ANOVA+Analysis

ANOVA Analysis (Analysis of Variance | Multivariate Methods) (GWU EMSE-271)
Index | Topics (Logical Lectures) | Lectures | Problems | Readings | Nomenclature | Concepts

ANOVA Analysis | ANOVA Table Formats | Constrasts | 2-Way | 2K Factorial | Assumptions **(** One-Way | Two-Way )

Analysis of Variance (ANOVA) **and ANCOVA**) are a special cases of regression analysis. - Lattin


 * Steps in an Analysis of Variance (ANOVA)**
 * **Step** || **Approach** || **Comments** ||
 * Exploratory Data Analysis and Pre Check ||  || Didn't seem to be any pre-checks in Lecture 13 or 14. ||
 * - Examine Data || Descriptive Statistics || Minitab works well ||
 * - Present Data || Total and Averages || Excel works well. (See Slide 294 for ANOVA; Slide 312 for 2-Way ANOVA; Slide 325 for 2**K Factorial ANOVA {may be redundant with previous descriptive data - didn't check.)** ||
 * - Determine Questions of Interest ||  ||   ||
 * - Check for correlation ??? || Bartlett's Sphericity Test || Minitab or Excel. See Cereal.xls (Session 13) for sample format. ||
 * - Scale Data || "Standardize" || Scale, like store size in Newfood example. - Lattin, pp 407-408 ||


 * Analyze ||  || This was build for 1-Way ANOVA; tweaked when 2-Way and may apply to the 2-Way or 2 to the K Factorial, but not checked in detail. ||
 * - State Assumptions ||  ||   ||
 * - Look at customary plot || Plot effects for treatments || Lattin, p. 406 ||
 * - Check p-value ||  || If low, "at least one of the treatment means differs." ||
 * - Look at Confidence Intervals || Output or Box Plot ||  ||
 * - Compare treatments || Confidence Intervals || Remember to use 2*MSe in formula ||
 * - Consider Contrasts || Orthogonal Combinations || Look at slides 304-5. Sample in tensile.xls spreadsheet ||


 * **Step** || **Approach** || **Comments** ||
 * Validate Model || Regression Analysis Techniques? || Check Model Adequacy ||
 * - Residuals || Observation and TBD || Compare plot of each treatment's residuals ((Minitab 4-way plot). Can check for normality (for 1-Way ANOVA?) by running a normal probability plot in Minitab (Van Dorp shows (slide 308), but standard error is not an obvious (to me) model output. There is a pooled standard deviation and the value it matched the StDev value in the graph on Slide 308. ||
 * - Equality of Variances || Observation || Compare plot residuals of residuals of each treatment against one another. This is one of the ANOVA (2-Way) output graphs. (May be in others, haven't checked). ||
 * -- OR Bartlett's Test for Equality of Variance || Minitab || Minitab will show Bartlett's Test, Levene's Test and Bonferroni Confidence Intervals for Standard Deviations. Go to Stat, select ANOVA; then select Test of Equal Variances. ||


 * Sources:**
 * Analyzing Multivariate Data, by James Lattin, Douglas Carroll and Green, (c) 2003 ([|Amazon]), Chapter 421
 * EMSE 271, Fall 2009