Questions tagged [nonparametric]

Use this tag to ask about the nature of nonparametric or parametric methods, or the difference between the two. Nonparametric methods generally rely on few assumptions about the underlying distributions, whereas parametric methods make assumptions that allow data to be described by a small number of parameters.

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101
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7answers
80k 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 ...
83
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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 ...
76
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5answers
70k 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?
61
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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 ...
57
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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. (...
49
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9answers
2k views

Are all models useless? Is any exact model possible — or useful?

This question has been festering in my mind for over a month. The February 2015 issue of Amstat News contains an article by Berkeley Professor Mark van der Laan that scolds people for using inexact ...
42
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3answers
29k 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 ...
34
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4answers
36k 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 ...
33
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1answer
7k views

Intuition behind tensor product interactions in GAMs (MGCV package in R)

Generalized additive models are those where $$ y = \alpha + f_1(x_1) + f_2(x_2) + e_i $$ for example. the functions are smooth, and to be estimated. Usually by penalized splines. MGCV is a package ...
31
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2answers
665 views

StackExchange fires a moderator, and now in response hundreds of moderators resign: is the increase in resignations statistically significant?

I am doing a study on StackExchange. The management of StackExchange has demodded (for unclear reasons) a moderator, and now the network is on fire. Currently many moderators resign or suspend their ...
30
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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 ...
28
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3answers
3k views

What are some illustrative applications of empirical likelihood?

I have heard of Owen's empirical likelihood, but until recently paid it no heed until I came across it in a paper of interest (Mengersen et al. 2012). In my efforts to understand it, I have gleaned ...
26
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3answers
9k 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 ...
26
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3answers
4k views

Why does the Kolmogorov-Smirnov test work?

In reading about the 2-sample KS test, I understand exactly what it is doing but I don't understand why it works. In other words, I can follow all the steps to compute the empirical distribution ...
25
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2answers
4k views

Is it true that Bayesian methods don't overfit?

Is it true that Bayesian methods don't overfit? (I saw some papers and tutorials making this claim) For example, if we apply a Gaussian Process to MNIST (handwritten digit classification), but only ...
24
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4answers
34k views

Is there a nonparametric equivalent of Tukey HSD?

I am using JMP to examine differences in vegetation cover in growth form groups (trees, shrubs, forbs, etc.) before and after three treatments with a control. My sample size is small (n=5) and most of ...
22
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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. ...
22
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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?
22
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1answer
39k 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 ...
21
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3answers
33k views

How can I calculate the confidence interval of a mean in a non-normally distributed sample?

How can I calculate the confidence interval of a mean in a non-normally distributed sample? I understand bootstrap methods are commonly used here, but I am open to other options. While I am looking ...
21
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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? ...
20
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3answers
3k views

Can the MIC algorithm for detecting non-linear correlations be explained intuitively ?

More recently, I read two articles. First one is about the history of the correlation and second is about the new method called Maximal Information Coefficient (MIC). I need your help regarding to ...
20
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3answers
18k views

Why is Pearson parametric and Spearman non-parametric

Apparently Pearson's correlation coefficient is parametric and Spearman's rho is non-parametric. I'm having trouble understanding this. As I understand it Pearson is computed as $$ r_{xy} = \frac{...
20
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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?
19
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2answers
1k views

Generalized additive models — who does research on them besides Simon Wood?

I use GAMs more and more. When I go to provide references for their various components (smoothing parameter selection, various spline bases, p-values of smooth terms), they are all from one ...
19
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2answers
8k views

If the Epanechnikov kernel is theoretically optimal when doing Kernel Density Estimation, why isn't it more commonly used?

I have read (for example, here) that the Epanechnikov kernel is optimal, at least in a theoretical sense, when doing kernel density estimation. If this is true, then why does the Gaussian show up so ...
17
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1answer
25k 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 ...
17
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2answers
8k views

Difference between LOESS and LOWESS

What is the difference between LOESS and LOWESS? From Wikipedia I can only see that LOESS is a generalization of LOWESS. Do they have slightly different parameters?
17
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2answers
5k views

Nonparametric Bayesian analysis in R

I am looking for a good tutorial on clustering data in R using hierarchical dirichlet process (HDP) (one of the recent and popular nonparametric Bayesian methods). ...
17
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3answers
776 views

Statistical test for two distributions where only 5-number summary is known

I have two distributions where only the 5-number summary (minimum, 1st quartile, median, 3rd quartile, maximum) and sample size are known. Cntrary to the question here, not all data points are ...
17
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4answers
21k views

How would one graph the results of subjective rank order?

I'm looking for way to visualize subjective rankings, separate from my non-parametric tests. I've asked 12 participants to rank 8 different items according to different subjective criterion (separate ...
17
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2answers
680 views

If variable kernel widths are often good for kernel regression, why are they generally not good for kernel density estimation?

This question is prompted by discussion elsewhere. Variable kernels are often used in local regression. For example, loess is widely used and works well as a regression smoother, and is based on a ...
16
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4answers
77k views

How do I perform a regression on non-normal data which remain non-normal when transformed?

I've got some data (158 cases) which was derived from a Likert scale answer to 21 questionnaire items. I really want/need to perform a regression analysis to see which items on the questionnaire ...
16
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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 ...
16
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4answers
28k 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?
16
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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 ...
16
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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 ...
15
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5answers
16k views

Is logistic regression a non-parametric test?

I recently received the following question via email. I'll post an answer below, but I was interested to hear what others thought. Would you call logistic regression a non-parametric test? My ...
15
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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....
15
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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
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1answer
7k views

Can bootstrap be used to replace non-parametric tests?

I am fairly new to statistics. The concept of bootstrapping has been confusing to me. I know that normality of the sampling distribution is required to use certain tests such as the t-test. In cases ...
15
votes
3answers
7k 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 ...
15
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1answer
1k views

When/where to use functional data analysis?

I am very new to functional data analysis (FDA). I am reading: Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York. However, I am still not ...
14
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3answers
3k views

Where is density estimation useful?

After going through some slightly terse mathematics, I think I have a slight intuition of kernel density estimation. But I am also aware that estimating multivariate density for more than three ...
14
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1answer
9k views

Is there an optimal bandwidth for a kernel density estimator of derivatives?

I need to estimate the density function based on a set of observations using the kernel density estimator. Based on the same set of observations, I also need to estimate the first and second ...
14
votes
1answer
6k views

Why are ties so difficult in nonparametric statistics?

My nonparametric text, Practical Nonparametric Statistics, often gives clean formulas for expectations, variances, test statistics, and the like, but includes the caveat that this only works if we ...
14
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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 ...
14
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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, ...
14
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3answers
2k views

How to scale violin plots for comparisons?

I'm trying to draw violin plots and wondering if there is an accepted best practice for scaling them across groups. Here are three options I've tried using the R ...
14
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1answer
2k views

Why use the parametric bootstrap?

I am currently trying to get my head around some things concerning parametric bootstrap. Most things are probably trivial but I still think I may have missed something. Suppose I want to get ...

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