POST%20HOC%20TESTS

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Week 2 PART III
POST-HOC TESTS
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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.

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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

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Sample data
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Post Hoc test button
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Select desired test
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ANOVA Table
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Post Hoc Tests
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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

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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

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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)

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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

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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

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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

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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

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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.

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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

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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.

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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 kgt3, 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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TEST OF LINEAR TREND
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TEST OF LINEAR TREND
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TEST OF LINEAR TREND