. The problem is as follows:
We have a finite set of actions we can take $\...
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NA for p value of intercept in permutation test through permutes package in R [closed]
I am looking for how FROH (inbreeding level) change with age, island and year are random. I got the following result and got NA for p value of intercept, what might be the cause of it and how to ...
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Prove that modified RBF function satisfies Mercer conditions
Suppose that I have a modified RBF kernel function.
$k(\mathbf{x},\mathbf{y}) = \exp{(-||\mathbf{x}-P\mathbf{y}||^2 })$
where $\mathbf{x},\mathbf{y}$ represent $d$ dimensional inputs and $P$ is the ...
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Order agnostic autoregressive sequence probability
Autoregressive models define the following probability of a sequence $x$ as $p(x)=\Pi p(x_t | x_{<t})$ using the probability chain rule.
Then Hoogeboom et al. 2022 state that if we uniformly sample ...
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How many distinct possibilities for the first $k$ elements of a permutation of $n$ items, when some of the items are identical?
Problem
If I have to rearrange $n$ items (which some of them are identical), taking the order into account and only selecting the first $k$ items of every permutation, how many permutations do I have ...
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Question on permutation and combination
I am having a trouble understanding how to answer the following question and what method to use. The final answer is $415800$
Suppose there are 4 committees A, B, C, and D. 11 candidates are
randomly ...
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How to evaluate whether a treatment effect is significant given variance in measurement
I have two samples I am using to evaluate the effect of a treatment. Group $T$ contains 60 treated objects and their scores and group $C$ contains 60 control objects and their scores. The two groups ...
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Making sense of importance measures offered in Ranger
I have trained a regression forest using the R package ranger. Now I would like to discuss the variable importance measures of the included features. However, I am having difficulties understanding ...
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Number of possible permutations for N groups from I items where each item is of a different size but group total is fixed across groups
this is my first post.
I am not sure how to approach this problem, I would like direction or even an algebraic solution please.
I have to sort 70 different sized items out into 12 groups.
Each group ...
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Is this a valid statement according to the de Finetti theorem?
Some background on my problem - Let us consider a discrete memoryless channel (DMC) $W_{Y|X}$ from Alice to Bob. A DMC is a conditional probability distribution over the random variable $Y$ given ...
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Bootstrapping or permuting as resampling methods for correlations?
I have many variables ( ~2000 and 320 samples) and I have found the correlation coefficient for each unqiue pair of these variables through Spearmann (underlying data does not have normal distribution)...
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Clarification of one sided vs two sided p value following permutation testing
I am unsure as to how to compute a two sided p value following permutation testing, following different examples online.
For example, this post Two-sided permutation test vs. two one-sided, gets the ...
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What's the difference between a Permutation and a Perturbation?
I frequently come across the terms Permutation and Perturbation within the field of explainable AI.
I understand that both terms refer to methods that make changes to a sample's features. However, I'm ...
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Number of ways you sit next to your friend with 4 other people at a round table [closed]
This is a question I have after seeing Q1 of this question. There are a total of 6 people including you and your friend, and you guys are about to sit at a round table. The method of counting the ...
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Permutation and order statistic
Let $X_1,…,X_n$ be i.i.d. random variables. Are these two equalities correct?
$P[X_{(2)}<x_2,…,X_{(n)}<x_n| X_{(1)}=x_1]=\\
=n!P[X_{2}<x_2,…,X_{n}<x_n| X_{1}=x_1]=\\
=n! P[X_{2}<x_2]…P[...
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Permutation Test for mean ratio
I am given three vectors of length 11, that represent blood levels of a
hormone measured after placebo, old and new treatment.
...
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How do you use numPerms to get the total number of unique permutations for a PERMANOVA?
I am trying to calculate the number of unique permutations for a PERMANOVA using the R adonis2 function but I am getting stuck on defining my permutation scheme.
As ...
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Advantage and disadvantage of Wilcoxon rank sum test compared to permutation test [closed]
What is the advantage and disadvantages of Wilcoxon rank sum test compared to permutation test? I want to know at least one each based on the shape of distribution of raw data.
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Question about how to think of the binomial distribution with a combination vs a permutation
I know there are many questions on why use a combination formula over a permutation formula for the binomial distribution ( for example here), but looking through multiple of these, I still don't ...
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if a feature appears as the most important among a variety of models, does that make this feature empirically important?
Lets say that I train a variety of different models - SVM, XGBoost, LogisticRegression, Random Forest, KNeighbors, etc. I then take the permutation importance of each model, and find that ...
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51
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Populating an even distribution of values across multiple axis?
I'm trying to design an experiment with:
x number of people
y number of tasks
z number of ...
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How many ways can you arrange the digits: {1,2,2}, so that the resulting number would be even?
To quote the whole question accurately:
Various 3 digit numbers can be formed by permitting the digits 122. All arrangements are equally likely. Given that any resulting number is even, in how many ...
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Calculate a permutation-based p-value for a risk ratio
Summary
How do you calculate a two-sided p-value for a risk ratio/relative risk (obtained from a GEE logistic regression via predicting risks with and without a treatment) based on a permutation test, ...
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sampling distribution of a test statistic when doing permutation test
In a permutation test, we have a test statistic $T$ (for example t-test, f-test, etc.) that is applied to the original data to obtain an observed value $o_{obs}$ for the test statistic. Next, the data ...
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How to order individuals within groups where group order must remain the same [closed]
I am attempting to get every ordered combination of individuals in groups while keeping the order of the groups consistent.
For example, there are four individuals in group 1, two individuals in group ...
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324
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What is the chance all choices are different?
Suppose everyone (7 people) chooses independently and randomly out of 7 choices.
What are the odds that no two people have picked the same option?
I feel like the answer is $5040/823543,$ but I am ...
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How to understand embedding dimension in permutation entropy when checking predictabilty in electric load data?
I am predicting electric load data with different deep learning models and I am trying to define the predictability of the data. So far I came across the permutation entropy (PE) as a measurement for ...
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effect size for pairwise permutation
I am reading a paper that is using permutations to compare the means of two different treatment groups (a nutrition study, took minimum - maximum) that have low sample sizes, and so the groups are ...
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Random samples within the Central Limit Theorem - why select with permutation with repetition?
"The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the ...
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Given 9 coat hangers (3 groups), what's the probability
If I had 9 coat hangers (for example: 4 green, 3 blue and 2 red), what would be the probability of the first four being [green, green, blue, blue], if I just chuck the coat hangers into the wardrobe ...
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Disagreement regarding the role of permutation/randomization/shuffling in permuation testing between two populations
A colleague and I recently got into a conversation/disagreement regarding permutation testing (e.g. for comparing the mean value of two populations). While i thought i had a fairly good understanding ...
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Post-hoc test of two-way permutation ANOVA
I have a 2x2 study design to test the interaction between two drugs, with a single variable outcome. The data are very much non-parametric and it seems that a good alternative to the traditional two-...
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How to correctly apply a PERMANOVA to a half-crossed experimental design
I'm a biologist and conducted an experiment in which I took analytical samples of aphid infested plants and analyzed them using metabolomics. The plants were chosen based on their Genotype (...
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Can I use a permutation test to test the null hypothesis ''The difference between two groups is X''?
From what I read on permutation test, the null hypothesis is usually that there is no difference between the two groups.
I want to test if the difference between the mean of the two groups is $\theta$ ...
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How many ways to order such that one group comes first?
This question arose while playing a board game that uses cards. Imagine we have 11 cards total. 3 are red (R), 1 is blue (B), and 7 are yellow (Y). How many ways can we randomly order the 11 cards so ...
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Schitt’s Creek David Ring Combination
So I’ve been trying to figure this one out. On Schitt’s Creek, David wears various combinations of rings. He has four rings and he can arrange them on his ten fingers in various ways - each ring is ...
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Quantitative/statistical comparison of two orderings/permutations
There is a couple, say, Theresa and Robert.
They assess their preferences on 5 books by ranking them from the most attractive to the least one.
Theresa: [0,4,3,2,1]...
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Probability of n persons picking multiple numbers from N numbers, that all choices are different
Given $N$ distinct numbers, $n$ persons each picks $x_i > 0$ numbers, what is the probability $P$ of them all picking different numbers?
The limiting case of $n > N$ is trivial, $P = 0$. Same ...
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Intuition behind permutations + probability
I'm new to stats so I'm struggling to grasp the intuition behind permutations + probability. Would anybody be able to help me with parts (b) and (c) of this question?
Any help is greatly appreciated :)...
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What does it mean to "permute" a predictor in the context of random forest?
I am reading the vignette for the R package randomForestExplainer.
There the result accuracy_decrease (classification) is defined as
mean decrease of prediction ...
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Permutations - counting [closed]
Four girls bought each a swimsuit , and they decided to share them . How many days are needed so that each girl will wear each swimsuit once ?
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One sample data with unusual structure, permutation test?
I have N sets, each of them consisting of 1000 integer values. Typically, more than 90 % of values within a set is zero, thus median is zero. The nonzero elements are positive integers. We take N ...
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One sample permutation test on skewed data
I have one sample of values, each of them is a z-score from mutually independent z-scored distributions. I aimed at testing that the mean value of the sample is larger than zero. Originally I wanted ...
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Distribution of a rate in a subsample after permutation of the total dataset
I need to estimate the distribution of a rate in a subsample after permutation of the total dataset. I was wondering whether it's sufficient to use the binomial distribution with the global rate ...
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