Forced ChoiceFree Response SubjectRitalinAdderallCaffeineControlRitalinAdderallCaffeineControl...

Forced Choice Free Response

Subject Ritalin Adderall Caffeine Control Ritalin Adderall Caffeine Control

1 13 11 8 10 8 8 2 2

2 6 6 9 3 8 12 6 6

3 12 12 13 14 12 8 6 6

4 11 14 10 8 13 15 7 9

This is a Repeated Measures Analysis with 2 factors Question and Drug

We’re going to find between subjects SS, between Drug SS and between Question SS

Then we’re going to find the interaction of SS_sub x drug and SS_sub x question which will be our error terms for our two factors of interest Drug and Question

(We don’t care about between subjects but will calculate it for later use)

The we calculate SS_drug x question interaction.

Then we will calculate Total SS and subtract all the previous SS to get our final interaction SS_sub x drug x question, which we will use as the error term for our SS_drug x question interaction.

Question

Drug



1 13 11 8 10 8 8 2 2

2 6 6 9 3 8 12 6 6

3 12 12 13 14 12 8 6 6

4 11 14 10 8 13 15 7 9

SSbetween_subjects = nLevelQ x nLevelD ∑ (Ms-M)2

1) ∑(Collapse (mean) across Subject 1 – Grand Mean)2

Then subject 2, etc… then sum

2) Multiply sum by

nLevelQ = 2, n LevelD = 4 2X4 = 8

(or number of x’s in mean across sub (in red) also 8)

df= number of subjects -1 4-1=4

─

SS_between_subjects



1 13 11 8 10 8 8 2 2

2 6 6 9 3 8 12 6 6

3 12 12 13 14 12 8 6 6

4 11 14 10 8 13 15 7 9

SSdrug = n*LevelQ ∑ (Mdrug-M)2

Collapse (mean) across drug, ignoring choice─

13114

12123

862

8131

RitalinRitalinSubject

=

12

12

7

10.5

Ritalin

1) ∑ (Mean Drug group (Ritalin) – Grand mean) 2

Then Adderall, etc…then sum

2) Multiply sum by n*LevelQ = 4*2 = 8

Also number of scores in Drug group mean (in red) = 8

df = number of drugs – 1 = 3

SS_between_drug



1 13 11 8 10 8 8 2 2

2 6 6 9 3 8 12 6 6

3 12 12 13 14 12 8 6 6

4 11 14 10 8 13 15 7 9

SS_between_question

SSquestion = n*LevelD ∑ (Mquestion-M)2

Collapse (mean) across question, ignoring choice

─

81014114

141312123

39662

10811131

ControlCaffeineAdderallRitalinSubject

Forced Choice

=

10.75

12.75

6

10.5

Forced Choice

1) ∑ (Mean Question group (Forced Choice) – Grand mean) 2

Then Free Response, then sum

2) Multiply sum by n*LevelQ = 4*4 = 16

Also number of scores in Question group mean (in red) = 16

df = number of drugs – 1 = 3



1 13 11 8 10 8 8 2 2

2 6 6 9 3 8 12 6 6

3 12 12 13 14 12 8 6 6

4 11 14 10 8 13 15 7 9

SSquestion x drug SSq X d = SSqd – SSq – SSd

SSqd =

SSqd is basically SSbetween_condacross all conditions

SSquestion = n ∑ (Meach_condition-M)2

(Mean Ritalin-Forced Choice – Grand Mean)2

Then (Mean Adderall-Forced Chioce – Grand Mean)2….

Eventually (Mean of Ritalin-Free Response – Grand Mean)2

Sum all together and multiply by n

Or number of x’s in one mean 4

SSq x d = subtract SSq and SSd (which we already have) from SSqd

df q x d = dfq X dfd

─



1 13 11 8 10 8 8 2 2

2 6 6 9 3 8 12 6 6

3 12 12 13 14 12 8 6 6

4 11 14 10 8 13 15 7 9

SSdrug = LevelQ ∑ (Msubject-drug-M)2

You’ve already collapse (mean) across drug, ignoring choice

1) ∑ (Subject1,Ritalin – Grand mean) 2

Then Subject1, Adderall, etc…then Subject 2, Ritalin,etc… and sum

2) Multiply sum by LevelQ = 2

Also number of scores in each x (in red) = 2

SSsubxdrug = subtract SSs and SSd from SSsd df = df_sub x df_drug

SSsub x drug SSs X d = SSsd– SSs – SSd

─

14.5124

10123

972

9.510.51

AdderallRitalinSubject

14.5

10

9

9.5

Caffeine

14.5

10

9

9.5

Ritalin Subtract each x from Grand Mean

Square and sum

9

9

9

9

Grand Mean

From SS_drug



1 13 11 8 10 8 8 2 2

2 6 6 9 3 8 12 6 6

3 12 12 13 14 12 8 6 6

4 11 14 10 8 13 15 7 9

SSdrug = LevelQ ∑ (Msubject-drug-M)2

You’ve already collapse (mean) across drug, ignoring choice

1) ∑ (Subject1,Forced Choice – Grand mean) 2

Then Subject1, Free Response, then Subject 2, Forced Choice,etc… and sum

2) Multiply sum by LevelD = 4

Also number of scores in each x (in red) = 4

SSsubxquestion = subtract SSs and SSq from SSsq df = df_sub x question

SSsub x question SSs X d = SSsd– SSs – SSd

─

Subtract each x from Grand Mean

Square and sum

From SS_drug

10.75

12.75

6

10.5

Forced Choice

11

8

8

5

Free Response

9

9

9

9

Grand Mean

4

3

2

1

Subject

SSsxdxq

At this point you have all the other SS’s. Just do a SStotal (every x minus the Grand Mean) and subtract all your SS’s from that SStotal.

That will give you SSsxdxq

SS df MS F

Subjects 87.75 3 32

Question 32 1 32 1.174312

Drug 79.25 3 26.41667 5.52907

SxQ 81.75 3 27.25

SxD 43 9 4.777778

QxD 31.25 3 10.41667 4.076087

SxQxD 23 9 2.555556

Error term = SxQ

Error term = SxD

Error term = SxDxQ

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Forced ChoiceFree Response SubjectRitalinAdderallCaffeineControlRitalinAdderallCaffeineControl...

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