ERIC Number: ED397088
Record Type: RIE
Publication Date: 1996-Jan-25
Reference Count: N/A
Understanding that ANOVA Effects Are Perfectly Uncorrelated.
Analysis of variance (ANOVA) was invented in the 1920s to partition variance of a single dependent variable into uncorrelated parts. Having uncorrelated parts makes the computations involved in ANOVA incredibly easier. This was important before computers were invented, when calculations were all done by hand, and also were done repeatedly to check for calculation errors. This paper demonstrates that ANOVA effects in a balanced design are perfectly uncorrelated. A mathematical proof that the four sums-of-squares (SOS) partitions (two main effect, one two-way interaction, and error) for a factorial two-way design are all uncorrelated, i.e., sum exactly to the SOS of the dependent variable is presented, and a small heuristic data set is included in an appendix to illustrate the proof. (Contains 71 references.) (Author/SLD)
Publication Type: Reports - Evaluative; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: Balanced Designs; Sum of Squares
Note: Paper presented at the Annual Meeting of the Southwest Educational Research Association (New Orleans, LA, January 1996).