Changes between Version 6 and Version 7 of StatisticalAnalysis

Timestamp:

02/01/13 10:45:23 (12 years ago)

Author:

abeham

Comment:

--

StatisticalAnalysis

@@ -8 +8 @@
  * Statistical hypotheses tests for unequality of two means
 
+== Statistical Background ==
+ * [http://en.wikipedia.org/wiki/Behrens%E2%80%93Fisher_problem Behrens-Fischer Problem]
+
 == Statistical Analysis Methods ==
  * Single comparison
   * [http://en.wikipedia.org/wiki/T-test t-test]
   * [http://en.wikipedia.org/wiki/Mann-Whitney_U_test Mann-Whitney U test]
+  * [http://en.wikipedia.org/wiki/Welch%27s_t_test Welch's t-test]
  * Multiple comparison
   * [http://en.wikipedia.org/wiki/ANOVA ANOVA]
   * [http://en.wikipedia.org/wiki/Friedman_test Friedman test]
+  * [http://en.wikipedia.org/wiki/Kruskal%E2%80%93Wallis_one-way_analysis_of_variance Kruskal-Wallis]
 
 == Possible Workflow / Methodology ==
- 1. Testing data for e.g. normal distributions to decide if parametric or non-parametric tests to apply
- 1. In case of multiple comparisons perform ANOVA, Friedman or another test
+ 1. Testing data for e.g. normal distributions, equalness of variances, etc. to decide if parametric or non-parametric tests to apply
+ 1. In case of multiple comparisons perform ANOVA, Friedman or other tests otherwise perform single comparison t-test, Mann-Whitney, etc.
  1. In case multiple comparisons are significant use pairwise comparisons with post hoc analysis adjustments
+
+One problem with such a workflow is that the error propagates in every step. So if testing for normal distributions has a certain error and ANOVA has a certain error, the final error would be a combination of the two. We should also identify and exclude cases where the application of tests would probably not be valid.
 
 == Critique == 
@@ -25 +32 @@
  1. Jacob Cohen. 1994. The Earth is Round (p < 0.05). American Psycologist. http://ist-socrates.berkeley.edu/~maccoun/PP279_Cohen1.pdf
  1. Hubbard, Bayarri. 2003. P-Values are not Error Probabilities. http://ftp.isds.duke.edu/WorkingPapers/03-26.pdf
+
 == References ==
  * García, Fernández, Luengo, Herrera. 2010. Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power. Information Sciences 180, pp. 2044–2064. (http://sci2s.ugr.es/sicidm/pdf/2010-Garcia-INS.pdf)