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What is a planned comparison?

Comparing two treatment means to see if they are significant. Planned to do them before you conduct the study - gives a statistical advantage.


Compare and contrast planned comparison with ANOVA

With planned comparison, we are only comparing two means, not all at once (as in ANOVA).
So, same thing conceptually as ANOVA. Only difference is that the planned comparison uses specific comparisons among pairs of treatment means. Where as the F from the over all ANOVA (i.e. the omnibus F), gives us an average effect for ALL possible pairswise comparisons.
ANOVA is a watered down average, so that's why we do planned comparisons.


Can you have a non-significant omnibus F and still find significance?

Yes, while the omnibus F may be non-significant, you could still find significance through a planned comparison F between two of your treatment means.


What is the conceptual formula for the planned comparison?

Variance of comparison divided by error variance:


What is the conceptual formula for the planned comparison (MScomp/MSerror) derived from?

YbarA1 - YbarA2, or some other combination of means.


How do you find Psycarrot?

(Co-efficient1)(YbarA1) + (Co-efficient2)(YbarA2) + (Co-efficient3)(YbarA3) etc for however many groups you have.


How do you determine the co-efficient's for Psycarrot?

1) They must sum to zero for each comparison
2) They must accurately reflect which means are being compared.


How do you calculate SScomp?


An example: (16)(15)² / (1)²+(-1/3)²+(-1/3)²+(-1/3)²


How do you calculate MScomp?

SScomp/dfcomp = SScomp/1
dfcomp will always = 1


How do you calculate F for planned comparison?

MScomp/MSerror = MScomp/MSw


Where do we get MSerror for planned comparison?

From our omnibus F, MSerror = MSw from omnibus F


What happens to alpha with multiple comparisons?

Overall alpha increases (for overall experiment - also called Alpha familywise, or alphafw, or experimental wise alpha)
Can't have this!


How do we get passed the problem of overall alpha increasing?

Use the Bonferoni inequality: This is how we keep our overall alpha at .05
Set alpha per group (alpha') = alpha/# of comparisons
so for a four group experiment, alpha' = .05/4 = .0125