1.5 Follow up Analyses to a Significant Omnibus Test or Main Effect Flashcards
If the factor has three or more levels, then the initial analysis is referred to as…
omnibus F test, or main effect in factorial ANOVA
What does a significant F ration indicate
that there are likely differences among the group means, but it does not indicate which means are different. Follow-up analyses are needed to determine any group mean differences
what are the two categories of follow-up analyses?
A-priori comparison & post hoc comparisons
A-priori comparisons are decided…
upon before data collection, which is driven by theory and based on the researcher’s predictions
A-priori comparisons tend to be more restrictive allowing for fewer comparisons to be made
(We will focus primarily on Bonferroni comparisons, which include different pre-packaged comparisons)
Post hoc comparisons are done to….
mine the data for potential differences among the group means
They are a fishing expedition, which may help to develop future theories
*However, there is concern about capitalizing on chance, so there must be controls in place for type 1 error, which is inflated by doing multiple comparisons
What is a A-priori comparisons: t-test or f test and what does t involve?
list two problems
Running multiple t or F tests
This involves performing a separate t test (or f test) for every pairwise comparison that is predicted
The problem with running multiple t test is that each test uses a numerically different error term for every comparison made
Another problem is that they do not provide any control for type 1 error.
A-priori comparisons: Contrasts Provide what?
flexible approach to making pairwise comparisons that utilize a common error term.
The error term will be the same as the omnibus test, increasing power to detect differences.
Contrast provides great flexibility by allowing the user to combine groups as desired.
A contrast is a weighted linear combination of the level means, such that:
Contrast = (C1 - M1) + (C2 - M2) + (C3 - M3)+ ….. (Ck - Mk)
Where C is a weight applied to the mean (M)
So lets compare the drug condition to the placebo condition, dropping out the control condition, where M1= drug, M2=placebo, M3=control, then:
Contrast 1 = (1 - M1) + (-1 - M2) + (0 - M3); where the weights are 1, -1, 0
Now let’s compare the drug condition to the control, dropping out the placebo, then:
(where M1= drug, M2=placebo, M3=control)
contrast 2= (1- M1) + (0 - M2) + (-1 - M3); where the weights are 1, 0, -1
And lets compare the drug condition to the average of the placebo and control conditions, then:
(where M1= drug, M2=placebo, M3=control)
Contrast 3= (1 - M1) + (-.5 - M2) + (-.5 - M3); where the weights are 1, -.5, -.5
A-priori comparisons: Bonferroni Comparisons
are an alternative form of contrast that provides for type 1 error
Bonferroni comparisons compute 95% confidence intervals around the mean difference between two comparison groups to determine significance differences
In Bonferroni, how are cofience interval computed?
Confidence intervals are computed around the mean difference of the two means being compared.
Mdiff = M1- M2
If the 95% confidence intervals around the mean difference do not include zero, then the mean difference is significant
95% CI= Mean difference ± (1.96 * SE)
Upper bound: Mean difference + (1.96 * SE) = ?
Lower bound: Mean difference - (1.96 * SE) = ?
Bonferroni: Interpretation of the contrast output.
Difference (estimate-hypothesis) is the difference between the two means
95% confidence intervals for difference shows the upper and lower bound intervals that surround the mean difference
If the upper and lower bound 95% CI do not include zero, then the difference is significantly different from zero
SPSS offers several different predetermined types of Bonferroni comparisons, including:
Simple which does what?
compares the mean of each level to the mean of a specified level. This type of contrast is useful when there is a control group. You can choose the first or last category (Helmert) as the reference
