# Parametric And Nonparametric Statistics Pdf

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In terms of selecting a statistical test, the most important question is "what is the main study hypothesis?

This book demonstrates that nonparametric statistics can be taught from a parametric point of view. As a result, one can exploit various parametric tools such as the use of the likelihood function, penalized likelihood and score functions to not only derive well-known tests but to also go beyond and make use of Bayesian methods to analyze ranking data.

Let us begin this article with the obvious—in the process of data analysis, always look at the data first. By that we mean investigators look first at the numerical and graphical summaries of the data. Checking out the data first provides an overview of the overall project, gives a clearer understanding of the variables and their values, and shows how the values are distributed.

## Nonparametric Statistics

In terms of selecting a statistical test, the most important question is "what is the main study hypothesis? For example, in a prevalence study there is no hypothesis to test, and the size of the study is determined by how accurately the investigator wants to determine the prevalence.

If there is no hypothesis, then there is no statistical test. It is important to decide a priori which hypotheses are confirmatory that is, are testing some presupposed relationship , and which are exploratory are suggested by 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 by the data, the P values should be used only as guidelines, and the results treated as tentative until confirmed by subsequent studies. A useful guide is to use a Bonferroni correction, which states simply that if one is testing n independent hypotheses, one should use a significance level of 0. Note that, since tests are rarely independent, this is a very conservative procedure — i.

The investigator should then ask "are the data 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.

The next question is "what types of data are being measured? The choice of test for matched or paired data is described in Table 1 and for independent data in Table 2. It 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 be some clinical measure perhaps Normally distributed. The required test is then the t -test Table 2.

However, if the input variable is continuous, say a clinical score, and the outcome is nominal, say cured or not cured, logistic regression is the required analysis. A t -test in this case may help but would not give us what we require, namely the probability of a cure for a given value of the clinical score.

As another example, suppose we have a cross-sectional study in which we ask a random sample of people whether they think their general practitioner is doing a good 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 outcome variable is the five point ordinal scale. Each person's opinion is independent of the others, so we have independent data. Note, however, if some people share a general practitioner and others do not, then the data are not independent and a more sophisticated analysis is called for. Note that these tables should be considered as guides only, and each case should be considered on its merits.

However, they require certain assumptions and it is often easier to either dichotomise the outcome variable or treat 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. Table 3 shows the non-parametric equivalent of a number of parametric tests. Non-parametric tests are valid for both non-Normally distributed data and Normally distributed data, so why not use them all the time?

It would seem prudent to use non-parametric tests in all cases, which would save one the bother of testing for Normality. Parametric tests are preferred, however, for the following reasons:. It is difficult to do flexible modelling with non-parametric tests, for example allowing for confounding factors using multiple regression.

Parametric tests usually have more statistical power than their non-parametric equivalents. It is a commonly held belief that a Mann-Whitney U test is in fact a test for differences in medians. However, two groups could have the same median and yet have a significant Mann-Whitney U test. Consider the following data for two groups, each with observations. Only if we are prepared to make the additional assumption that the difference in the two groups is simply a shift in location that is, the distribution of the data in one group is simply shifted by a fixed amount from the other can we say that the test is a test of the difference in medians.

However, if the groups have the same distribution, then a shift in location will move medians and means by the same amount and so the difference in medians is the same as the difference in means. Thus the Mann-Whitney U test is also a test for the difference in means. How is the Mann- Whitney U test related to the t -test?

If one 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 close to that produced by a Mann-Whitney U test. Skip to main content. Create new account Request new password. You are here 1b - Statistical Methods. Analysis should reflect the design, and so a matched design should be followed by a matched analysis. Results measured over time require special care.

For example, suppose we were looking at treatment of leg ulcers, in which some people had an ulcer on each leg. Table 1 Choice of statistical test from paired or matched observation. Normal, Poisson, Binomial and their uses Sampling Distributions Principles of Making Inferences from a Sample to a Population Measures of Location and Dispersion and their appropriate uses Graphical methods in Statistics Hypothesis Testing Type I and Type II errors Problems of Multiple Comparisons Parametric and Non-parametric tests for comparing two or more groups Sample size and statistical power Regression and correlation Multiple linear regression The appropriate use, objectives and value of multiple linear regression, multiple logistic regression, principles of life-tables, and Cox regression Principles of life-tables and Cox regression Comparisons of survival rates; heterogeneity; funnel plots; the role of Bayes' theorem Heterogeneity: funnel plots The role of Bayes' theorem Rates definitions Glossary.

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Section 1: The theoretical perspectives and methods of enquiry of the sciences concerned with human behaviour. Inequalities in health e. The impact of political, economic, socio-cultural, environmental and other external influences. Introduction to study designs - intervention studies and randomised controlled trials. Parametric and Non-parametric tests for comparing two or more groups. Recently updated content 3c - Applications.

## Nonparametric Methods

Non-parametric methods are used to analyze data when the distributional assumptions of more common procedures are not satisfied. For example, many statistical procedures assume that the underlying error distribution is Gaussian, hence the widespread use of means and standard deviations. When the error distribution is not known, non-parametric statistical tests may be safer to apply. The non-parametric methods in Statgraphics are options within the same procedures that apply the classical tests. These non-parametric statistical methods are classified below according to their application. Goodness-of-fit tests are used to compare the frequency of occurrence of observations either quantitative or categorical to a probabilistic model.

If a nonparametric test is required, more data will be needed to make the same conclu-sion. The tests dealt with in this handout are used when you have one or more scores from each subject. Student t-test parametric and non-parametric tests in SPSS. Non-Parametric Paired T-Test. First, nonparametric tests are less powerful.

independent samples ttest (cis true)—was used instead. Non-parametric methods make no assumptions about the. distribution of data in the.

## What is the difference between a parametric and a nonparametric test?

Ben Derrick Ben. Derrick uwe. Paul White Paul.

Need a hand? All the help you want just a few clicks away. Therefore, several conditions of validity must be met so that the result of a parametric test is reliable. They can thus be applied even if parametric conditions of validity are not met. Parametric tests often have nonparametric equivalents.

### Parametric and Non-parametric tests for comparing two or more groups

Quantitative Methods 2 Reading Hypothesis Testing Subject Parametric and Non-Parametric Tests. Why should I choose AnalystNotes? AnalystNotes specializes in helping candidates pass. Find out more. Subject

Nonparametric statistics sometimes uses data that is ordinal, meaning it does not rely on numbers, but rather on a ranking or order of sorts. For example, a survey conveying consumer preferences ranging from like to dislike would be considered ordinal data. Nonparametric statistics includes nonparametric descriptive statistics , statistical models, inference, and statistical tests. The model structure of nonparametric models is not specified a priori but is instead determined from data. The term nonparametric is not meant to imply that such models completely lack parameters, but rather that the number and nature of the parameters are flexible and not fixed in advance.

Simply put: AnalystNotes offers the best value and the best product available to help you pass your exams. Quantitative Methods 2 Reading Hypothesis Testing Subject Parametric and Non-Parametric Tests. Why should I choose AnalystNotes? Find out more.

#### Derrick, Ben; White, Paul; Toher, Deirdre

Before you order, simply sign up for a free user account and in seconds you'll be experiencing the best in CFA exam preparation. Quantitative Methods 2 Reading Hypothesis Testing Subject Parametric and Non-Parametric Tests. Seeing is believing! Find out more.

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