Ch' 12 ANOVA

1
Ch. 12 ANOVA

• ANOVA Analysis of Variance. It is a ratio of
  between groups (BG) and within groups (WG)
  variability. BG effect of experimental
  manipulation of the independent variable. WG
  chance fluctuations (individual differences,
  measurement error, experimental error)
• The F ratio
• F IV chance fluctuations (error)
• chance fluctuations alone (error)

2
Ch. 12, cont.

• If the IV has no systematic effect, the value of
  F 1.0. As the effect size of the IV increases,
  the value of F increases.
• To compute ANOVA, one must know the number of
  treatment conditions (k), the number of scores in
  each treatment condition (n), and the total
  number of scores in the data set (N).
• Degrees of freedom in BS-ANOVA
• df number of scores in a sum of squares that
  are independent of each other and the total (?X)
• total N 1 (where N total number of scores)
• BG k 1 (where k treatment conditions)
• WG N k

3
Ch. 12, cont.

• One-way BS-ANOVA, p. 349
• Treatment Treatment Treatment
• A B
  C
• 2 5
  7
• 4 4
  3
• 3 6
  6
• Three treatment conditions, k 3
• Groups have 3 scores each, n 3
• Total subjects, N 9
• See SPSS Output for these data and compare to
  calculations in the text

4
Ch. 12, cont.

• One-way RM-ANOVA
• (Will be covered next week)
• Two-way BS ANOVA
• (Will be covered in 2 weeks)

5
Ch. 12, cont.

• Degrees of freedom in WS-ANOVA
• Subjects n - 1 (where n subjects)
• Main effect kIV 1 (where kIV levels
  of IV)
• (calculated for each main effect)
• Interactions ( rows 1) x (columns 1)
• or dfA x dfB.x dfn
• Post Hoc comparisons
• - Dunns Multiple Comparisons Procedure

6
Ch. 12, cont.

• Two-way BS ANOVA
• 2 or more IV, one DV
• 2 Main Effects (each IV all by itself)
• 1 Interaction (effects of one IV depend upon
  level of second IV)
• df for two-way BS ANOVA
• N total scores k total experimental groups
• kIV1 levels IV1 kIV2 levels IV2
• dfTotal N 1 dfBG k - 1
  dfWG N k
• dfIV1 kIV1 1 dfIV2 kIV2 1
• dfIV1xIV2 dfIV1 x dfIV2

7
Ch. 12, cont.

• Use the data in Ch. 12 and Appendix 12 (pp. 373
  399) to work several examples of ANOVAS. The
  Appendix data has already been entered into files
  that are located on the course website under
  4632 SPSS
• For practice with WS ANOVA, try problems 5 6 at
  the end of chapter 12 exercises. (eliminate item
  2)
• For practice with two-way BS ANOVA, do appendix
  12-B and items 3 4 in the chapter exercises