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Week 2 – PART III. POST-HOC TESTS. POST HOC TESTS. When we get a significant F test result in an ANOVA test for a main effect of a factor with more than two levels, this tells us we can reject H o i.e. the samples are not all from populations with the same mean.
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Week 2 – PART III POST-HOC TESTS
POST HOC TESTS • When we get a significant F test result in an ANOVA test for a main effect of a factor with more than two levels, this tells us we can reject Ho • i.e. the samples are not all from populations with the same mean. • We can use post hoc tests to tell us which groups differ from the rest.
POST HOC TESTS • There are a number of tests which can be used. SPSS has them in the ONEWAY and General Linear Model procedures • SPSS does post hoc tests on repeated measures factors, within the Options menu
Choice of post-hoc test • There are many different post hoc tests, making different assumptions about equality of variance, group sizes etc. • The simplest is the Bonferroni procedure
Bonferroni Test • first decide which pairwise comparisons you will wish to test (with reasonable justification) • get SPSS to calculate t-tests for each comparison • set your significance criterion alpha to be .05 divided by the total number of tests made
Bonferroni test • repeated measures factors are best handled this way • ask SPSS to do related t-tests between all possible pairs of means • only accept results that are significant below .05/k as being reliable (where k is the number of comparisons made)
PLANNED COMPARISONS/ CONTRASTS • It may happen that there are specific hypotheses which you plan to test in advance, beyond the general rejection of the set of null hypotheses
PLANNED COMPARISONS • For example: • a) you may wish to compare each of three patient groups with a control group • b) you may have a specific hypothesis that for some subgroup of your design • c) you may predict that the means of the four groups of your design will be in a particular order
PLANNED COMPARISONS • Each of these can be tested by specifying them beforehand - hence planned comparisons. • The hypotheses should be orthogonal - that is independent of each other
PLANNED COMPARISONS • To compute the comparisons, calculate a t-test, taking the difference in means and dividing by the standard error as estimated from MSwithin from the ANOVA table
TEST OF LINEAR TREND – planned contrast • for more than 2 levels, we might predict a constantly increasing change across levels of a factor • In this case we can try fitting a model to the data with the constraint that the means of each condition are in a particular rank order, and that they are equidistant apart.
TEST OF LINEAR TREND • The Between Group Sum of Squares is then partitioned into two components. • the best fitting straight line model through the group means • the deviation of the observed group means from this model
TEST OF LINEAR TREND • The linear trend component will have one degree of freedom corresponding to the slope of the line. • Deviation from linearity will have (k-2) df. • Each of these components can be tested, using the Within SS, to see whether it is significant.
TEST OF LINEAR TREND • If there is a significant linear trend, and non-significant deviation from linearity, then the linear model is a good one. • For k>3, The same process can be done for a quadratic trend - a parabola is fit to the means. For example, you may be testing a hypothesis that as dosage level increases, the measure initially rises and then falls (or vice versa).
