# Parametric and non-parametric tests

What is the difference between parametric and non-parametric statistics, their purpose and applications in biological sciences?

What is the difference between parametric and non-parametric statistics, their purpose and applications in biological sciences?

## Popular Answers

Deletedwhile the non-parametric are distribution free methods. They rely on ordering (ranking) of observations.

.

More specifically, the data distribution is significant in the choice between parametric and non-parametric procedures.If we believe that the populations are normally distributed then we use parametric methods. If we are not sure or we suspect that they do not behave normally then we use non-parametric methods.

Similarly the scale of the data is important. That is categorical (nominal) or ordinal scale data demand the use of non-parametric methods while in the case of interval and ratio scale data where we cannot assume population normality then again non-parametric methods have to be used.

As an example ANOVA is a parametric method while Kruskal Wallis is the corresponding non-parametric method which has to be used in case the assumption of normality is rejected in the before the use of ANOVA tests (equality of variances with Bartlett's test and normality with Kolmogorov-Smirnov test).

Similarly the Mann-Whitney in non-parametric corresponds to the pooled t test in parametrics. The paired t test in parametrics to Wilcoxon signed rank test and in the case of one mean the Z, t tests in parametrics correspond to Wilcoxon signed test.

It is important to mention also the use of the non-parametric procedure of chi-square for testing frequencies in categories. Chi-square can be used for testing goodness of fit, independence and homogeneity.

Fathi M Sherif· University of Tripolia. whether you wish to make decisions about differences between the populations from which your samples come, or whether you wish to make decisions about associations between features wthin the population from which your sample come.

b. whether your measurements are at the interval, ordinal or categorical level

C. whether your measurements are matched or unmatched

Once you are certain about these things, you might use the appropraite test according to the rationale of test. Indeed, all the statistical techniques have both advantages and disadvantages, and it is up to you to weigh them up in the context of your own project.

Non-parametric tests are ones that test hypotheses which do not make assumpations about the population parameters, while distribution free tests do not make assumptions about the population distribution. Thy have the advantage that they can applied in more general conditions than can parametric tests. The sample sizes are also playing a role in choosing the test.

## All Answers (21)

Fathi M Sherif· University of Tripolia. whether you wish to make decisions about differences between the populations from which your samples come, or whether you wish to make decisions about associations between features wthin the population from which your sample come.

b. whether your measurements are at the interval, ordinal or categorical level

C. whether your measurements are matched or unmatched

Once you are certain about these things, you might use the appropraite test according to the rationale of test. Indeed, all the statistical techniques have both advantages and disadvantages, and it is up to you to weigh them up in the context of your own project.

Non-parametric tests are ones that test hypotheses which do not make assumpations about the population parameters, while distribution free tests do not make assumptions about the population distribution. Thy have the advantage that they can applied in more general conditions than can parametric tests. The sample sizes are also playing a role in choosing the test.

Abdul Majeed· Hazara UniversityFathi M Sherif· University of TripoliAlessandro Giuliani· Istituto Superiore di SanitàAbdul Majeed· Hazara Universityfor useful comments

Jochen Wilhelm· Justus-Liebig-Universität GießenVery often, the t-test is compared to its non-parametric alternative (Mann-Whitney/Wilcoxon test). Notably, the latter compares distributions, i.e., it is sensitive to whole bunch of distributional properties. This test can be used to specifically test a location shift ONLY when ALL OTHER distributional properties are identical. This is often overseen. Many papers show results of a MW/W-test to test a location shift on data with clearly different variances between the groups. In this case, the test result does not specifically represent the location shift. I would be required to transform the data. But often, for the transformed data there is a reasonable model for which again the parameters can be tested directly...

Deletedwhile the non-parametric are distribution free methods. They rely on ordering (ranking) of observations.

.

More specifically, the data distribution is significant in the choice between parametric and non-parametric procedures.If we believe that the populations are normally distributed then we use parametric methods. If we are not sure or we suspect that they do not behave normally then we use non-parametric methods.

Similarly the scale of the data is important. That is categorical (nominal) or ordinal scale data demand the use of non-parametric methods while in the case of interval and ratio scale data where we cannot assume population normality then again non-parametric methods have to be used.

As an example ANOVA is a parametric method while Kruskal Wallis is the corresponding non-parametric method which has to be used in case the assumption of normality is rejected in the before the use of ANOVA tests (equality of variances with Bartlett's test and normality with Kolmogorov-Smirnov test).

Similarly the Mann-Whitney in non-parametric corresponds to the pooled t test in parametrics. The paired t test in parametrics to Wilcoxon signed rank test and in the case of one mean the Z, t tests in parametrics correspond to Wilcoxon signed test.

It is important to mention also the use of the non-parametric procedure of chi-square for testing frequencies in categories. Chi-square can be used for testing goodness of fit, independence and homogeneity.

Ahmed Abdella Osman· Ministry of Health Saudi ArabiaAhmed Abdella Osman· Ministry of Health Saudi ArabiaWaqas Latif· University of Health Sciences LahoreJochen Wilhelm· Justus-Liebig-Universität GießenFurther, I do not know any "non-parametric" test that would specifically and generally test medians. Do you mean Wilcoxon/Mann-Whitney? This test compares rank distributions, not medians. It is especially sensitive to location shifts, that's right. But is well "detects" other differences in the rank distributions. This test is equivalent to a test of the medians ONLY when the shapes of the distributions are equal except the location (i.e. a plain shift towards higher or lower values, without changing the variance, skew, kurtosis and all other higher moments). And this test is typically recommended when the data are heteroscedastic, and just then it *won't* be a test of the medians. I can give you sample data to demonstrate that this test will give tiny p-values for samples with *identical* medians (but different means). I have never encountered a real-world example where a location-shift (without alterng the shape of the distribution) was the case. Usually, people simply do not recognize the correct model. In the biomed field it is often one of beta-, gamma-, Poisson-, or a log-normal model.

If medians are to be tested, I would recommend a bootstrap approach on the median.

Carles Grijalbo· University of ValenciaHello!! my problem is that i have normal and no normal data distributions in the subscales of a questionary!!

What i could do?, two different analisys? or can i normalice the data?

Thanks

Waqas Latif· University of Health Sciences Lahoreyou can use both method two analyse the data.

Godwin Oyedokun· Saffron Professional ServicesThank you all for your insight to the question.

These are very useful

Paul Klawinski· William Jewell CollegeRegarding some of the comments above, nonparametric tests are not distribution free. They assume that the distributions, whatever their shape, are similar in form and only differ in location (e.g., an ANOVA or t-test). Cases of heteroscedaticity mean that the populations being compared have different forms and so nonparametric tests are no better (and in some cases, more biased) than their parametric counterparts. Search for a paper by Zimmerman (1998) as a reference

Jochen Wilhelm· Justus-Liebig-Universität GießenPaul, I don't think this is correct the way you wrote it.

For instance, the Wilcoxon test does not require that the distributions of the compared populations are equal. This test is just often described (or "sold as") as test on a location shift, or a test on the "difference in medians". When Wilcoxon test is used to test this, then, and only then, it requires that the population distributions are equal except for their location. Otherwise it tests the stochastic inequality: the tested null hypothesis is P(X>Y)=0.5. The problem is that many users are not aware of the tested null and what it means.

I still want to wave a waring sign when people compare different tests, like saying that the t-test would be a "counterpart" or an "alternative" to the Wilcoxon test (or vice versa). This is very misleading because these two tests are about different (null)hypotheses. The Wilcoxon test does not test expected differences - again only with the exeption of the very special case that the distribution shapes are equal

andsymmetric! If a test on expected differences is desired, and the asusmptions for a t-test are considerably or obviousely violated, the Wilcoxon test is usually justnota viable alternative! It would test a different kind of hypothesis! But the much more interesting question is why the assumptions of the t-test are violated. It is possibly not very sensible to ask for an expected difference in the first place. It is often the case that not the value itself but some underlying parameter of a data.gerenating model is what should be infered (like, for instance, a proportion, a rate, a count-expectation ore something more complex). This would start a process ofthinkingabout the data and open possibilities to get to a betterunderstandingand newinsights. The usual mechanic procedure of "oh, t-test won't work, so I will use Wilcoxon" is a rather dumb escape and misses/ignores the most important point: to understand your data.Paul Klawinski· William Jewell CollegeFrom Kruskal and Wallis' original paper: "Only very general assumptions are made about the kind of distributions from which the observations come. The only assumptions underlying the use of ranks made in this paper are that the observations are all independent, that all those within a given sample come from a single population, and that the populations are of approximately the same form." (Kruskal & Wallis 1952:585).

Bishwo Pokharel· University of GuelphHello, my data doesn't follow normal distribution. They are obtained from behavioral experiment. I am using Poisson distribution. What should be my approach?

Jochen Wilhelm· Justus-Liebig-Universität GießenIf your data are counts your options are:

Poisson model

zero-inflated Poisson

negative-binomial mode

hurdle models

Bishwo Pokharel· University of Guelph@Jochen, Thank you for the info..I have count, duration and latency data.. The duration comes after counting and carefully recording the timing of that behavior. Can I use poisson for both duration and latency also?

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