Applications of Parametric and Non-parametric Tests - Term Paper Example

A Critique Of “Attitudes Of Undergraduate Health Science Students” Introduction The application of statistical knowledge spans across almost all modern academic and professional disciplines. However, learners in many non-mathematical disciplines have difficulty differentiating the exact tests to apply, despite knowing the kind of results they desired at the end of a particular analysis. The most commonly mistaken fields are the applications of parametric and non-parametric tests. A survey through various published works reveals that distinguishing between corresponding parametric and non-parametric tests has not really taken into the imaginations of most learners. In this review, the mishandling of the various parametric tests has been reviewed, including the most common error of its kind being reported by many critiques in the field- the application of ANOVA tests on non-parametric data in the article Attitudes of Undergraduate Health Science Students: Staff Regard Towards Working with Substance Users: A European Multi-centre Study.. This work represents one of many cases out there when researchers fail to conduct necessary investigations into the nature of the data they obtained for analysis. Statistically speaking, the requisites of conducting analysis on a set of data include cleaning the data, and classifying the same (that is according to its right distribution), so that the results will be cohesive with the distribution type. This paper begins by explaining the contrasting parametric tests and their non-parametric equivalents. It also explains lucidly why certain tests befit a certain category of data, and why their use may fail to impress when used on a different category of data. The instances that bear criticism for their wrongful representation are examined, and their suggested remedies listed. The paper concludes with the recommendation that the researchers re-test the original data so that they can overcome this standing shortcoming. Background Information: The study Staff Regard towards Working with Substance Users: a European Multi-centre Study is the work of seven medical researchers: Gail Gilchrist, Jacek Moskalewicz, Silvia Slezakova, Lubomir Okruhlica, Marta Torrens, Rajko Vajd and Alex Baldacchino. The aim of the study was to compare the levels of regard that medical practitioners have for working with various groups of patients across eight European nations- Bulgaria, Greece, Italy, Poland, Scotland, Slovakia, Slovenia and Spain. Unwillingness to treat certain categories of patients stems from the perceived difficulties in handling them, lesser rewards from the intensive care required of the medics, and the general feeling of inadequacy of skills (Gilchrist et al 2011). The researchers note that the medical practitioners prefer treating other categories of patients, for instance those suffering from diabetes. Of special interest to this study is the section from which the researchers apply the t-tests and Analysis of Variance (ANOVA). On top of the ANOVA tests carried out inappropriately in this study (where the researchers should have used the non-parametric equal of ANOVA, the Mann-Whitney U-test. The overall implication of the errors presented by these researchers is that their findings can rightfully be termed as wrong and inappropriate, because they could not use the wrong approach to reach at their conclusions. In the end, the researchers confirmed that the medical practitioners surveyed in the eight countries were least willing to work with patients who needed treatment for use of illicit drugs. It is not certain whether the same conclusion would have been reached if the correct tests were applied on the data. The source of the assumption that the data worked on by the researchers could be assumed to be normally distributed is not explained through out their work. Descriptions of Parametric and Non-parametric Tests Discussed Parametric Tests These tests are normally carried out where a justified assumption regarding the distribution of the measurement variable(s) has been established prior to the test. Analysis of Variance: This is the most commonly used model of analysis, as it is relatively easy to grasp for varied categories of learners. Analysis of Variance or ANOVA as it is commonly referred to is a test that examines whether the factors in a multi-factor model are significant. ANOVA assumes two forms; the one-way ANOVA models and the two-way ANOVA models. The one factor model is a generalization of the two-sample t-test, which tests the hypothesis that two population means are not significantly unequal. In essence, the one factor ANOVA tests the hypothesis that ‘k’ population means are equal (NIST 2003; Smith 2012). The Kruskal-Wallis test is the befitting non-parametric replacement for the one factor ANOVA test. ANOVA finds its ground from the clarification that the data in question does not fail the normality test. Thus whenever a one factor data set fails this test the next obvious thing is to apply the Kruskal-Wallis test. T-tests The t tests are used to compare two sets of data in order to reach the conclusion whether the data sets are significantly different (Dayton n.d.). Basically, t tests are used to establish a probability that the sampled populations are similar in the sense of the value being tested (Caprette n.d). These tests are conducted to establish relationships in data sets at various levels for instance: i) Paired data As the name implies, the data are presented in matching pairs, with a suspected relationship being assumed to exist as a link between the two pairs, and for each joint pair. In this case the second or newer set of data is the result of treatment of the first set of data. According to the article Students t-tests, for this type of data, the paired samples t-test is carried out (n.d. par3). ii) Independent samples In this case the data are collected independently of each other. For example a researcher may want to know whether the average height of a randomly picked man in the streets of Riyadh is the same as that of a man randomly selected from the streets of Tripoli. Non-parametric Tests These tests are normally carried out where a justified assumption regarding the distribution of the measurement variable(s) can not be established prior to the test. Kruskal-Wallis Test: McDonald notes that this test is commonly used when there is one nominal variable and one measurement variable (2009, pp165; Pauling 1989; Plitcha 2012). In this case, the measurement variable does not meet the normality assumption requisite for undertaking an ANOVA test on the data (StatsDirect 2011; Han et al 2011). In the case that data are not normally distributed, the one way ANOVA will be susceptible to yielding inaccurate p-values. This test relies on the ranks assigned to the data set, where the least rank, 1, is assigned to the smallest value in the data set. The test basically draws its weakest attribute on the basis that it loses its power owing to the interchange of information from original to derived data. For understanding, the Kruskal-Wallis test is compulsory whenever we want to determine hypothesis on a data set that has one nominal variable and one ranked variable. The requisites for conducting a Kruskal-Wallis test on a data set are:  The data points must be independent from each other; the distributions do not have to be normal and the variances do not have to be equal; you should ideally have more than five data points per sample; all individuals must be selected at random from the population; all individuals must have equal chance of being selected; sample sizes should be as equal as possible but some differences are allowed (Gaten par1; EFSA 2011; Nishiumi et al 2012). Mann-Whitney U-test: The Mann-Whitney U-test is the non-parametric equivalent of the parametric t-test. The test applies when the nominal variable has got only two values. Despite the fact that they use different test statistics (H and U) for the Kruskal-Wallis and the Mann-Whitney U-test respectively, the p-value in both cases is arithmetically identical/ similar. These tests (Kruskal-Wallis and the Mann-Whitney U-test) revolve around the median, unlike most parametric tests that resonate around such parameters as the mean. Discussion: Review of the Data and Tests Used by Gilchrist et al in Staff Regard towards Substance Users: To ascertain the correctness of the tests applied by Gilchrist et al, we shall take a few samples of the data they have presented in tables and use it to determine whether the data really obeys the normality assumption so as to warrant the parametric tests done on it. For demonstration, two representatives from the Table 2 are picked to represent each category that is primary Care, General Psychiatry and Specialist Addiction Services. From each of these categories one of the simplest tests of normal distribution of data is performed, drawing the histogram. To avoid superfluous representation, the representatives among each category have been kept low to the physicians and nurses only. Below is the output obtained for the tests. (Having failed this test collectively it is clearly unlikely that the researchers’ work would find the basis for justification of the normality assumption made prior to investigations into their stated hypothesis). From the above diagrams, the only data that comes closest to exhibiting a normal distribution is the Nurses: Primary Health Care. For this reason we conclude that the ANOVA tests carried out on the data were undeserved, because the data failed the mandatory normality test for carrying out ANOVA studies on it. As earlier noted, whenever the normality assumption fails, we take on the Kruskal-Wallis test, and it was supposed to have been used by this group of researchers. This finding represents an instance of statistics abuse in analysis. Having established that the data the researchers used was non-parametric, it is again a fault that they used parametric t-tests. Again, reading from Table 2, the researchers converted single digit Likert scale into two digits, another statistical error. Trochim reaffirms Stevens definition of scaling as “the assignment of objects to numbers according to a rule.” Conclusion From the above discussions, it is apparent that Gilchrist et al used the inaccurate p-values, which is an unfortunate observation for the study. This stems from the fact that this group of researchers ignored the test for normality that is a requirement before ANOVA tests are carried out on the data. The group also made use of t-tests, again on a set of non-parametric data. Instead they should have made use of Mann-Whitney U-test, which replaces the t-test when the data in question are not exactly parametric. These findings put to question the authenticity of the conclusions drawn by the researchers. It is unclear whether prior tests were done on the data to classify it accordingly. In deed, a review of their work in line with these non-parametric recommendations would be the most justified response to compensate for the misleading findings. Bibliography Caprette, D. R. (n .d.). Experimental Biosciences: Resources for Introductory and Intermediate Level Laboratory Courses. Students T Test (For Independent Sample). Web 23rd December 2012. Dayton University. (n. d.). Using SPSS for t-tests. Web 22nd December 2012. EFSA Journal 2011. Scientific Report of EFSA: Statistical Analysis of Temporal and Spatial Trends of Zoonotic Agents in Animals and Food. p.25 Gaten, Ted. (2000). On-line Statistics. Kruskal-Wallis Nonparametric ANOVA. Gilchrist, G., Moskalewicz, J., Slezakova, S., Okruhlica, L., Torrens, M., Vajd, R. & Baldacchino, A. (2011). Addiction Research Report. Staff Regard towards Working with Substance Users: A European Multi-centre Study. pp 1114-1126 Han, X. et al. (2011). 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Statistical Methods for Health Care Research. (6th edition). (2012). Smith, G. L. et al. (2012). Association Between Treatment With Brachytherapy vs Whole-Breast Irradiation and Subsequent Mastectomy, Complications, and Survival Among Older Women With Invasive Breast Cancer. The Journal of the American Medical Association. par 17. StatsDirect Limited. (2011). Kruskal-Wallis Test. Students T-tests. (n. d.). Web 22nd December 2012. Trochim, W. M. K. (2006). Research Methods Knowledge Base. General Issues in Scaling. Web. Read More