|
⇤ ← Revision 1 as of 2011-06-21 13:11:51
Size: 920
Comment:
|
Size: 2231
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 1: | Line 1: |
| = A note about using ranked outcomes in t-tests and ANOVAs | |
| Line 3: | Line 2: |
| Conover and Iman, (1981) showed that the Mann-Whitney test is equivalent to a t-test on ranked responses. Huitema (1980) in Chapter 12 interprets and uses with a worked example an analysis of covariance on ranks. Shirley (1987) extends this and gives a worked example on a full factorial between subjects analysis of variance. Shirley |
= A note about using ranked outcomes in t-tests and ANOVAs |
| Line 6: | Line 4: |
| Conover and Iman, (1981) showed that the Mann-Whitney test is equivalent to a t-test on ranked responses. Huitema (1980) in Chapter 12 and Shirley (1981) illustrate the use and interpretation of an analysis of covariance on ranked outcomes with worked examples. Shirley (1987) extends Conover and Iman's work to investigating interactions by presenting a worked example involving a full factorial between subjects analysis of variance. Blair, Sawilowsky and Higgins (1987) and Wilcox (2003, p.604) do not advocate using ranked outcomes to test for interactions 'in more complex designs'. More recently Zimmerman (2011) has shown that using t-tests on ranked outcomes, even when there are a large proportion of equal scores (having tied ranks), have greater power and smaller type I error than the conventional t-test on raw scores when the outcome is not normally distributed. He also claims using ranked outcomes works well with one-way ANOVAs. __References__ Blair RC, Sawilowsky SS and Higgins JJ (1987). Limitations of the rank transform statistic in tests for itneractions. ''Communications in Statistics - Simulation and Computation'' '''16''' 1133-1145. Conover WJ and Iman RL (1981). Rank transformations as a bridge between parametric and nonparametric statistics. ''American Statistician'' '''35''' 124-129. doi:10.2307/2683975 |
|
| Line 14: | Line 21: |
Wilcox RR (2003, p.604). Applying contemporary statistical techniques. Academic Press:New York. Zimmerman DW (2010). Power comparisons of significance tests of location using scores, ranks, and modular ranks. ''British Journal of Mathematical and Statistical Psychology'' '''64''' 233-243. |
- = A note about using ranked outcomes in t-tests and ANOVAs
Conover and Iman, (1981) showed that the Mann-Whitney test is equivalent to a t-test on ranked responses. Huitema (1980) in Chapter 12 and Shirley (1981) illustrate the use and interpretation of an analysis of covariance on ranked outcomes with worked examples. Shirley (1987) extends Conover and Iman's work to investigating interactions by presenting a worked example involving a full factorial between subjects analysis of variance. Blair, Sawilowsky and Higgins (1987) and Wilcox (2003, p.604) do not advocate using ranked outcomes to test for interactions 'in more complex designs'.
More recently Zimmerman (2011) has shown that using t-tests on ranked outcomes, even when there are a large proportion of equal scores (having tied ranks), have greater power and smaller type I error than the conventional t-test on raw scores when the outcome is not normally distributed. He also claims using ranked outcomes works well with one-way ANOVAs.
References
Blair RC, Sawilowsky SS and Higgins JJ (1987). Limitations of the rank transform statistic in tests for itneractions. Communications in Statistics - Simulation and Computation 16 1133-1145.
Conover WJ and Iman RL (1981). Rank transformations as a bridge between parametric and nonparametric statistics. American Statistician 35 124-129. doi:10.2307/2683975
Huitema BE (1980). The analysis of covariance and alternatives. 2nd Edition. Wiley: New York.
Quade D (1967). Rank analysis of covariance. Journal of the American Statistical Association 62 1187-1200.
Shirley EAC (1981). A distribution-free method for analysis of covariance based on ranked data. Applied Statistics 30 158-162.
Shirley EAC (1987). Applications of ranking methods to multiple comparison procedures and factorial experiments. Applied Statistics 36(2) 205-213.
Wilcox RR (2003, p.604). Applying contemporary statistical techniques. Academic Press:New York.
Zimmerman DW (2010). Power comparisons of significance tests of location using scores, ranks, and modular ranks. British Journal of Mathematical and Statistical Psychology 64 233-243.