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. • 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

Sample data

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Post Hoc test button

Select desired test

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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

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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 MS within 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).

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