Parametric Tests Can Be Used With Any Type of Data.

Parametric and Non-parametric tests for comparison two or more than groups

Statistics: Parametric and not-parametric tests

This section covers:

•        Choosing a test
•        Parametric tests
•        Not-parametric tests

Choosing a Exam

In terms of selecting a statistical test, the near important question is "what is the main study hypothesis?" In some cases there is no hypothesis; the investigator just wants to "encounter what is at that place". For example, in a prevalence study in that location is no hypothesis to test, and the size of the written report is determined by how accurately the investigator wants to decide the prevalence. If there is no hypothesis, and so there is no statistical exam. It is important to determine a priori which hypotheses are confirmatory (that is, are testing some presupposed human relationship), and which are exploratory (are suggested past the data). No single study can support a whole series of hypotheses. A sensible plan is to limit severely the number of confirmatory hypotheses. Although it is valid to use statistical tests on hypotheses suggested past the information, the P values should be used but as guidelines, and the results treated equally tentative until confirmed by subsequent studies. A useful guide is to use a Bonferroni correction, which states simply that if ane is testing n contained hypotheses, i should use a significance level of 0.05/north. Thus if there were ii independent hypotheses a upshot would be declared meaning but if P<0.025. Note that, since tests are rarely independent, this is a very conservative procedure – i.east. one that is unlikely to turn down the null hypothesis. The investigator should then ask "are the data contained?" This can be difficult to decide simply as a rule of thumb results on the same individual, or from matched individuals, are non independent. Thus results from a crossover trial, or from a case-control study in which the controls were matched to the cases by age, sex and social class, are not independent.

•        Analysis should reflect the design, and then a matched design should be followed past a matched analysis.
•        Results measured over time crave special care. One of the nearly mutual mistakes in statistical analysis is to care for correlated variables as if they were
  contained.  For example, suppose we were looking at treatment of leg ulcers, in which some people had an ulcer on each leg. We might have xx subjects with
  thirty ulcers just the number of independent pieces of information is xx considering the land of ulcers on each leg for 1 person may be influenced by the land of
  health of the person and an analysis that considered ulcers as independent observations would exist wrong. For a correct analysis of mixed paired and unpaired
  information consult a statistician.

The side by side question is "what types of data are being measured?" The test used should be determined by the data. The pick of exam for matched or paired data is described in Tabular array 1 and for independent data in Tabular array 2.

Table i Selection of statistical test from paired or matched observation

Information technology is helpful to decide the input variables and the outcome variables. For example, in a clinical trial the input variable is the type of treatment - a nominal variable - and the outcome may exist some clinical mensurate peradventure Usually distributed. The required test is then the t-exam (Table ii). Yet, if the input variable is continuous, say a clinical score, and the issue is nominal, say cured or not cured, logistic regression is the required assay. A t-test in this example may help only would not give us what we require, namely the probability of a cure for a given value of the clinical score. As another instance, suppose nosotros have a cross-exclusive study in which we ask a random sample of people whether they retrieve their general practitioner is doing a adept job, on a five point scale, and we wish to ascertain whether women have a higher opinion of general practitioners than men have. The input variable is gender, which is nominal. The result variable is the 5 betoken ordinal scale. Each person's opinion is contained of the others, and then nosotros take independent data. From Table 2 we should use a χⁱⁱ test for trend, or a Isle of mann-Whitney U examination with a correction for ties (Northward.B. a tie occurs where two or more values are the same, so in that location is no strictly increasing gild of ranks – where this happens, one can boilerplate the ranks for tied values). Note, however, if some people share a general practitioner and others do not, then the data are non contained and a more than sophisticated analysis is called for. Note that these tables should exist considered every bit guides only, and each example should exist considered on its merits.

Table 2 Choice of statistical test for independent observations

^a If information are censored. ^b The Kruskal-Wallis exam is used for comparing ordinal or non-Normal variables for more than ii groups, and is a generalisation of the Mann-Whitney U exam. ^c Analysis of variance is a general technique, and one version (one way analysis of variance) is used to compare Normally distributed variables for more than ii groups, and is the parametric equivalent of the Kruskal-Wallistest. ^d If the outcome variable is the dependent variable, then provided the residuals (the differences between the observed values and the predicted responses from regression) are plausibly Normally distributed, and so the distribution of the contained variable is not of import. ^e There are a number of more avant-garde techniques, such as Poisson regression, for dealing with these situations. Still, they crave certain assumptions and it is often easier to either dichotomise the outcome variable or care for it as continuous.

Parametric tests are those that make assumptions about the parameters of the population distribution from which the sample is drawn. This is often the assumption that the population data are normally distributed. Non-parametric tests are "distribution-costless" and, as such, can be used for non-Normal variables. Table iii shows the non-parametric equivalent of a number of parametric tests.

Table 3 Parametric and Non-parametric tests for comparing ii or more groups

Non-parametric tests are valid for both non-Commonly distributed information and Normally distributed data, so why not apply them all the time?

It would seem prudent to use non-parametric tests in all cases, which would save i the carp of testing for Normality. Parametric tests are preferred, however, for the following reasons:

ane. We are rarely interested in a significance exam alone; we would like to say something virtually the population from which the samples came, and this is best done with
estimates of parameters and confidence intervals.

ii. Information technology is hard to exercise flexible modelling with not-parametric tests, for example allowing for confounding factors using multiple regression.

3. Parametric tests usually take more statistical power than their non-parametric equivalents. In other words, one is more than probable to detect significant differences when
they truly exist.

Do non-parametric tests compare medians?

It is a usually held belief that a Mann-Whitney U exam is in fact a exam for differences in medians. Nonetheless, 2 groups could accept the same median and all the same take a significant Mann-Whitney U test. Consider the following data for two groups, each with 100 observations. Group 1: 98 (0), 1, 2; Group ii: 51 (0), 1, 48 (2). The median in both cases is 0, but from the Isle of mann-Whitney test P<0.0001. But if nosotros are prepared to make the boosted assumption that the difference in the two groups is just a shift in location (that is, the distribution of the data in one group is but shifted by a fixed amount from the other) can we say that the test is a test of the divergence in medians. Still, if the groups have the same distribution, then a shift in location will move medians and means by the same amount and and then the difference in medians is the same as the departure in means. Thus the Mann-Whitney U test is also a examination for the divergence in means. How is the Mann- Whitney U test related to the t-test? If 1 were to input the ranks of the data rather than the data themselves into a two sample t-test program, the P value obtained would be very shut to that produced by a Mann-Whitney U test.

Reference

•        Campbell MJ and Swinscow TDV. Statistics at Foursquare One 11th ed. Wiley-Blackwell: BMJ Books 2009.

© MJ Campbell 2016, S Shantikumar 2016

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Source: https://www.healthknowledge.org.uk/public-health-textbook/research-methods/1b-statistical-methods/parametric-nonparametric-tests