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A:
Difference Between Parametric Statistics and Non-Parametric Statistics.
Parametric statistics is a branch of statistics that undertakes that particular data set emanates from a populace which can be demonstrated by a probability distribution containing a standard set of parameters. Alternatively, non-parametric statistics is a statistical branch that is not founded upon standardized groups of probability distributions (Brodsky & Darkhovsky 2013). The major differences between these two statistical branches re; parametric statistics apply underlying statistical data distribution. Forthwith, several validity conditions must be met for the parametric test reliability. On the other hand, non-parametric statistics do not depend on any probability distribution. It means that it does not require any parametric conditions of validity for its application.
Advantages and Disadvantages of Non-parametric Statistics
Non-parametric have numerous advantages as well as disadvantages. Non-parametric statistics are easy to conduct, therefore, easily understandable. Additionally, this statistical method requires short calculations (Hoskin 2016). It is also applicable to all data forms. Finally, in this form of statistics, the assumption of distribution is not needed. The disadvantages of this statistical form include; they are less efficient when compared to parametric statistics. Additionally, since they are distribution-free, the results depicted from non-parametric statistics might not be accurate.
The Procedure for Ranking which is used in both the Wilcoxon Signed-Rank Test and the Wilcoxon Rank-Sum Test
The Wilcoxon signed-rank test does not imply that info is gathered from a gaussian distribution. It takes data distributed proportionally around the median (Rey & Neuhäuser 2011). If the distribution is proportional, the P does not pass information concerning the median is different from the theoretical value. Explained below is the ranking procedure utilized for the Wilcoxon Signed Rank test and Wilcoxon Rank-sum.
Analyze the distance of each value from the proposed median
Disregard figures that equal the proposed value and name the number of the rest of the value N.
Rank the value distances and ignore the quantity values in-case they are higher or lesser than the proposed value.
Incase the hypothetical value is higher than any value, multiply the lower value by
Add up the positive ranks and prism report the value.
Sum up the values. The result is the sum of signed ranks.
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B:
Parametric tests assume underlying statistical distributions in the data. Therefore, several conditions of validity must be met so that the result of a parametric test is reliable Nonparametric tests do not rely on any distribution. They can thus be applied even if parametric conditions of validity are not met. The parametric test is one which has information about the population parameter. On the other hand, the nonparametric test is one where the researcher has no idea regarding the population parameter.
Nonparametric statistics can be used in place of parametric statistics when the assumption of normality cannot be met. There are both advantages and disadvantages of nonparametric statistics over parametric statistics. The advantages of nonparametric statistics over parametric statistics: (a) They can be used when the variable is not normally distributed. (b) They can be used to analyses the nominal and ranked data. (c) The calculations are easier in non-parametric statistics when compared to parametric statistics. There are three disadvantages of nonparametric statistics including they are less sensitive than their parametric counterparts when the assumptions of parametric methods are met. In addition, they tend to use less information than the parametric tests. Example: The sign test requires determining only whether the data values are above or below the median, not how much above or below the media each value is. They are less efficient than their parametric counterparts when the assumptions of parametric methods are met. Larger sample sizes are needed to overcome this loss of information.
In Wilcoxon signed rank test the populations to be paired. Here the data type is interval and also, it requires the data to be quantitative. For large samples, paired t test is better one than signed rank test. In Wilcoxon rank sum test, the samples to be drawn from independent populations. Here the data type is ordinal and also, the data need not be quantitative. For large samples, independent two sample t test is better one than Wilcoxon rank sum test.
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Recommended Textbooks:
1.Discovering Statistics and Data, 3rd Edition, by Hawkes. Published by Hawkes Learning Systems.
2.Lind, Marchal, Wathen, Statistical Techniques in Business and Economics, 16th Edition.
