Nonparametric-test_Fazlul.pptNonparametric-test_Fazlul.pptNonparametric-test_Fazlul.pptNonparametric-test_Fazlul.ppt
- 1. Nonparametric Statistical Methods Dr. Md Fazlul Haque Associate Professor Dept. of Zoology University of Rajshahi
- 2. Definition When the data is generated from process (model) that is known except for finite number of unknown parameters the model is called a parametric model. Otherwise, the model is called a non-parametric model The branch of inferential statistics devoted to distribution-free tests is called nonparametric. Distribution-free tests are statistical tests that do not rely on any underlying assumptions about the probability distribution of the sampled population.
- 3. For example If you assume that your data has come from a normal distribution with mean and standard deviation (both unknown) then the data is generated from process (model) that is known except for two of parameters ( and ). The model is called a parametric model. Models that do not assume normality (or some other distribution with a finite no. of parameters) are non-parametric
- 4. © 2011 Pearson Education, Inc
- 5. Scales of Measurement • Nominal scale:A nominal scale is really a list of categories to which objects can be classified. • Ordinal scale:is a measurement scale that assigns values to objects based on their ranking with respect to one another. • Interval scale: one unit on the scale represents the same magnitude on the trait or characteristic being measured across the whole range of the scale. For example, if anxiety were measured on an interval scale, then a difference between a score of 10 and a score of 11 would represent the same difference in anxiety as would a difference between a score of 50 and a score of 51. • Ratio scale: Ratio scales are like interval scales except they have true zero points.
- 6. © 2011 Pearson Education, Inc Parametric Test Procedures • Involve population parameters — Example: population mean, standard deviations or probabilities • Require interval scale or ratio scale — Whole numbers or fractions — Example: height in inches (72, 60.5, 54.7) • Have stringent assumptions — Example: normal distribution • Examples: z-test, t-test, F-test
- 7. © 2011 Pearson Education, Inc Nonparametric Test Procedures • Do not involve population parameters — Example: probability distributions, independence • Data measured on any scale — Ratio or interval — Ordinal Example: good-better-best — Nominal Example: male-female • Example: Wilcoxon rank sum test
- 8. © 2011 Pearson Education, Inc Advantages of Nonparametric Tests • Used with all scales • Easier to compute — Developed originally before wide computer use • Make fewer assumptions • Need not involve population parameters • Results may be as exact as parametric procedures © 1984-1994 T/Maker Co.
- 9. © 2011 Pearson Education, Inc Disadvantages of Nonparametric Tests • May waste information — If data permit using parametric procedures — Example: converting data from ratio to ordinal scale • Difficult to compute by hand for large samples • Tables not widely available © 1984-1994 T/Maker Co.
- 10. Differences between independent groups • Two samples – compare mean value for some variable of interest Parametric Nonparametric t-test for independent samples Wald-Wolfowitz runs test Mann-Whitney U test Kolmogorov- Smirnov two sample test
- 11. Differences between independent groups • Multiple groups Parametric Nonparametric Analysis of variance (ANOVA/ MANOVA) Kruskal-Wallis analysis of ranks Median test
- 12. Differences between dependent groups • Compare two variables measured in the same sample • If more than two variables are measured in same sample Parametric Nonparametric t-test for dependent samples Sign test Wilcoxon’s matched pairs test Repeated measures ANOVA Friedman’s two way analysis of variance Cochran Q
- 13. Relationships between variables • Two variables of interest are categorical Parametric Nonparametric Correlation coefficient Spearman R Kendall Tau Coefficient Gamma Chi square Phi coefficient Fisher exact test Kendall coefficient of concordance