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# Psyc3001 Topic 6 Essay

3604 words - 15 pages

UNSW PSYC3001 Research Methods 3 ‐ Topic 6 Lecture Slides

Dr Melanie Gleitzman

Topic 6 – Post-hoc contrast analysis, controlling Familywise error rate
What inferential procedure should follow a significant ANOVA test? When ANOVA F test is significant, and have rejected homogeneity hypothesis, what should happen next is to make inferences regarding hypotheses implied by homogeneity hypothesis  make confident inferences for contrasts (and comparisons).

The ANOVA F Simultaneous Test Procedure (Scheffé method) An overall test (a test of the homogeneity of population means) can be used as the basis for a simultaneous test procedure (STP), allowing for tests on all hypotheses implied by ...view middle of the document...

sav)

(Treatment 1, Treatment 2, Control; dependent measure = performance) (i) Test of homogeneity hypothesis, H0: 1 = 2 = 3
ANOVA y Sum of Squares 682.000 472.000 1154.000 df 2 30 32 Mean Square 341.000 15.733 F 21.674 Sig. .000

1 = J – 1 =2, 2 = J(n – 1) = 3(10) =30 Fc = F.05; 2, 30 = 3.316

Between Groups Within Groups Total

We can reject H0: 1 = 2 = 3 , since F = 21.674 > 3.316 What inference follows? [heterogeneity inference ...... ]

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UNSW PSYC3001 Research Methods 3 ‐ Topic 6 Lecture Slides

Dr Melanie Gleitzman

(ii) Follow-up inferences on contrasts – post-hoc analysis The ANOVA F STP allows for tests of any H0 implied by the homogeneity hypothesis. This means we are at liberty to choose any number of contrasts for our follow-up analysis, and contrasts can be based on the pattern of sample means. We call this a post-hoc analysis strategy. For follow-up contrasts, Scheffé SSc: SSc = 1 F; 1, 2 MSE = 2  3.316  15.733 = 104.34 Decision rule for contrast H0’s: Reject H0: g = 0, if
ˆ SS  g   SS c  104.34

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UNSW PSYC3001 Research Methods 3 ‐ Topic 6 Lecture Slides

Dr Melanie Gleitzman

Sample Means T1 Mj M1 = 39 T2 M2 = 46 C M3 = 35 (M = 40)

Suppose the following contrasts are to be included in the analysis: contrasts coefficients: 1 = ½1 + ½2 - 3 (average of Treatment ES) 2 = 1 – 2 3 = 1 – 3 4 = 2 – 3 (T1 ES vs T2 ES) (T1 ES) (T2 ES)

1 2  1  1  0 

1 2

1 0 1

 1  0    1   1 

Each contrast null hypothesis states that the population value (parameter) of contrast is 0, i.e., H0:  = 0.

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UNSW PSYC3001 Research Methods 3 ‐ Topic 6 Lecture Slides

Dr Melanie Gleitzman

Source Between 1 = ½ (1 + 2) – 3 2 = 1 – 2 3 = 1 – 3 4 = 2 – 3

SS Inference 682.00 Population means are heterogeneous 412.50 269.50 88.00 665.50 ½ (1 + 2) > 3 1 < 2 None 2 > 3

SSc = 104.34; significant test outcomes for 1, 2 and 4. Directional inference (referring to population of interest): Average performance is higher for treatments compared to no treatment (1), higher for T2 compared C (4) and higher for T2 compared to T1 (2). No inference can be made regarding T1 Es (3). Note: Each contrast SS is less than SSB, and so accounts for some of the variation between groups.

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UNSW PSYC3001 Research Methods 3 ‐ Topic 6 Lecture Slides

Dr Melanie Gleitzman

INSERT

ˆ Calculating SS (1)
ˆ 2 Sample value of 1 :   1  M 1  M 2   M 3  1  39  46   35  7.5 2

c

2 j

 .52  .52  1  1.5

n = 11

n( )2 11(7.5) 2 ˆ SS (1)  ˆ 2   412.5 1.5 c

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UNSW PSYC3001 Research Methods 3 ‐ Topic 6 Lecture Slides

Dr Melanie Gleitzman

The Scheffé Simultaneous Confidence Interval (SCI) procedure In general, the limits of 100(1-)% CI for the gth contrast in an analysis can be written as:
g

ˆ ˆˆ  g  CC  g

where CC is a critical constant that depends on the error rate chosen, and whether the analysis is unrestricted (post hoc) or restricted to...

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