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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39 views

Find population characteristics from survey proportions

I want to launch surveys on very specific binary questions with low "Yes" answer rate, for example Do you have a Ferrari ?, Did you buy a Chanel bag ? I'm able to do that on at least 20 ...
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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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15 views

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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34 views

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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Analysing a product ranking over time: where to start?

Context: I have a ranking (top 10) of products for sequential periods, stretching to 3 years. This gives me a total of about 150 top 10 lists, in which the products are a subset of the total set of ...
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Determine if a distribution of ranks is significantly skewed towards low values

I have N vectors of varying length. The values are samples of ranks that have been normalized to be between zero and one. I would like to determine the M vectors (M < N), for which the distribution ...
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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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37 views

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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24 views

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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When is it appropriate to use rank outcome instead of raw outcome values?

thanks in advance for advice. When is it appropriate to use the rank of your outcome variable instead of its raw values in regression? I have been sent a manuscript to review by a colleague. The ...
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Regression with multiple independent samples and rank dependent variable

I am trying to estimate parameters of a regression function, where: Independent Variables are continuous (and I might have up to 7 IVs) Dependent Variable is rank The twist is that the sample is ...
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41 views

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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29 views

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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119 views

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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Regression for continuous response and ordinal predictors ranked relative to each other

I would like to predict the value of a continuous response variable $y$ from some predictor variables $x_1, ..., x_n$ which are all ordinal insofar as their numerical values in my observations are ...
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Can I use multiple regression on a ranked response variable as a significance test for multiple covariates?

This blog post illustrates the relationship between inference tests on groups (t-test, ANOVA, etc.) and equivalent linear models. It also claims that for reasonable sample size, regression of a ranked ...
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214 views

Variance of rank of means

Consider an $n\times m$ matrix of scores obtained by measuring $n$ items $m$ times. Items are assumed independent with unique variances. The sample mean of each row is calculated and the resulting ...
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Identify difficult parameter to measure [closed]

I am using different tools to measure x on some objects. The tools were tested on a small set of objects for which the true x is known. And so the predicted values were found to not be accurate for ...
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Consistency test

I have data that consists of 7 characteristics for each participant. There are about 170 participants. The test was repeated in some time and the same 7 characteristics were acquired. I need to find ...
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Rank error metric for time series

Suppose I have a collection of MAE across multiple time series (say, 10), and 3 models. However, MAE cannot be compared across time series. I compare the errors in this way: assign ranks to models, ...
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133 views

Correlation between an observation and its rank in a random sample

Suppose $X_1,X_2,\ldots,X_n$ are i.i.d random variables with an absolutely continuous distribution. We say the observation $X_i$ has rank $R_i$ if $$X_i=X_{(R_i)}\quad,\,i=1,2,\ldots,n,$$ where $X_{(...
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Is ratio of ranks a well-studied statistic?

I have two lists of recommendations: that is, two different algorithms have assigned ranks to the same list of objects. I would like to know if they're similar. I specifically care more about ...
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31 views

Statistical test for a difference in ranked groups

I have an odd problem; I'm computing the axis lengths of ellipsoids, these are sorted based on their length (i.e. longest axis and shortest axis). The problem is that I want to say the long axes are ...
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26 views

Proper names for data - quantile and rank

Say I have data from a sample of 100 experiments. For a variable, I'm interested in showing the value x with 0.9 probability of non-exceedance, which is equivalent ...
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436 views

How to compare different rankings/recommendations using an ROC curve?

I have two ranking lists(A & B) and a list C combined from the two lists, I want to use ROC curve to get the contribution of A and B to build C. How does that work? Example, For list A the order ...
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360 views

Theoretical computation Kendall's tau [closed]

While working with rank correlation statistics of samples, specifically Spearman's rho and Kendall's tau, I came across the interesting theoretical interpretation of Kendall's tau. It can be viewed as ...
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61 views

Internal consistency

I have to analyse a dataset in which there are drugs and used animals based on article review. The datasets looks like this: ...
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Get final rank from ranked list [duplicate]

i got exactly same problem with this question Overall rank from multiple ranked lists but i didnt get any references and answer for that. example : ...
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Is it mathematically correct to re-analyse data as ordinal after having analysed as continuous using the same rank based method (nparLD)?

Please tell me why I'm wrong :) I have a dataset collected in a 2 by 4 repeated measures design, where 2 separate groups of people were tested 4 times on the same task. I have analysed my data with ...
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885 views

Help with the rank-ordered logit model (exploded logit model)

I am hoping for some help with rank-ordered logit models. I get logit models, but Im having trouble when there are multiple levels, and when these are ordered. Moreover, I'm uncertain how to interpret ...
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2k views

Which regression analysis should I use for ranked data?

I have output data from an aggregator website comparing insurance premiums. Each unique input (incl variables such as age, medical screening score, territorial limits, duration, etc) produces an ...
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5k views

Difference between using a z-score or a percentiles to summarize data in normal and skewed distributions

I have a dataset with multiple variables having different distributions - some are normal and others are skewed. I want to summarize locations for some identified values on both kinds of distributions....
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64 views

Cars: Price vs Rank

Okay so long story short, I have a list of 184 cars with a bunch of info for each of them in Excel. I want to be able to compare the price of the cars to the rank of them so that I can essentially ...
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637 views

What is the logic behind ANOVA on ranks?

I've read a few sources that describe ANOVA on ranks, and I am still confused on how the calculation is done, and why. Specifically: Is ANOVA on ranks just applying a rank transformation to the data ...
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Application of Bayesian Averaging for Ranking

I have a sample with two metrics and one ratio per attribute. I am trying to rank the attributes based on the ratio and variable amounts and from my research I have found that most people find ...
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322 views

KS test and independence of data

For A two sample KS test data should be independent. Which of the following has to be true to use the KS test reliably(i.e. what does independent mean) Data should be Independent within each sample ...
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39 views

Ranked Set Sampling

In ranked set sampling, we select $n$ random sets, each of size $n$. Then we choose the largest unit from the 1st set, 2nd largest from the 2nd set, and thus $n$th largest from the $n$th set. This ...
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300 views

Mathematical function that maps a vector to an ordered version of that vector

Given a vector $x \in \mathbb{R}^n$, I would like to refer to a vector $x'$ that contains the components of $x$ ordered in ascending order. I would like to define the function $f(x)$ that maps $x$ to $...
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235 views

How to Analyze Rank Data

Suppose I have 3 columns and n rows. Each row represents a school and the columns represent variables of interest and have ordinal ranks (1,2,3,4....n; 1 being the best and n being the worst). ...
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95 views

R precision in operations [closed]

If you try to calculate the difference between (9.1 - 8.9) - (6.9-6.7) in R, you'll get ...
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9 views

Correlation of entrance rank to subsequent performance

As part of my M Tech Thesis, I have to find the correlation between the Rank in Engineering Entrance Test and performance in 1st Year Engineering in terms of GPA i.e. Gross Performance Average. Can ...
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54 views

Let $\mathbf{R}^{*}$ be rank vector of a random sample and $V=R_{1}^{*}-R_{N}^{*}$. Then $\mathsf{P}(V=k)= \frac{N-|k|}{N(N-1)}$

Let $Z_{1},\ldots, Z_{N}$ be i.i.d. continuous random variables with rank vector $\mathbf{R}^{*}=(R^{*}_{1},\ldots,R_{N}^{*})$, where $R_{i}^{*}$ denotes the rank of $Z_{i}$ among $Z_{1},\ldots, Z_{N}$...
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Ranking candidates based on their accuracy and efficiency

I have a dataset of 1000 candidates whom I have assessed for a skill. I have calculated accuracy of correct answers of each user as well as efficiency of each user based on number of attempts taken by ...