# 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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### 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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### 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....
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### 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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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
845 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 ...
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### 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 ...
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### 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 ...
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### 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 / ...
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### 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 ...
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### 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 ...
132 views

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### 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 ...
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### 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 ...
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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 ...
601 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 ...
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### 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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### 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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### 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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### 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 ...
179 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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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### 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 ...
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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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### 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 ...
332 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 ...