# Questions tagged [permutation]

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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 ...
22 views

### Besides computational feasibility, what kind of problems may occur when imputing missing data by exhaustive permutation?

I don't know if "exhaustive permutation" is the correct term, but happy to be corrected if it isn't. Here's an example, which hopefully will clarify what I mean. Let's say I have the ...
13 views

### 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 ...
23 views

### 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 ...
37 views

### 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 ...
33 views

### 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 ...
41 views

### 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 ...
101 views

### 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-...
1 vote
10 views

### 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 (...
28 views

### Two equivalent ways of sampling with replacement

The original context of this problem is for a derivation of the lookdown model https://projecteuclid.org/journals/annals-of-probability/volume-24/issue-2/A-countable-representation-of-the-Fleming-Viot-...
49 views

### 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 $\theta$ ...
26 views

### 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 ...
75 views

### 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 ...
29 views

### Permuting data to seperate marginal and interaction effects

I've read a bit on permutation tests for discovering interactions. Are there permutations I can perform on my dataset to try to separate the interactions from the marginals? In particular, I want to ...
33 views

### Find an extreme point (of a convex polytope) with the minimum of a quadratic cost function

For example, I am trying to do the following: Doubly stochastic matrices (i.e. matrices whose rows and columns sum to 1) form a polytope with permutation matrices as extreme points (Birkhoff–von ...
53 views

### 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]...
32 views

### 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 ...
37 views

### 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 :)...
42 views

### 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 ...
40 views

### 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 ?
10 views

### 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 ...
160 views

### 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 ...
10 views

### 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 ...
37 views

### Evaluate clustering accuracy based on an adjacency/similarity/connection matrix

Description In the classification tasks, the classification accuracy is computed by accuracy=n_correct/n_total For example, if I have three samples, and the ...
1 vote
65 views

### Interpretation of the adjusted rand-index

I'm trying to understand the adjusted Rand index for a metric review that I'm doing. I found this question most helpful so far: Calculating the adjusted rand index? https://en.wikipedia.org/wiki/...
335 views

### Adjusting P values for multiple comparisons using permutation tests

I have a number of continuous predictors (biomarker measurements) which I would like to test for association with a binary outcome variable (disease status), adjusting for multiple comparisons. As ...
1k views

### Finding most likely permutation

[Hoping that this is the right Stackexchange site; inspired from a true story seen at work] Joe has a measuring instrument and $n$ objects to be measured (say, a scale and $n$ weights). He measures ...
1 vote
76 views

### Probability that Secret Santa arrangement for couples will result in perfect pairings

4 couples, 8 people total, participate in a Secret Santa gift exchange. Call the people A, B, C, D, E, F, G, H. Assume A+B are a married couple. Likewise, assume C+D, E+F, and G+H are all couples. All ...
99 views

### Probability that Secret Santa arrangement will result in perfect pairings for couples

4 couples, 8 people total, participate in a Secret Santa gift exchange. Call the people A, B, C, D, E, F, G, H. Assume A+B are a married couple. Likewise, assume C+D, E+F, and G+H are all couples. ...
35 views

### Equal probability of random permutations

For $n$ distinct elements $x_1, x_2, .., x_n$. If we generate a random permutation $\pi$ of length n (so of all elements), how to prove that for every $i$th element $\pi_i$ of it, the probability \$P(\...