PSY248 Lecture Notes - Lecture 6: Orthogonality, Data Dredging, Null Hypothesis
2 Jun 2018
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PSY248: ANOVA Week 6 – second-stage analysis
Second stage analysis
• Error rate – two decisions we have to make
o Planned
o Post hoc
• Decision rules
• A post-hoc analysis using the Scheffe decision rule
Contrasts
• Definition of a contrast: a linear combination of population means in which
the sum of the coefficient is zero
• Contrasts compare a subset of means to another subset of means
The sample value of a contrast:
• We substitiute Xbar’s (sample means) for populations means
• Y = w(1)Xbar(1) + w(2)Xbar(2) + … + w(k)Xbar(k)
Example 1: analysis suggested by design
• 3 groups
o Control group
o Affective therapy (AT)
o Desensitisation therapy (DT)
• Do AT and DT lead to better results than the control group?
• Or you could decide to do pairwise comparisons
o E.g. AT vs. control, DT vs control, then AT vs DT
o Test whether there are any differences between the three conditions
pairwise
• Both are reasonable
• First one is probably better to create a problem → as AT and DT’s means are
very similar (14, 16) compared to the mean of the control group
• Obtained F = 14 (compare it to 1 which you find in the F tables)
• Define sufficiently unlikely at .05, 2 degrees of freedom for the numerator
(model), 27 degrees of freedom for the denominator (residual),
• Thus, look up the F table and you read off = 3.35 (thus bigger than 1 → you
have an overall significant test)
• Are post-hoc tests sensible?
o What contrasts does this design suggest?
o Is therapy effective?
o Create coefficients
• Testing a contrast for significance
o Calculate the sample value of a contrast
o SS(contrast) = n x sample value of contrast squared/sum of the squared
coefficients
• F(contrast) = MS(contrast)/MS(residual)
• MS(contrast) = SS(contrast)/df (contrast)
• Df(contrast) = 1
• SO MS(contrast) = SS (contrast)
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Second stage analysis: error rate two decisions we have to make, planned, post hoc, decision rules, a post-hoc analysis using the scheffe decision rule. Contrasts: definition of a contrast: a linear combination of population means in which the sum of the coefficient is zero, contrasts compare a subset of means to another subset of means. The sample value of a contrast: we substitiute xbar"s (sample means) for populations means, y = w(1)xbar(1) + w(2)xbar(2) + + w(k)xbar(k) Example 1: analysis suggested by design: 3 groups, control group, affective therapy (at, desensitisation therapy (dt, do at and dt lead to better results than the control group, or you could decide to do pairwise comparisons, e. g. Scheffe decision rule: reject null hypothesis is, f(contrast) > df(model) x f (from the overall anova test) i. e. 3. 35. The maximised contrast: use - (cid:3034)(cid:3045)(cid:3041)(cid:3031) Guaranteed to have at least 1 significant contrast if overall test is significant: 4.
