EDRM 711 Midterm

  1. Total Means - SStot
    The measure of an individual's score compared to the grand mean. sum((x11.-x...)...(xii.-x...)

  2. Between Group Means - SSbg
    The measure of a group's mean compared to the grand mean. sum((x.1.-x..)...(x.i.-x...)

    • df=k-1
    • MSbg=SSbg/dfbg
  3. Within Group Means - SSwg
    The measure of an individual's mean compared to the group's mean. sum((x11-x.1)..(xii-x.i)

    df= n-k

  4. F-statistics
  5. Cohen's D values
    • 0.2 - small
    • 0.5 - medium
    • 0.8 - large
  6. Cohen's f values
    • 0.1 - small
    • 0.25 - medium
    • 0.4 - large
  7. Interaction Types
    Disordinal: non-parallel with an intersection

    Ordinal: non-parallel with no intersection

    No interaction: parallel lines
  8. SSwg for factorial ANOVA
    SSwg=SSerror= Sum of the individual deviations from the cell means.


  9. SSa*b
    Sum of cell mean-row margin+column margin+grand mean)2 for all columns and rows.


  10. Mathematical Model for factorial ANOVA
    yijk= μ +α j + β k +φ jk + eijk

    μ = overall average in the population j  

    α= effect of being in jth achievement levelj

    μ +α = population average for the jth achievement levelk

    β= effect of being in kth CAI methodk μ + β = population mean for kth CAI methodjk

    φ = effect of having the jkth combination of achievement level and CAI methodj k jk

    μ +α + β +φ = population mean for the jkth combination ofachievement level and CAI method ijk

    e = individual error
  11. Key to the factorial ANOVA equation
    yijk= μ +α j + β k +φ jk + eijk

    • α=SSa
    • β= SSb
    • μ +α + β +φ = SSa*b
  12. Full Regression SS
    • Type III or unique SS
    • Adjust each effect for all other effects in the design to obtain its unique contribution (nothing is being counted twice)
  13. Experimental SS
    Type II estimates main effects adjusting for the other main effects, but ignoring the interaction. Estimates the interaction adjusting for main effects. SS for A and B are too big. A and B are not unique, but A*B is.
  14. Hierarchical SS
    • Type I
    • Uses theory or previous research to establish order for the effects, Adjusts each effect only for those preceding it in order.
  15. Repeated Measures ANOVA - SSbg
    Sum of the mean for time group and the grand mean to the jth group
  16. Repeated Measures ANOVA - SSwg
    Block score minus average score at each time point
  17. Repeated Measures ANOVA - SSbl
    Row block minus grand mean
  18. Repeated Measures ANOVA - SSerror
    SSerror=SSwg-SSbl - how much error gets pulled out from the blocks
  19. Repeated Measures ANOVA - MSerror
    SSerror/dferror = SSerror/(N-1)(k-1)

    where N= # of blocks and k=# of time points
  20. Repeated Measures ANOVA - F-stat

    df=(k-1, (N-1)(k-1))
  21. Repeated Measures ANOVA - Sphericity
    E is less than or equal to 1. The closer E is to 1, the smaller the violation of the sphericity assumption.

    If close to or equal to one, do not adjust F values
  22. Nominal alpha
    Level of significance - type 1 error rate (If assumptions are not violated)
  23. Actual alpha
    Percentage of making a type 1 error when at least 1 assumption has been violated. Test statistic is robust if actual alpha is very close to nominal alpha.
  24. Experimental alpha
    The alpha level set for the whole study (usually 0.05)
  25. orthogonal contrast
    Non-independent contrasts
  26. Type II Error
    Falsely rejecting the a true null hypothesis
Card Set
EDRM 711 Midterm