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 & 7.2 6.60 & 7.1 The p-value resulting from the test…
Mog
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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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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 scores are either 0, 1, 2, or 3 for each…
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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 Rank test), then do we need to be concerned with…
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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 the use of alternative measures such as the…
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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 are they are supposed to give the exact same…
Jimj
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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 seems immensely practical, especially for…
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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 heard of that before. A search on Google pointed me…
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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 about 10 predictors. I haven't had much success…
frelk
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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 R2. R1: 1,2,3,6,4,5 R2: 1,4,2,3,5,6 From Wikipedia Kendall's tau ranking correlation coefficient is given…
Ayushi Dalmia
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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 Spearman's rank correlation above, it's clear to see…
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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 staff are, stuff like that. I want to check to see…
Chris Beeley
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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 $X_{(k)}$ is the $k$-th order statistic. I am looking…
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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 insurer, a premium quote, and their respective rank in…
Ben
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