PUH 5302, Applied Biostatistics 2
UNIT x STUDY GUIDE
Title
Comparing Parametric and Nonparametric Methods (Summary)
Parametric statistics depend on normal distribution, but nonparametric statistics do not.
There are less assumptions made in parametric than nonparametric statistics.
Parametric statistics use simpler formulae in comparison to nonparametric statistics.
Parametric statistics are used for normal or close to normal distribution. Nonparametric methods are used for data that are not normally distributed.
Parametric statistics are commonly used in preliminary data analysis, while nonparametric statistics are not used as often and generally only apply to special cases (Sullivan, 2018).
Applications of Nonparametric Methods Nonparametric methods are mostly used in studies involving populations with attributes that can be ranked. Data that can be ranked with no clear numerical underpinnings or interpretations are normally used in nonparametric analysis. Ordinal data are examples of such. Nonparametric methods are applied widely because they make fewer assumptions about the population under study. In addition, because there are fewer assumptions, they facilitate robust statistics by seeking to provide methods that follow popular statistical methods. However, one of the differences is that nonparametric methods are not affected by outliers or values that are plus or minus a few departures from the mean. Nonparametric methods have been associated with simplicity because they save the researcher from committing to other analyses to justify the use of parametric methods. However, this simplicity may serve as a weakness in that, in cases where a parametric test would be appropriate, the researcher may decide to choose the parametric method over the nonparametric method. Types of Data and Tests Used in Nonparametric Statistics Nonparametric statistics are used on nominal or ordinal data or scales of measurement. The table below gives you a summary of the type of tests used in nonparametric testing. The Chi-squ
are statistics and their modifications are used for nominal data. All other nonparametric statistics are appropriate only when data are measured on an ordinal scale of measurement. See table below for examples of the different tests used for nominal and ordinal data.
Nominal Data Ordinal Data
Chi-Square Goodness-of-Fit Test Mann-Whitney U Test
Chi-Square Test of Independence Wilcoxon Signed Rank Test
McNemar’s Test Kruskal-Wallis Test Friedman Two-way Analysis of Variance (ANOVA) by Ranks Test Spearman rs
For a more comprehensive look at some of the tests above as well as other nonparametric tests read the information below:
The Chi-Square Goodness-of-Fit is a nonparametric test deployed to establish the significant difference between the observed value and the expected value. It helps to discern how the theoretical value fits the calculated value. It is most used to compare samples involving intervals.
The Fisher Exact Probability is used to test the statistical significance in certain samples of data. It falls in one of the classes of exact tests because the exact significance of the deviation from the null hypothesis can be calculated instead of approximated. The Fisher Exact Probability test is useful for categorical data to examine the significance of the association between the two categories.
The Mann-Whitney U test is the nonparametric counterpart of the parametric t-test. It does not require a normal distribution for its calculation, and it is equally effective as the t-test. In order to calculate the Mann-Whitney U test, some assumptions must be made: All observations are independent, they have ordinal data, distributions are equal for null hypothesis, and distributions are not equal for the alternative hypothesis. With these assumptions, the researcher can effectively conduct the test with reliable results.
The Wilcoxon Signed-Rank test is a nonparametric test used in evaluating the differences in two groups that are correlated. The basic requirement for using this test is that the data must be matched,