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Treatment by Subject Design

Treatment by Subject Design. Structural Approach. Simple Model. Source E(MS) Subject Condition (T) Error. This is not the model that we use!. Complex Model. Source E(MS) Subject Condition (T) Error. This IS the model that we use!. Treatment by Subject Design. Treatment.

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Treatment by Subject Design

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  1. Treatment by Subject Design Structural Approach

  2. Simple Model SourceE(MS) Subject Condition (T) Error This is not the model that we use!

  3. Complex Model SourceE(MS) Subject Condition (T) Error This IS the model that we use!

  4. Treatment by Subject Design Treatment

  5. Correcting for Dependence Treatment Equate Subject Means Treatment

  6. Treatment Remove GM effect Treatment

  7. Treatment by Subject Design Treatment Treatments are no longer independent. We must remove (partial out) the dependence. Treatment

  8. Remove Subject Effects Treatment

  9. Remove Treatment Effects Treatment SSTreat = ? SSbs = ?

  10. TxS or Repeated Measures df

  11. Repeated Measures Design Partitioning SSTotal SSTotal SSbs SSws

  12. SSws sum across subjects in the jth condition continued…

  13. SSws(continued) now, sum across treatments or conditions. SSws = SSTreat + SSres (k-1)df + (n-1)(k-1)df n(k-1)df =

  14. SSws df The mean for each subject is fixed. With 3 treatments we have 2df within each subject. We have 5 subjects. Thus, 2 x 5 = 10df

  15. SSTreat df Treatment The GM is fixed. With 3 treatments only two are free to vary. Thus, 3 – 1 = 2df

  16. SSres df Treatment The mean for each subject is fixed. Thus, (k-1) The mean for each treatment is fixed. Thus, (n-1) The GM is fixed. But nothing is lost since all treatment means are fixed already. Thus, (k-1)(n-1)

  17. Treatment by Subject Design SSbs SSws SSTreat SSres(error)

  18. Treatments = SSTotal = = 227.6 = SSbs = = 177.6 = SSTreat = = 43.2 SS(res)error = = = 6.8 SSws = SSTotal – SSbs or SSTreat + SSerror

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