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Parametric versus NonparametricStatistics – When to use them and which is more powerful? By Rama Krishna Kompella
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Parametric Assumptions• The observations must be independent• The observations must be drawn from normally distributed populations• These populations must have the same variances• Observations are independent• Variable under study has underlying continuity
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Nonparametric Alternative• The parametric assumptions cannot be justified: normal distribution, equal variances, etc.• The data as gathered are measured on nominal or ordinal data• Sample size is small. 3
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Nonparametric Methods• There is at least one nonparametric test equivalent to a parametric test• These tests fall into several categories 1. Tests of differences between groups (independent samples) 2. Tests of differences between variables (dependent samples) 3. Tests of relationships between variables
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Differences between independent groups• Two samples – compare Parametric Nonparametric mean value for some variable of interest t-test for Wald-Wolfowitz independent runs test samples Mann-Whitney U test Kolmogorov- Smirnov two sample test
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Differences between independent groups Parametric Nonparametric• Multiple groups Analysis of Kruskal-Wallis variance analysis of ranks (ANOVA/ MANOVA) Median test
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Differences between dependent groups• Compare two variables Parametric Nonparametric measured in the same sample t-test for dependent Sign test samples Wilcoxon’s matched pairs• If more than two variables test are measured in same Repeated Friedman’s two sample measures way analysis of ANOVA variance Cochran Q
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Relationships between variables Parametric Nonparametric Correlation Spearman R coefficient Kendall Tau Coefficient Gamma Chi square• Two variables Phi coefficientof interest are Fisher exact testcategorical Kendall coefficient of concordance
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Summary Table of Statistical Tests Level of Sample Characteristics CorrelationMeasurement 1 2 Sample K Sample (i.e., >2) Sample Independent Dependent Independent DependentCategorical Χ2 or Χ2 Macnarmar’ Χ2 Cochran’s Qor Nominal bi- s Χ2 nomial Rank or Mann Wilcoxin Kruskal Wallis Friendman’s Spearman’s Ordinal Whitney U Matched H ANOVA rho Pairs Signed Ranks Parametric z test t test t test within 1 way ANOVA 1 way Pearson’s r (Interval & or t test between groups between ANOVA Ratio) groups groups (within or repeated measure) Factorial (2 way) ANOVA (Plonskey, 2001)
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Advantages of Nonparametric Tests• Probability statements obtained from most nonparametric statistics are exact probabilities, regardless of the shape of the population distribution from which the random sample was drawn• If sample sizes as small as N=6 are used, there is no alternative to using a nonparametric test Siegel, 1956
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Advantages of Nonparametric Tests• Treat samples made up of observations from several different populations.• Can treat data which are inherently in ranks as well as data whose seemingly numerical scores have the strength in ranks• They are available to treat data which are classificatory• Easier to learn and apply than parametric tests Siegel, 1956
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Criticisms of Nonparametric Procedures• Losing precision/wasteful of data• Low power• False sense of security• Lack of software• Testing distributions only• Higher-ordered interactions not dealt with
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