1 / 15

ANALYSIS OF VARIANCE

This document provides a detailed exploration of Analysis of Variance (ANOVA) techniques for comparing three or more groups within a multigroup experimental design. It elaborates on the purposes of ANOVA, including testing complex hypotheses and leveraging larger sample sizes. The text covers practical procedures such as defining groups, operationalizing metrics, and coding methods including dummy and contrast coding. It also discusses constructing hypotheses, analyzing variance tables, and understanding power calculations, making it essential for researchers in various fields.

eagan-becker
Download Presentation

ANALYSIS OF VARIANCE

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ANALYSIS OF VARIANCE

  2. Multigroup experimental design • PURPOSES: • COMPARE 3 OR MORE GROUPS SIMULTANEOUSLY • TAKE ADVANTAGE OF POWER OF LARGER TOTAL SAMPLE SIZE • CONSTRUCT MORE COMPLEX HYPOTHESES THAT BETTER REPRESENT OUR PREDICTIONS

  3. Multigroup experimental design • PROCEDURES • DEFINE GROUPS TO BE STUDIES: • Experimental Assignment VS • Intact or Existing Groups • OPERATIONALIZE NOMINAL, ORDINAL, OR INTERVAL/RATIO MEASUREMENT OF GROUPS • eg. Nominal: SPECIAL ED, LD, AND NON-LABELED • Ordinal: Warned, Acceptable, Exemplary Schools • Interval: 0 years’, 1 years’, 2 years’ experience

  4. Multigroup experimental design • PATH REPRESENTATION Ry.T e Treat y

  5. Multigroup experimental design • VENN DIAGRAM REPRESENTATION Treat SS SSy R2=SStreat/SSy SSerror SStreat

  6. Multigroup experimental design • dummy coding. Since the values are arbitrary we can use any two numerical values, much as we can name things arbitrarily- 0 or 1 A or B • Another nominal assignment of values is 1 and –1, called contrast coding: -1 = control, 1=experimental group Compares exp. with control: 1(E) -1(C)

  7. Multigroup experimental design • NOMINAL: If the three are simply different treatments or conditions then there is no preferred labeling, and we can give them values 1, 2, and 3 • Forms: • arbitrary (A,B,C) • interval (1,2,3) assumes interval quality to groups such as amount of treatment • Contrast (-2, 1, 1) compares groups • Dummy (1, 0, 0), different for each group

  8. Dummy Coding Regression Vars • Subject Treatment x1 x2 y • 01 A 1 0 17 • 02 A 1 0 19 • 03 B 0 1 22 • 04 B 0 1 27 • 05 C 0 0 33 • 06 C 0 0 21

  9. Contrast Coding Regression Vars • Subject Treatment x1 x2 y • 01 A 1 0 17 • 02 A 1 0 19 • 03 B 0 1 22 • 04 B 0 1 27 • 05 C -1 -1 33 • 06 C -1 -1 21

  10. Hypotheses about Means • The usual null hypothesis about three group means is that they are all equal: • H0 : 1 = 2 = 3 • while the alternative hypothesis is typically represented as • H1 : ij for some i,j .

  11. ANOVA TABLE • SOURCE df Sum of Mean F Squares Square • Treatment… k-1 SStreat SStreatSStreat/ k (k-1) SSe /k(n-1) • error k(n-1) SSe SSe / k(n-1) • total kn-1 SSy SSy / (n-1) • Table 9.2: Analysis of variance table for Sums of Squares

  12. F-DISTRIBUTION Central F-distribution power alpha Fig. 9.5: Central and noncentral F-distributions

  13. POWER for ANOVA • Power nomographs- available from some texts on statistics • Simulations- tryouts using SPSS • requires creating a known set of differences among groups • best understanding using means and SDs comparable to those to be used in the study • post hoc results from previous studies are useful; summary data can be used

  14. ANOVA TABLE QUIZ SOURCE DF SS MS F PROB GROUP 2 ___ 50 __ .05 ERROR __ ___ ___ TOTAL 20 R2 = ____

More Related