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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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16
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4answers
25k views

What is tied data in the context of a rank correlation coefficient?

I am not in statistics field. I have seen the word "tied data" while reading about Rank Correlation Coefficients. What is tied data? What is an example of tied data?
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2answers
3k views

Why is the Mann–Whitney U test significant when the medians are equal?

I've received a results from a Mann-Whitney rank test that I don't understand. The median of the 2 populations is identical (6.9). The uppper and lower quantiles of each population are: 6.64 & 7....
11
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1answer
12k views

Displaying Ordinal Data - Means, Medians, and Mean Ranks

I have some ordinal data that is not normally distributed, so I decided to do non-parametric testing using the Mann-Whitney U Test. I am looking at differences between groups for seven scores - these ...
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2answers
1k views

Why is a Pearson correlation of ranks valid despite normality assumption?

I am currently reading up on assumptions for Pearson correlations. An important assumption for the ensuing t-test seems to be that both variables come from normal distributions; if they don't, then ...
8
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1answer
24k views

How does ties.method argument of R's rank function work?

I am using rank(a, ties.method="max") to rank a. But I am not quite sure what does ties.method="max" do. Can you please help?
8
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2answers
5k views

Do we need to worry about outliers when using rank-based tests?

Apologies if this is a very basic question. If we have data that are not normally distributed (e.g. skewed, Shapiro-Wilk test is significant) and we resort to rank-based methods (e.g. Wilcoxon Signed ...
8
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1answer
657 views

Rank and z-transform instead of Wilcoxon?

Andrew Gelman in a recent post in his blog suggests using a rank, transforming the rank to a z-score, and then using parametric tests and tools instead of performing non-parametric tests. I never ...
7
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2answers
698 views

Equivalence of Mann-Whitney U-test and t-test on ranks

What does it mean when people say that a t-test performed on ranked data is equivalent to a Mann-Whitney U-test? Does that mean they just test the same hypothesis/are useful in the same situations or ...
6
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1answer
3k views

Rank transformed 2-way ANOVA

I know I'm asking a lot of questions these days! Sorry about that, but I'm trying to work through my grad thesis data collected over the last 4 years, and am repeatedly tripping on my beginner's grasp ...
6
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1answer
2k views

Compare rank orders of population members across different variables

I have some data which describe residential units for people with learning disability, variables like how nice the furnishings are, the level of psychiatric symptomology on the unit, how happy the ...
6
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1answer
116 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_{(...
6
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3answers
1k views

Weighted Kendall tau rank correlation coefficient

I need to use a measure to compare two rankings: Consider the ground truth as 1,2,3,4,5,6. Let two rankings be R1 and ...
6
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1answer
2k views

Regression methods for predicting rank

Is there a canonical regression approach for predicting the ranks of a response? I'd like to fit a regression to a dataset where the response is highly non-normal with very large outliers. There are ...
6
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1answer
1k views

Are parametric tests on rank transformed data equivalent to non-parametric test on raw data?

Many non-parametric tests are identical to their parametric equivalent on ranked data. At least, that's what I learned from this blog post on Friedman's test and skimming this 1981 article.. This ...
5
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1answer
298 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 $...
4
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2answers
3k views

Algorithm and R code for dealing with ties in Wilcoxon rank-sum test

I think one of the algorithms used to handle ties for the Wilcoxon rank-sum test (a.k.a., Mann-Whitney U test) is Streitberg / Rohmel. I could not find a good source which explains the algorithm / ...
4
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1answer
499 views

Rank versus Box-Cox transformation

I'm attempting to assess the relationship between two quantitative variables, but the DV is highly skewed (and so are the residuals). I work among biologists who tend to favor non-parametric ...
4
votes
1answer
279 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 ...
4
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1answer
978 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 ...
4
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1answer
3k views

Difference between point-biserial and rank-biserial correlations

According to the wikipedia article the point-biserial correlation is just Pearson correlation where one variable is continuous but the other is dichotomous (e.g. Yes/No, Male/Female). However the ...
4
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0answers
326 views

What model contains Wilcoxon's rank sum test?

As Frank Harrel mentions in the answer to Logistic regression and Wilcoxon test, Wilcoxon's rank sum test (aka Mann-Whithey test) is contained in the proportional odds logistic regression, which would ...
3
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3answers
3k views

Is there a two-way Friedman's test?

I have ranked concentrations (from 0 to 5) of 5 different proteins from 3 different locations from the same patient. In total, 15 measures per patient and 61 patients, so 915 observations. What I'd ...
3
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2answers
163 views

Calculate percentile from ranks

I am trying to come up with a formula to calculate my percentile finish in fantasy sports games while also learning some statistics along the way. Rather than trying to work with the complete list of ...
3
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2answers
76 views

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 ...
3
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3answers
59 views

Statistical test if one sample is placed higher in rank

I have a rank array, say from 0 to 100 (0 being the smallest and 100 being the largest). If my data contains 89, 91, 94, and 98, I can say my data is significantly high in the rank. In other words, my ...
3
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2answers
4k views

What correlation coefficient and graph is appropriate with this data?

I'm not in Statistics field. I conducted the case study and collected the data as shown below I have data as shown in the table below: I would like to find correlation coefficient from this two table ...
3
votes
1answer
7k views

ANOVA on ranks vs. Mann-Whitney U test

What exactly is the difference between performing a t-test on data that has been ranked and performing a Mann-Whitney U test on the unranked data? I keep reading things like: For example, the ...
3
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0answers
177 views

Structural shifts

I am using the R programming language to analyze the cointegration of 5 data sets. I have determined that the series share 3 cointegrating vectors after taking structural shifts into account following ...
2
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1answer
684 views

Rank data from 1 to N (N may not be equal to number of elements in the dataset)

I calculate percentile ranks based on the method at http://www.psychstat.missouristate.edu/introbook/sbk14m.htm I need to assign ranks to a dataset where ranks are ...
2
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1answer
56 views

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 ...
2
votes
1answer
314 views

Equivalent to K-S test on discrete data with uneven quantization

I have some data resulting from a simulation that consists of several groups, each containing a single real datapoint and a variable number of matched controls. I take the rank of each real value ...
2
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1answer
313 views

Wilcoxon signed rank statistic

It seems there are two formulas to perform a wilcoxon signed rank test - one where the sum of all the signed ranks is w and another where the minimum of the sum of the negative ranks and positive ...
2
votes
2answers
75 views

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 ...
2
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1answer
23 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 ...
2
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1answer
38 views

Is the rank of $x$ within a set of iid draws from the same distribution uniform? [closed]

I have one realization $x$ drawn from any random distribution. I also have a large set $X$ of other (iid) draws from the very same distribution. Now I'm interested in the distribution of the rank of $...
2
votes
1answer
56 views

Testing ranks rather than actual numbers with parameteric tests

An answer on this page Non parametric analysis states: "You can perform ANOVA using ranks of your variable instead of variable itself. This will lead to the same results with Kruskal-Wallis ...
2
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0answers
198 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 ...
2
votes
0answers
91 views

Variable Importance's reliability when model accuracy is low

I am trying to predict the termination events for a company. I also want to rank the most important variables that lead to termination. I ran a decision tree model and have the following questions: ...
2
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0answers
105 views

Can I use proportion data and continous data for estimate of Spearman' s rho ? what if monotonic relatioship does not come out for a dataset ?

I want to use Spearman's rho test on proportional data for one variable and continuous data for the second variable (e.g. % survival of fish related to concentration of arsenic)? Further I want to ...
2
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0answers
62 views

Can rank ordered mixed logit handle varying set sizes?

I have data that consist of numerous trials, where each trial is a ranked set of items. The set of items for each trial is a subset of varying size of all possible items. (I.e. the items are shared ...
2
votes
1answer
696 views

Difference between samples in terms of frequency ranks

I have 3 different texts, and for each one of them, I have the frequencies of 25 letters appearing in those texts (Text A, letter A, freq = 5013; Text A, letter B, freq = 1462,...). These texts have ...
2
votes
0answers
52 views

Statistical test for changes in ranks

I am investigating changes in rankings of schools. For example, in year $t$ school X may have been in the 17th percentile (poor performer) but in year $t+1$ it may have improved to be in the 94th ...
2
votes
0answers
104 views

How to analyze ranks as responses?

A client has data where multiple subjects (people) have been presented with with four product alternatives, and after experiencing all four, were asked to rank the products. The data look like this:...
2
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0answers
428 views

ANOVA on ranks?

Once in a statistics class I've seen the suggestion that one non-parametric approach for ANOVA would be to perform the ANOVA analysis on the ranks of the original data (basically as an alternative to ...
2
votes
0answers
78 views

Patterns in binary data sorted with rank indices

I have a sequence of binary data, each row of which has seemingly random bits and associated with an integer value ("rank"). When we have a binary datum, we always can calculate the rank related to it ...
2
votes
0answers
523 views

How to compute composite score of rank order variables?

I have several rank order items about the use of languages in different contexts. Specifically, respondents were asked to order three languages from most to least used in situations such as at work, ...
1
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1answer
96 views

Usefulness of Rank Tests

I know that rank tests are useful because we they are more or less performed without distribution assumptions of the unranked data; they are particular cases of permutation tests... But what are the ...
1
vote
1answer
68 views

How are ranks calculated in tie cases?

I am considering the following question: when there are ties, how are ranks calculated? In some references, they first rank them without repeating the ranks, and then average the ranks of those ties ...
1
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1answer
134 views

Spearman's Rho - from partial ranked variables

I have two variables which represent two performance measures. I ranked a finite set of elements according these two variables. Therefore, I have to ranks. Suppose the ranks are performed in ...
1
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1answer
62 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 ...