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 Subject: Advanced Statistics Category: Reference, Education and News > General Reference Asked by: lgl1-ga List Price: \$50.00 Posted: 23 Oct 2003 20:02 PDT Expires: 22 Nov 2003 19:02 PST Question ID: 269250
 ```Question: Compare and contrast parametric statistics and non-parametric statistics in terms of: 1) When and why we use each. 2) Strengths and weaknesses of using each. 3) The costs and benefits of using each. Discuss two (2) parametric statistics and two (2) non-parametric statistics in your answer to illustrate your points. Text: Basic Statistical Analysis (6th edition) by Richard Sprinthall```
 ```lgl1-ga, 1) When and why we use each”: Let’s start with a basic definition of non-parametric statistics, from [ http://www.lakeheadu.ca/~kinesiology/Wmontelp/mannWhit/tsld002.htm ]: “Often referred to as distribution free statistics, non-parametric statistics are used when the data may not demonstrate the characteristics of normality (i.e. follow a normal distribution). Non-parametric statistics are used with nominal data, where the response set can be converted to counts of events, and the measurement scale is ignored. Non-parametric statistics can be used when data are converted to ranks.” Getting into more detail, a look at non-parametric statistics from “Statistics Glossary, v. 1.1” by Valerie J. Easton & John H. McColl [ http://www.cas.lancs.ac.uk/glossary_v1.1/nonparam.html#nonparat ]: “Non-Parametric tests are often used in place of their parametric counterparts when certain assumptions about the underlying population are questionable. For example, when comparing two independent samples, the Wilcoxon Mann-Whitney test does not assume that the difference between the samples is normally distributed whereas its parametric counterpart, the two sample t-test does. Non-Parametric tests may be, and often are, more powerful in detecting population differences when certain assumptions are not satisfied. All tests involving ranked data, i.e. data that can be put in order, are non-parametric.” Here’s a description of the Wilcoxon Mann-Whitney Test from the same site at [ http://www.cas.lancs.ac.uk/glossary_v1.1/nonparam.html#wmwt ]: The Wilcoxon Mann-Whitney Test is one of the most powerful of the non-parametric tests for comparing two populations. It is used to test the null hypothesis that two populations have identical distribution functions against the alternative hypothesis that the two distribution functions differ only with respect to location (median), if at all.” And, here is a description of the (parametric) two sample t-test, also from the same site atb [ http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#2sampt ]: “A two sample t-test is a hypothesis test for answering questions about the mean where the data are collected from two random samples of independent observations, each from an underlying normal distribution: [ Note: see site for equation itself, as it is a graphic with characters that cannot be displayed properly in the GA Answer box]. When carrying out a two sample t-test, it is usual to assume that the variances for the two populations are equal, that is: [ Note: see site for equation ]. The null hypothesis for the two sample t-test is: [ Note: see site for equation ]. That is, the two samples have both been drawn from the same population. This null hypothesis is tested against one of the following alternative hypotheses, depending on the question posed: [Note: see site for equation ].” Several other non-parametric and parametric statistical analysis methods are discussed here as well : [ http://www.cas.lancs.ac.uk/glossary_v1.1/nonparam.html#nonparat ], including the non-parametric “Kolmogorov-Smirnov Test”: “For a single sample of data, the Kolmogorov-Smirnov test is used to test whether or not the sample of data is consistent with a specified distribution function. When there are two samples of data, it is used to test whether or not these two samples may reasonably be assumed to come from the same distribution. The Kolmogorov-Smirnov test does not require the assumption that the population is normally distributed. Compare Chi-Squared Goodness of Fit Test.” 2) Strengths and weaknesses of using each.”: Part of this has already been covered of, in particular: “Non-Parametric tests may be, and often are, more powerful in detecting population differences when certain assumptions are not satisfied. All tests involving ranked data, i.e. data that can be put in order, are non-parametric.” A parametric test, on the other hand, is “A statistical test in which assumptions are made about the underlying distribution of observed data.” So in situations where these assumptions cannot be made, non-parametric tests must be used. In cases where you know you can make certain assumptions, parametric testing is more reliable. [ http://mathworld.wolfram.com/ParametricTest.html ]. 3. “The costs and benefits of using each.” Again, this is largely related to the points covered above concerning strengths, weaknesses and when to apply parametric vs. non-parametric statistical testing, but I'll go into more detail and provide examples at this point. Which type of test is better for a particular case depends on what type of assumptions can be (or cannot be) made. The following website offers worked-through examples of parametric and non-parametric statistical tests, such as the sign test and the Kruskal-Wallis test: [ http://campus.houghton.edu/orgs/psychology/stat19/ ]. Also, “Distribution free-tests – or Non-parametric tests – do not rely on parameter estimation and/or distribution assumptions. That means that the assumptions made about distribution of a data set are much more general than they would be in a parametric test. Normality assumptions are usually left out altogether. Examples are the Wilcoxon Signed-Ranks Test, Chi-squared, and SPEARMAN’S RANK ORDER CORRELATION.” The above comes from : [ http://www.psybox.com/web_dictionary/Distfree.htm ]. The following observations on parametric tests, by Dr. Chong-ho Yu [ http://seamonkey.ed.asu.edu/~alex/teaching/WBI/parametric_test.html ] are also valuable: “Restrictions of parametric tests Conventional statistical procedures are also called parametric tests. In a parametric test a sample statistic is obtained to estimate the population parameter. Because this estimation process involves a sample, a sampling distribution, and a population, certain parametric assumptions are required to ensure all components are compatible with each other. For example, in Analysis of Variance (ANOVA) there are three assumptions: • Observations are independent. • The sample data have a normal distribution. • Scores in different groups have homogeneous variances." Another important example from the above site: “Take ANOVA as an example. ANOVA is a procedure of comparing means in terms of variance with reference to a normal distribution. The inventor of ANOVA, Sir R. A. Fisher (1935) clearly explained the relationship among the mean, the variance, and the normal distribution: "The normal distribution has only two characteristics, its mean and its variance. The mean determines the bias of our estimate, and the variance determines its precision." (p.42) It is generally known that the estimation is more precise as the variance becomes smaller and smaller. Put it in another way: the purpose of ANOVA is to extract precise information out of bias, or to filter signal out of noise. When the data are skewed (non-normal), the means can no longer reflect the central location and thus the signal is biased. When the variances are unequal, not every group has the same level of noise and thus the comparison is invalid. More importantly, the purpose of parametric test is to make inferences from the sample statistic to the population parameter through sampling distributions. When the assumptions are not met in the sample data, the statistic may not be a good estimation to the parameter. It is incorrect to say that the population is assumed to be normal and equal in variance, therefore the researcher demands the same properties in the sample. Actually, the population is infinite and unknown. It may or may not possess those attributes. The required assumptions are imposed on the data because those attributes are found in sampling distributions. However, very often the acquired data do not meet these assumptions.” The following series of links will lead you to further information on this topic-- Google search strategy: Keywords, “nonparametric statistics”: ://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&safe=off&q=++nonparametric+statistics&spell=1 , “parametric statistics”: ://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-. 8&safe=off&q=parametric+statistics&btnG=Google+Search , “parametric tests examples”: ://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&safe=off&q=parametric+tests+examples I hope this information is more than sufficient to assist you with your project. If I have left anything out that you feel is important to you, such as specific examples, please don’t hesitate to request Clarification to this Answer. Good luck on your project! Sincerely, omniscientbeing-ga Google Answers Researcher```
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 ```lgl1-ga, Thank you very much! omniscientbeing-ga Google Answers Researcher```