Questions tagged [nonparametric]

Procedures that rely on relatively few assumptions about underlying probability distributions.

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97
votes
7answers
79k views

How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples

Certain hypotheses can be tested using Student's t-test (maybe using Welch's correction for unequal variances in the two-sample case), or by a non-parametric test like the Wilcoxon paired signed rank ...
74
votes
5answers
69k views

Kendall Tau or Spearman's rho?

In which cases should one prefer the one over the other? I found someone who claims an advantage for Kendall, for pedagogical reasons, are there other reasons?
22
votes
5answers
9k views

What exactly does a non-parametric test accomplish & What do you do with the results?

I have a feeling this may have been asked elsewhere, but not really with the type of basic description I need. I know non-parametric relies on the median instead of the mean to compare... something. ...
57
votes
6answers
40k views

Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?

I have data from an experiment that I analyzed using t-tests. The dependent variable is interval scaled and the data are either unpaired (i.e., 2 groups) or paired (i.e., within-subjects). E.g. (...
21
votes
1answer
38k views

What is the non-parametric equivalent of a two-way ANOVA that can include interactions?

Hi I am trying to find the non-parametric equivalent of a two-way ANOVA (3x4 design) which is capable of including interactions. From my reading in Zar 1984 "Biostatistical analysis" this is possible ...
12
votes
3answers
742 views

Determine if a heavy tailed distributed process has improved significantly

I observe processing times of a process before and after a change in order to find out, if the process has improved by the change. The process has improved, if the processing time is reduced. The ...
41
votes
3answers
28k views

Bootstrap vs. permutation hypothesis testing

There are several popular resampling techniques, which are often used in practice, such as bootstrapping, permutation test, jackknife, etc. There are numerous articles & books discuss these ...
15
votes
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....
9
votes
1answer
3k views

Relative efficiency of Wilcoxon signed rank in small samples

I have seen in published literature (and posted on here) that the asymptotic relative efficiency of the Wilcoxon signed rank test is at least 0.864 when compared to the t test. I have also heard that ...
13
votes
3answers
3k views

Why is the asymptotic relative efficiency of the Wilcoxon test $3/\pi$ compared to Student's t-test for normally distributed data?

It is well-known that the asymptotic relative efficiency (ARE) of the Wilcoxon signed rank test is $\frac{3}{\pi} \approx 0.955$ compared to Student's t-test, if the data are drawn from a normally ...
6
votes
4answers
7k views

Should I use t-test on highly skewed and discrete data?

I have samples from a highly skewed dataset about users' participation (e.g.: number of posts), that have different sizes (but not less than 200) and I want to compare their mean. For that, I'm using ...
60
votes
15answers
8k views

Why would parametric statistics ever be preferred over nonparametric?

Can someone explain to me why would anyone choose a parametric over a nonparametric statistical method for hypothesis testing or regression analysis? In my mind, it's like going for rafting and ...
12
votes
2answers
3k views

Non-parametric measure of strength of association between an ordinal and a continuous random variable

I'm throwing here the problem as I received it. I have two random variables. One of which is continuous (Y) and the other one which is discrete and will be approached as ordinal (X). I put below the ...
16
votes
3answers
15k views

A non-parametric repeated-measures multi-way Anova in R?

The following question is one of those holy grails for me for some time now, I hope someone might be able to offer a good advice. I wish to perform a non-parametric repeated measures multiway anova ...
20
votes
3answers
12k views

Is there an equivalent to Kruskal Wallis one-way test for a two-way model?

If the model does not satisfy ANOVA assumptions (normality in particular), if one-way, Kruskal-Wallis non-parametric test is recommended. But, what if you have multiple factors?
13
votes
2answers
10k views

Applicability of chi-square test if many cells have frequencies less than 5

To find association between peer's support (independent variable) and work satisfaction (dependent variable) I wish to apply chi-square test. Peer's support is categories in four groups according to ...
30
votes
2answers
3k views

Is there a reliable nonparametric confidence interval for the mean of a skewed distribution?

Very skewed distributions such as the log-normal do not result in accurate bootstrap confidence intervals. Here is an example showing that the left and right tail areas are far from the ideal 0.025 ...
34
votes
4answers
35k views

What is the weak side of decision trees?

Decision trees seems to be a very understandable machine learning method. Once created it can be easily inspected by a human which is a great advantage in some applications. What are the practical ...
26
votes
3answers
8k views

Why are Gaussian process models called non-parametric?

I am a bit confused. Why are Gaussian processes called non parametric models? They do assume that the functional values, or a subset of them, have a Gaussian prior with mean 0 and covariance function ...
12
votes
3answers
13k views

Is there a multiple-sample version or alternative to the Kolmogorov-Smirnov Test?

I am comparing the size distribution of trees in six pairs of plots where one plot received a treatment and the other a control. Using a Kolmogorov-Smirnov test on each pair of plots I find that $p$ ...
20
votes
4answers
8k views

Is there any statistical test that is parametric and non-parametric?

Is there any statistical test that is parametric and non-parametric? This question was asked by an interview panel. Is it valid question?
14
votes
1answer
8k views

Is there an alternative to the Kolmogorov-Smirnov test for tied data with correction?

I've got a bunch of data from two samples (control and treated), each containing several thousand values which are to undergo significance testing in R. Theoretically, the values should be continuous, ...
6
votes
1answer
8k views

Friedman's test and post-hoc analysis

I am carrying out a statistical analysis for my research. I am using a Friedman's test with post hoc analysis. At present I am using the function ...
5
votes
1answer
3k views

Difference of 'centers' of 2 non-normal samples with Mann-Whitney test

I have 2 non-normally distributed samples of different sizes (N1~=N2). To evaluate whether there is a significant difference between these samples, I used the Mann Whitney U test (...
5
votes
1answer
198 views

Why are all the permutations of i.i.d. samples from a continuous distribution equally likely?

Suppose $X$ is i.i.d from a continuous distribution Why is$$P(X_{i_1}<X_{i_2}<\cdots<X_{i_3})=P(X_{j_1}<X_{j_2}<\cdots<X_{j_3})=\frac{1}{n!}$$for all $i,j$? I think we can reason ...
5
votes
2answers
19k views

Nonparametric equivalent of ANCOVA for continuous dependent variables

I have an independent categorical variable ($X$ with two categories, $x_{1}$ and $x_{2}$) and two continuous dependent variables ($y$ and $z$). Using a Mann Whitney test, I know that $y$ is ...
4
votes
1answer
1k views

Non-parametric confidence interval about the difference of means for unpaired data

Consider two samples ${(x_i)}_{i=1}^m$ and ${(y_i)}_{i=1}^n$. Assume that the $x_i$ are independent replicates from a distribution with expectation $\mu_X$ and similarly the $y_i$ are independent ...
3
votes
1answer
607 views

How can I measure difference between non-parametric data with many zeros?

I'm comparing two groups of students by their course activity and I'm struggling a little to determine the best way to test for significant difference. The data is non-normal, and very prevalent with ...
7
votes
2answers
4k views

Permutation test in R

I have the following data for 10 subjects based on before and after measurements: ...
7
votes
2answers
1k views

“One-tailed” Levene Test

F-tests can be two-tailed (to test that $s_1^2 \ne s_2^2$) or one-tailed (to test that $s_1^2 > s_2^2$). How can I modify Levene/Brown-Forsythe to be "one-tailed", that is, to test $s_1^2 > s_2^...
6
votes
2answers
3k views

Jonckheere-Terpstra interpretation

I am running the Jonckheere-Terpstra in place of Kruskal-Wallis test, as my factor is in ordinal scale (i.e. groups can be ordered). The Asymptotic significance (2-tailed) is 0.000, so it seems there ...
3
votes
2answers
1k views

Estimate population quantiles from subpopulations' quantiles

Suppose there is a population partitioned arbitrarily into a set of subpopulations that completely cover the original population. Assume that for some variable, we know each subpopulation's quintiles ...
11
votes
1answer
6k views

Friedman test vs Wilcoxon test

I'm trying to assess performance of a supervised machine learning classification algorithm. The observations fall into nominal classes (2 for the time being, however I'd like to generalize this to ...
10
votes
2answers
6k views

Is ordinal or interval data required for the Wilcoxon signed rank test?

Having looked at multiple online sources, I can't seem to get a straight answer. Could someone please clarify for me if ordinal data is sufficient to use for the WSRT and if not, is the sign test an ...
2
votes
3answers
4k views

non-parametric two-sample equivalence tests with unequal sample sizes

I would like to compare means/medians of two samples that may be very skewed in size, e.g. 25 points and 1 or 2 points and test them for similarity, rather than difference. I realize that the power ...
83
votes
14answers
6k views

Why haven't robust (and resistant) statistics replaced classical techniques?

When solving business problems using data, it's common that at least one key assumption that under-pins classical statistics is invalid. Most of the time, no one bothers to check those assumptions so ...
15
votes
1answer
3k views

What is “Targeted Maximum Likelihood Expectation”?

I'm trying to understand some papers by Mark van der Laan. He's a theoretical statistician at Berkeley working on problems overlap significantly with machine learning. One problem for me (besides ...
15
votes
1answer
24k views

Should I use t-test on highly skewed data ? Scientific proof, please?

I have samples from a highly skewed (looking like an exponential distribution) dataset about users' participation (e.g.: number of posts), that have different sizes (but not less than 200) and I want ...
16
votes
5answers
4k views

Checking ANOVA assumptions

A few months ago I posted a question about homoscedasticity tests in R on SO, and Ian Fellows answered that (I'll paraphrase his answer very loosely): Homoscedasticity tests are not a good tool ...
15
votes
3answers
6k views

Test if multidimensional distributions are the same

Lets say I have two or more sample populations of n-dimensional continuous-valued vectors. Is there a nonparametric way to test if these samples are from the same distribution? If so, is there a ...
16
votes
2answers
33k views

How to run two-way ANOVA on data with neither normality nor equality of variance in R?

I am working on my master thesis at the moment and planned on running the statistics with SigmaPlot. However, after spending some time with my data I came to the conclusion that SigmaPlot might not be ...
19
votes
1answer
9k views

Non-parametric test if two samples are drawn from the same distribution

I would like to test the hypothesis that two samples are drawn from the same population, without making any assumptions about the distributions of the samples or the population. How should I do this? ...
6
votes
2answers
2k views

Density estimation for large dataset

I have a unidimensional data set with more than 1000000 observations. Assuming that those observations are independent realizations of the same random variable I need to estimate the underling ...
8
votes
2answers
9k views

Non-parametric for two-way ANOVA (3x3)

My dependent variable is continuous, non-normal (skewed left according to Shapiro-Wilk test). I have two independent variables (treatment group by colour, food type). There are 3 levels within each ...
6
votes
1answer
1k views

Two broad categories of dimensionality reduction: with and without an explicit mapping function

I think there are two very broad categories of dimensionality reduction (DR) techniques: We can compute an analytic form of mapping from the training data, say $x\mapsto y: y=f(x)$, where $f(\cdot)$ ...
6
votes
3answers
2k views

Wilcoxon Signed Rank Symmetry Assumption

The assumption of symmetricity for signed rank test (and its relevance) is becoming extremely confusing for me. I am hypothesizing that sub-population A (before treatment) and sub-population B (after ...
6
votes
2answers
533 views

Correlation between vegetation and erosion

I am wanting to find the correlation between two variables: a categorical vegetation variable (with categories 1-4) and a continuous variable of erosion (with values anywhere between 0.2 and 9). I ...
4
votes
1answer
784 views

Plotting non-parametric (E)CDEF confidence envelopes for comparison

I have previously asked about a way to test whether two samples are drawn from the same distribution (Non-parametric test if two samples are drawn from the same distribution). I was very glad to learn ...
3
votes
0answers
127 views

Can “non-parametric” tests be achieved with generalized linear models?

I recently read @Kodiologist's answer to a post here looking for clarification on the relation between GLMs and non-parametric tests. His answer is along the lines of "the approach is not non-...
2
votes
1answer
1k views

How do I estimate a smooth cdf from a set of observations?

I have a set of observation, let's call it $X$ and would like to fit a cdf to it. $X$ has a distribution which is roughly approximable with the normal distribution. This CDF should correspond to a ...

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