A priori comparisons Flashcards
multiple t-tests
:) Simple and widely used
:( only useful for small amount of planned comparisons
:( aFW will be unacceptably high for too many comparisons
Assumes homogeneity of variance
Welch t-test: use if heterogeneity or unequal sample sizes (look at the equal variances not assumed box)
linear contrasts
Orthogonal or non-orthogonal
t-test just compares 1 mean to another, linear compares 1 (or a SET) or means to another (or another SET)
:) more flexible that a t-test
Linear combination
A set of means that corresponds to the number of IV levels (number of groups)
Known as psi
psi= sum of means
Weighting coefficients in a linear combination
Weight assigned to each mean
Weight of 0 for those left out
At least 2 need a non 0 weight (need to be comparing 2 chunks of data)
Those contrasted have opposite signs (+/-)
Must =0
t-test to assess significance
e. g. T1(high) T2(low) T3(placebo)
1) treatment vs placebo 1/2 1/2 -1
2) high dose vs low dose 1 -1 0
Orthogonal contrasts
Uncorrelated, independent of each other
One being significant as no bearing on the rest
Analyse the non-overlapping variance (this all together is the variance in the omnibus F attributable by the IV)
Corrections in orthogonal contrasts
A different a applied to different tests, but this need to be pre-decided
e.g. a LIBERAL alpha for those of interest (e.g. .05), a STRINGENT for secondary comparisons (e.g. .01)
Criteria for orthogonal
(how do you check that is is orthogonal?
1) sum of the different contrasts= 0
2) sum of the CROSS-PRODUCTS of the coefficients of every pair of contrasts, if sums=0, this shows the contrasts are uncorrelated
(any 2 pairs multiplied together should =0)
3) number of comparisons is k-1 (K is the number of IV levels, this is the same as the df)
4) No single group can be singled out more that once
Example of orthogonal contrasts
E.g. for 6 groups:
1) groups 1-5 vs 6 [1, 1, 1, 1, 1, -5]
2) groups 1-4 vs 5 [1, 1, 1, 1, -4, 0]
3) groups 1-3 vs 4 [1, 1, 1, -3, 0, 0]
4) groups 1-2 vs 3 [1, 1, -2, 0, 0, 0]
5) groups 1 vs 2 [1, -1, 0, 0, 0, 0]
They all =0
If multiplied together, and of these pairs =0
There are 6 groups and 5 comparisons (k-1)
No group has been singled out more that once
Partitioning in orthogonal contrasts
common approach:
1) compare ALL of the experimental groups to the control group(s)
2) compare groups WITHIN experimental or control groups
Non-orthogonal contrasts
Contrasts are NOT independent
Groups could be singled out more that once
The sum of the cross-products of contrast does not =0
there may more more than k-1 number of contrasts (e.g. 5 groups 5 contrasts)
Generally not advised- nothing inherently wrong but p values could be correlated so might need a more conservative alpha to protect against Type 1 errors (use a correction)
