EDRM 711 Midterm

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

df=n-1

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

The measure of an individual's mean compared to the group's mean. sum((x11-x.1)..(xii-x.i)

df= n-k

MS=SSwg/dfbg

F=MSbg/MSwg

• 0.2 - small
• 0.5 - medium
• 0.8 - large

• 0.1 - small
• 0.25 - medium
• 0.4 - large

Disordinal: non-parallel with an intersection

Ordinal: non-parallel with no intersection

No interaction: parallel lines

SSwg=SSerror= Sum of the individual deviations from the cell means.

dfwg=dferror=N-a*b=(n11-1)+(n12-1)+(n21-1)+(n22-1)

MSwg=MSerror=SSwg/dfwg

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

dfa*b=(a-1)(b-1)

MSa*b=SSa*b/dfa*b

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

yijk= μ +α j + β k +φ jk + eijk

• α=SSa
• β= SSb
• μ +α + β +φ = SSa*b

• 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)

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.

• Type I
• Uses theory or previous research to establish order for the effects, Adjusts each effect only for those preceding it in order.

Sum of the mean for time group and the grand mean to the jth group

Block score minus average score at each time point

Row block minus grand mean

SSerror=SSwg-SSbl - how much error gets pulled out from the blocks

SSerror/dferror = SSerror/(N-1)(k-1)

where N= # of blocks and k=# of time points

F=MSbg/MSerror

df=(k-1, (N-1)(k-1))

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

Level of significance - type 1 error rate (If assumptions are not violated)

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.

The alpha level set for the whole study (usually 0.05)

Non-independent contrasts

Falsely rejecting the a true null hypothesis