Observational Data Time Interval = 20 secs

Factorial Analysis of Variance What is a factorial design?What is a factorial design? Main effectsMain effects InteractionsInteractions Simple effectsSimple effects Magnitude of effectMagnitude of effect Cont.

What is a Factorial At least two independent variablesAt least two independent variables All combinations of each variableAll combinations of each variable R X C factorialR X C factorial CellsCells

2 X 2 Factorial

If you have two factors in the experiment: Age and Instruction Condition. If you look at the effect of age, ignoring Instruction for the time being, you are looking at the main effect of age. If we look at the effect of instruction, ignoring age, then you are looking at the main effect of instruction. Main effects

If you look at the effect of age at one level of instruction, then that is a simple effect. If you could restrict yourself to one level of one IV for the time being, and looking at the effect of the other IV within that level. Simple effects

Interactions

F ratio is biased because it goes up with sample size. For a true estimate for the treatment effect size, use eta squared (the proportion of the treatment effect / total variance in the experiment). Eta Squared is a better estimate than F but it is still a biased estimate. A better index is Omega Squared. Magnitude of Effect

Eta SquaredEta Squared XInterpretation Omega squaredOmega squared XLess biased estimate k = number of levels for the effect in question

Omega Squared

R2 is also often used. It is based on the sum of squares. For experiments use Omega Squared. For correlations use R squared. Value of R square is greater than omega squared. Cohen classified effects as Small Effect:.01 Medium Effect:.06 Large Effect:.15

The Data (cell means and standard deviations)

Plotting Results

Effects to be estimated Differences due to instructionsDifferences due to instructions XErrors more in condition without instructions Differences due to genderDifferences due to gender XMales appear higher than females Interaction of video and genderInteraction of video and gender XWhat is an interaction? XDo instructions effect males and females equally? Cont.

Estimated Effects--cont. ErrorError Xaverage within-cell variance Sum of squares and mean squaresSum of squares and mean squares XExtension of the same concepts in the one-way

Calculations Total sum of squaresTotal sum of squares Main effect sum of squaresMain effect sum of squares Cont.

Calculations--cont. Interaction sum of squaresInteraction sum of squares XCalculate SS cells and subtract SS V and SS G SS error = SS total - SS cellsSS error = SS total - SS cells Xor, MS error can be found as average of cell variances

Degrees of Freedom df for main effects = number of levels - 1df for main effects = number of levels - 1 df for interaction = product of df main effectsdf for interaction = product of df main effects df error = N - ab = N - # cellsdf error = N - ab = N - # cells df total = N - 1df total = N - 1

Calculations for Data SS total requires raw data.SS total requires raw data. XIt is actually = SS video SS video Cont.

Calculations--cont. SS genderSS gender Cont.

Calculations--cont. SS cellsSS cells SS VXG = SS cells - SS instruction - SS gender = = 0.125SS VXG = SS cells - SS instruction - SS gender = = Cont.

Calculations--cont. MS error = average of cell variances = ( )/4 =58.89/4 = MS error = average of cell variances = ( )/4 =58.89/4 = Note that this is MS error and not SS errorNote that this is MS error and not SS error

Summary Table

Elaborate on Interactions Diagrammed on next slide as line graphDiagrammed on next slide as line graph Note parallelism of linesNote parallelism of lines XInstruction differences did not depend on gender

Line Graph of Interaction