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# T11 types of tests

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• 1. Parametric versus NonparametricStatistics &#x2013; When to use them and which is more powerful? By Rama Krishna Kompella
• 2. Parametric Assumptions&#x2022; The observations must be independent&#x2022; The observations must be drawn from normally distributed populations&#x2022; These populations must have the same variances&#x2022; Observations are independent&#x2022; Variable under study has underlying continuity
• 3. Nonparametric Alternative&#x2022; The parametric assumptions cannot be justified: normal distribution, equal variances, etc.&#x2022; The data as gathered are measured on nominal or ordinal data&#x2022; Sample size is small. 3
• 4. Nonparametric Methods&#x2022; There is at least one nonparametric test equivalent to a parametric test&#x2022; 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
• 5. Differences between independent groups&#x2022; Two samples &#x2013; 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
• 6. Differences between independent groups Parametric Nonparametric&#x2022; Multiple groups Analysis of Kruskal-Wallis variance analysis of ranks (ANOVA/ MANOVA) Median test
• 7. Differences between dependent groups&#x2022; Compare two variables Parametric Nonparametric measured in the same sample t-test for dependent Sign test samples Wilcoxon&#x2019;s matched pairs&#x2022; If more than two variables test are measured in same Repeated Friedman&#x2019;s two sample measures way analysis of ANOVA variance Cochran Q
• 8. Relationships between variables Parametric Nonparametric Correlation Spearman R coefficient Kendall Tau Coefficient Gamma Chi square&#x2022; Two variables Phi coefficientof interest are Fisher exact testcategorical Kendall coefficient of concordance
• 9. Summary Table of Statistical Tests Level of Sample Characteristics CorrelationMeasurement 1 2 Sample K Sample (i.e., &gt;2) Sample Independent Dependent Independent DependentCategorical &#x3A7;2 or &#x3A7;2 Macnarmar&#x2019; &#x3A7;2 Cochran&#x2019;s Qor Nominal bi- s &#x3A7;2 nomial Rank or Mann Wilcoxin Kruskal Wallis Friendman&#x2019;s Spearman&#x2019;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&#x2019;s r (Interval &amp; or t test between groups between ANOVA Ratio) groups groups (within or repeated measure) Factorial (2 way) ANOVA (Plonskey, 2001)
• 10. Advantages of Nonparametric Tests&#x2022; 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&#x2022; If sample sizes as small as N=6 are used, there is no alternative to using a nonparametric test Siegel, 1956
• 11. Advantages of Nonparametric Tests&#x2022; Treat samples made up of observations from several different populations.&#x2022; Can treat data which are inherently in ranks as well as data whose seemingly numerical scores have the strength in ranks&#x2022; They are available to treat data which are classificatory&#x2022; Easier to learn and apply than parametric tests Siegel, 1956
• 12. Criticisms of Nonparametric Procedures&#x2022; Losing precision/wasteful of data&#x2022; Low power&#x2022; False sense of security&#x2022; Lack of software&#x2022; Testing distributions only&#x2022; Higher-ordered interactions not dealt with
• 13. Questions?