Non-parametric regression

[CuriousArv]

Hello all

I am forced to get famiilar with this topic quickly and I am struggling with the following after reading it in a paper. Can someone help with the underlined ones. I also have a follow up question which I will introduce after this.

From the paper: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC153434/, i saw the following and wanted to get clear.

Advantages of nonparametric methods

Nonparametric methods require no or very limited assumptions to be made about the format of the data, and they may therefore be preferable when the assumptions required for parametric methods are not valid.

Nonparametric methods can be useful for dealing with unexpected, outlying observations that might be problematic with a parametric approach.

Nonparametric methods are intuitive and are simple to carry out by hand, for small samples at least.

Nonparametric methods are often useful in the analysis of ordered categorical data in which assignation of scores to individual categories may be inappropriate. For example, non-parametric methods can be used to analyse alcohol consumption directly using the categories never, a few times per year, monthly, weekly, a few times per week, daily and a few times per day. In contrast, parametric methods require scores (i.e. 1–7) to be assigned to each category, with the implicit assumption that the effect of moving from one category to the next is fixed.

Disadvantages of nonparametric methods

Nonparametric methods may lack power as compared with more traditional approaches. This is a particular concern if the sample size is small or if the assumptions for the corresponding parametric method (e.g. Normality of the data) hold.

Nonparametric methods are geared toward hypothesis testing rather than estimation of effects. It is often possible to obtain nonparametric estimates and associated confidence intervals, but this is not generally straightforward.

Tied values can be problematic when these are common, and adjustments to the test statistic may be necessary.

 

[Dale]

Sorry, what is your question here?

 

[CuriousArv]

My question is

Is it possible to illustrate the underlined points with examples, so I can get a clear understanding

 

[Dale]

Can you focus on the one most important point?

What you are currently asking would be more along the lines of a textbook rather than an internet post. I can help with any of the points except the last, but not with all of them together. It is too much.

 

[Hornbein]

My question is

Is it possible to illustrate the underlined points with examples, so I can get a clear understanding

I'd google for nonparametric tests of statistics. Parametric tests assume that the distribution from which the sample is taken is known. Normal, binomial, Poisson, whateve. Non-parametric tests make no such assumptions.

 

[CuriousArv]

hello

okay will make it more narrower for now.

Nonparametric methods are geared toward hypothesis testing rather than estimation of effects. ~ okay, i don't follow this one.

Secondly whenever people write: Parametric tests assume that the distribution from which the sample is taken is known. Non-parametric does not, some other people write that the form of the functional is not known. Are these two different things? If the distribution is unknown, i understand that to mean that if one collected a lot of data during sampling, the residual around the line of best fit for each point in the line is not necessarily normally distributed. Is that correct?

 

[CuriousArv]

if people are uncomfortable explaining because I should do it by myself, please let me know so I can close this thread. For people doing research who need to tie together knowledge from multiple fields and the resulting drain -> collab and asking questions on forums -> allowable? protocol -> exhaustion thinking about protocols...anyway..

 

[Dale]

Nonparametric methods are geared toward hypothesis testing rather than estimation of effects. ~ okay, i don't follow this one.

So for this one, suppose that you have a typical placebo controlled randomized trial testing a weight loss treatment. You would certainly measure the subject's weight change, but you might also have the subjects report their perceived energy level on a 5-point scale like "lethargic" to "tired" to "normal" to "energized" to "hyperactive".

So you would want to use parametric methods on the weight. That would allow you to determine whether the treatment and control groups lost different amounts of weight (hypothesis test) and if so then how many more kilograms of weight were lost on average (effect size).

But for energy level you would only use non-parametric methods. You could determine if the treatment and control groups had different levels of energy (hypothesis test) But if they did then you would not be able to determine how much more energy. After all, on this scale what would effect size even mean? Like for example what would it mean to have 1.2 more energy.

 

[Dale]

if people are uncomfortable explaining because I should do it by myself, please let me know

No problem. I just couldn't tackle all of the topics at once.

 

[FactChecker]

I have not seen a non-parametric method that is similar to regression, but there may be some. It may help you to see an example of a non-parametric methods. There are probably many examples on the internet.

A typical non-parametric test would be to test if the mean of distribution A is greater than the mean of distribution B with some confidence (say 95%). You can put the the numbers from a sample of A and a sample of B in order from smallest to largest, like: a1 < a2 < b1 < a3 < b2 < b3 < a4 < a5 < b4 < b5. The "rank ordering" of the numbers can be used in a statistical test. The statistical test does not need to know the distributions A and B. It is a non-parametric test.