Questions tagged [ranks]

Ranks are ordinal numbers of the quantitative data values sorted ascendingly or descendingly. Various methods to assign ranks to equal values (ties) exist. Transform of values to ranks is often done in nonparametric data analysis. (Not to confuse with [ranking] task..) (See related: [order-statistics])

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Two-Sample Rank Statistics

Assume we got two models, either regression or RF or whatever. I'm trying to observe the relative importance of each feature by using ranks. That is, if we look at a regression model, we have a t-test ...
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Algorthm for discerning which top X values in a list are statistically ranked higher than the bottom Y

Given a ranked list, which contains values with high uncertainty, I would like to remove as many of the middle values that have high overlap in uncertainties as possible, and be left with more or less ...
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What is the best way to represent Spearman’s correlation graphically?

For my thesis research I have to do Spearman’s correlation tests on a set of ordinal variables. I would like to represent the correlations graphically to include them in the report and give a clearer ...
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Quantifying agreement of ordinally ranked sequences

I've been using a very particular set of closely related metrics to quantify how well two ranked sequences agree with one another. I'd like to know if this way of thinking is well-known and if any of ...
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Testing for differential ranking between lists relative to a reference list

I am interested in comparing ranked lists in order to find elements that are differently ranked. Suppose we have 10 lists, each ranked (and for simplicity assuming the elements overlap and only the ...
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Interaction between variables to create a ranking system

I was wondering if there is a standard way to rank cases by multiple variables. When we have only 1 quantitative variable, the ranking is trivial, you sort the cases by comparing the magnitude between ...
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Arrange data so that two variables are linear

I have the following set of rainfall intensity data and I want to make a compilation of the rainfall intensities above some practical minimum as shown in the figure below. So the intensity and the ...
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Why Spearman's rank correlation ranges from from -1 to 1

$$\rho = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)}$$ $\rho$ = Spearman's rank correlation coefficient $d_i$ = difference between the two ranks of each observation $n$ = number of observations Given the ...
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Correlation Test Between a Categorical Variable and an Ordinal (In the form of a ranking) Variable

I have a dataset of book sales by rank and the color of the cover. I would like to find a relationship between the rank of the book and the color of the cover. I'd like to know how to do this analysis ...
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How to check if two lists of rankings lists are statistically significant different

To make my problem more clear I will give some examples of my data: Measure A Measure B Set 1 5 3 1 4 2 5 4 2 3 1 Set 2 5 1 3 4 2 5 4 1 3 2 Set 3 2 4 3 5 1 5 2 3 4 1 Set 4 3 4 1 5 2 5 3 2 4 1 ...
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Are there any surveys of the opinions of statisticians on the usefulness of classical rank-based nonparametric statistics?

The following comes from a YouTube video: Robustness in Statistics, which I have tried to quote verbatim. In Biology and Medicine these procedures are extremely popular, and I don't know why. They're ...
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bootstrap time series using the rank

Don Walpola wrote a good overview of the bootstrap techniques used for time series (https://stats.stackexchange.com/a/450894). I searched through the literature, and did not find a single method ...
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Do statistical models allow for "ranking their outputs"?

Suppose you create a regression model that predicts the hourly salary based on age and height. Suppose you have some new age and height measurements for 5 new people. The regression model predicts the ...
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Which items in two ranked lists are ranked significantly different?

I have 91 items ranked by different demographic groups of questionnaire participants. The rank lists for each group are all the same length and contain identical items. I understand that I can perform ...
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Why are extreme correlations so common in this Monte Carlo simulation? [duplicate]

Consider the following simple Monte Carlo: ...
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How can I determine the rank of matrix $X$ given the LSE of $X\beta$?

I am given the LSE of $X\beta$, but I need to find the rank of $X$. Is there any result or theorem that allows me to obtain $r(X)$?
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Compare rank-order stability over different periods of time

I have a large dataset of repeated measures of students' performance in several domains. Among other things, I want to look at the (rank-order) stability of performance between measurement times. ...
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utilising ipsative measures

I am using a data set containing ipsative measures resulting from forced ranks. For example, respondents are asked to rank in terms of importance various methods of employee development (training, ...
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How to weight ranks?

I have a set of responses ranked by my participants. For example, they gave responses A, B, C and ranked them as 3, 2, 1 (or C, B, A). I computed relative frequencies of each responses (A, B, C) and ...
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How to calculate Hodges-Lehmann estimator of slope in rank regression?

Suppose we have $n$ paired observations $(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)$, where $y$ is the response variable and $x$ is the covariate. Consider a simple linear regression model $$y_i=\alpha+\...
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Consistency of Wilcoxon rank sum statistic

In Chapter 1 of E. L. Lehmann's book Nonparametrics, he refers to the Wilcoxon Rank Sum test in treatment-control experiments. Using Lehmann's notation, let $N$ be the total number of units, $n$ the ...
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Invertibility of $E(X^\top X)$ and $\tilde{X}^\top \tilde{X}$

Consider the linear regression model with 3 regressors $$ Y=\beta_1 Q+\beta_2 W+\beta_3 Z+\epsilon $$ Let $X\equiv (Q, W, Z)$ and $\beta\equiv (\beta_1,\beta_2,\beta_3)^\top$. Also suppose that $Q,W,...
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Ranking subjective datasets

I hope this is the right forum for this question. Please point me to the right one if it isnt. Suppose there is a factory where there are workers who assemble widgets that come down a manufacturing ...
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Understanding a proof of the relation between Walsh averages and Wilcoxon signed rank test statistic

I am trying to understand a particular proof of the relation between Walsh averages and the Wilcoxon signed rank test statistic, as given in the book Statistical Inference Based on Ranks by T.P. ...
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Median ranks and percentile ranks

In Statistics by Freedman et al. there's this example Suppose the percentile rank of one student on the SAT is $90\%$, among the first-year students. Predict his percentile rank on first-year GPA. ...
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rank of an expected value of a matrix

x is (a * 1) vector y is (b * 1) vector x and y are independent then what is rank(E[xy']) I know that xy' should be (a*b) matrix and since they are independent. , however I am not sure about the rank
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Testing a hypothesis involving ranks with an unequality in the null hypothesis

Here's a toy example of the problem I'm dealing with I have gene expression data from two patients' multiple tissues ...
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Creating a combined rank score using variables a, b, c, and d, (each is a score 1-100) for constituents using a platform?

I am tasked with creating an overall score that will be used to represent a supplier's holistic value on our site. For example, consumers of supplier's service will want to find suppliers on our site ...
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Is Kendall's tau adequate to test for a non-monotonic relationship?

Goal Networks can have so many nodes that it's hard to study them. That is why in some cases nodes are clustered together. I am looking at whether the betweenness of a node is maintained after the ...
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Computing statistical Significance of Rank Order Question

In my questionnaire, I have a rank order question concerning three different videos. Each respondent must rank each of the videos either on position 1, 2 or 3. All respondents are in the same group (...
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Can I use Kruskal Wallis test to analyze ranked data? If not, what analysis method should I use?

I am currently conducting a survey study for a project. Unfortunately, I would not at all consider myself proficient in statistics, and am struggling with choosing the appropriate analysis method for ...
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Interpret the results of Wilcoxon signed rank test using mean ranks?

I have two dependent samples that I want to compare using the Wilcoxon signed rank test. I've now run into a problem with a few of my variables. The difference is significant so I want to know the ...
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can you use a rank as an outcome in a regression?

I have data where people ranked their preferences for products A to J (ten in total), so I have 10 variables now for product A, B, C, ... , which all range from 1 to 10. I'm wondering if it's ok to ...
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Why does the formula of Somers' D remove number of Y ties in this formula?

I am researching how to calculate Somers' D in python for a discrete dependent variable and continuous independent variable, I found this answer on stack overflow: https://stackoverflow.com/questions/...
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Is it valid to use rank data with a general linear model?

I have electrophysiological data in the form of skin resistance in fish. I wish to explore if there is any variation in resistance based on the location on the body where the skin is taken from. In ...
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Why is the Shapiro-Wilk $W$ statistic defined the way it is?

In the original paper (section 2.2.), we can see that derivation of the $W$ statistic goes along these lines: Let let $m_i$ be the expected value of the $i$-th order statistic of a random sample of $...
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Bootstrap for nonlinear regression and ranked explanatory variable

I've been wondering how the bootstrap method works in the case of nonlinear regression models where the order of the x-axis (suppose just 1 explanatory variable) matters. In the case of univariate ...
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Is there an algorithm with linear time complexity to calculate the rank sum statistic?

Definition 1: For a real array $x = (x_1, \dots, x_n)$, denote the rank of $x_i$ in $(x_1,\dots, x_n)$ by the following: $$ r_{i}=\sum_{j=1}^{n} I_{\left(x_{j} \leq x_{i}\right)}, \quad 1 \leq i \leq ...
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How should I visually represent these preference rankings?

I'm trying to visually represent the following rankings in a clear and intuitive way, but am unsure of how to best do that. Here's the data: There are 4 outcomes: A1, A2, B1, B2 The letters are the ...
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Is it possible to calculate spearman rank correlation between three generations?

In my analysis I determine the intergenerational transmission of social status. In the literature it is common to use OLS regressions for this purpose. In addition to these regressions, I also ...
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How can I rank values that are not normally distributed?

I have one metric value changing between 0 and 1 for 650 observations. When I analyze frequency distribution I see that the values are right skewed. I need to classify values as high/medium/low. I ...
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Ranks from a sample written as a function

Can sample rank be defined as a function of a sample? Suppose $X_1, X_2, \dots X_n \sim F$ where $F$ is defined on space $\mathcal{X}$. Consider the order statistics $X_{(1)}, X_{(2)}, \dots, X_{(n)}...
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Ranking theory for rainfall station

I have 10 rainfall stations. Each station has a rain day, no-rain day, and NA value, all in percentages. How can I rank these stations based on the condition that the best station is station that ...
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Perform signed rank test where there are duplicates in data?

How do you perform a rank test when there are duplicates in the data? that is, we have a dataset with numbers $1,1,1,1,3,3,3,3,4,4,4,4.$ and another dataset also with duplicates.... Is the sum of ...
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Do rank transformations induce dependence?

I am interested in an explanation of whether rank-transforming continuous variables induces dependence in model errors that violates the typical i.i.d assumption of generalized linear models. Suppose ...
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Clustering with ranking data [duplicate]

I'm just trying to get some practice with implementing some Machine Learning algorithms with a variety of data. I'm just getting started so I'm pretty new to the whole process and would appreciate any ...
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Please tell me whether the regression coefficient calculation by Moore-Penrose generalized inverse matrix is correct or not

...
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how to apply correction for ties in Conover squared Ranks Test

I am writing code for Conover Squared rank test in Python but I am unable to find right formula to make corrections for ties in order to calculate the p value. I understand the average of the tied ...
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Regression with ranked and truncated dependent variable

I'm struggling to find a model that will best fit this data. The dependent variable is the ranking of a observation based on how many votes it received based of a list of choices (number of votes is ...
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Rank-ordered logit model: question

I have a dataset in which each individual ranks four attributes of a product. This task (with the same attributes) is repeated three times under different conditions. The product is still the same, so ...
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