????

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????µetaß??t? a????s? d?a??µa?s?? (MANOVA)

• G?????? Spa???d??
• ?µ?µa ????????a?

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St????

• ??te ?a? ??at? ???s?µ?p????µe t? MANOV? ?a? t?
  MANCOVA
• T?µata s?et??? µe t?? a????s? MANOVA ?a? ???COVA
• ? ?e???a p?s? ap? t? MANOVA
• ??t?e? SSCP
• ??a??????se? (Discriminant Variates)
• ??e???? stat?st???? MANOVA

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??te ?a? ??at?

• G?a ?a e??????µe d?af???? µeta?? ?µ?d?? (?
  MANOVA e????e? a? ?? µ?se? d?af???? µeta?? t??
  ?µ?d?? t?? ?? p??? se µ?a s???et??? µetaß??t? p??
  p????pte? ap? t?? ??, e??a? p??a?? ?a e??a?
  t??a?e?
• ?p??tas? t?? ANOVA st?? ?p??a ?? ????e?
  ep?d??se?? ?a? ?? a????ep?d??se?? e?t?µ??ta? ep?
  t? ß?se? t?? s??d?asµ?? t?? ??
• ?ta? ????µe pe??ss?te?e? ap? µ?a e?a?t?µe?e?
  µetaß??t?? (Outcome variables) (???)
• Saf?? ?a??te?? ap? t?? ep????? t?? p???ap???
  ANOVA. G?at?
• ??a µetaß??t? spa???? µa? d??e? µ?a p???? e????a
  t?? ?p? µe??t? fa???µ????
• ?????e? t? familywise error (Type I error)
• ?aµß??e? ?p??? t?? s??se?? µeta?? t?? ??? (t?
  ???eta? µe t?? s?s?et?se?? µeta?? t?? ??)
• ?p????µe ?a d??µe t?? s??se?? t?? ?? e?t?? ???e
  ep?p?d?? t?? ??
• ?a??d??e? t?? e?e???t? st?? p??sp??e?a t?? ?a
  µe??se? t? a???µ? t?? ??
• ?p?t??pe? ?a a?a?????s??µe p??a ? p??e? ap? t??
  ?? pa?????? t? µe?a??te?? d?????s? t?? ep?p?d??
  t?? ??
• ?p?t??pe? ?a ap??a?????µe d?af???? sta ep?peda
  t?? ?? p?? ap??a??pt??ta? µ???? se s?????e?
  a???µ???? ?s???? t?? p???µetaß??t?? e??????

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??te ?a? ??at?

• ?p?????? ?a? pe??pt?se?? p?? ?a ?ta? ?a??te?? ?a
  ap?f????µe t? ???s? t?? ????VAs. ??te ..
• ?? ?? ?? e??a? as?s??t?ste? (a?t??eta ?ta? e??a?
  µ?t??a s?s?et?sµ??e? e??a? ?da???? ? ???s? t??
  ????VAs)
• ?? ?? ?? pa???s?????? ????? s?s??t?s?
• ? MANOVA d?µ?????e? µ?a ??a ?? ? ?p??a e??a?
  ??aµµ???? s??d?asµ?? t?? ep?µ????? ?? p???e?µ????
  ?a µe??st?p???se? t? d?af??? t?? ep?p?d??
  (?µ?d??) t?? ??.
• Sta pa?a???t??? s??d?a ??a? d?af??et????
  ??aµµ???? s??d?asµ?? (variate) d?µ?????e?ta?
  ?e????st? ??a ???e ????a ep?d?as? ?a?
  a????ep?d?as? ? ?p???? µe??st?p??e? t? d?af???
  t?? ?µ?d?? (ep?p?d?? t?? ??).
• St?? pe??pt?s? t?? MANCOVA p?? e??a? ep??tas? t??
  ANCOVA ? ??aµµ???? s??d?asµ?? t?? ??
  p??sa?µ??eta? µe ???t???? µ?a ? pe??ss?te?e?
  s??e?e?? s??d?a??µa????se? µetaß??t??.
• ? s??d?a??µa????sa (covariate) e??a? µ?a
  µetaß??t? p?? s?et??eta? µe t?? ??, t?? ?p??a de?
  µp????µe ?a ?e???st??µe a??? ?????µe ?a
  afa???s??µe t?? ep?d??se?? t?? (t? s?s??t?s? t??)
  p??? st?? ?? p??t?? e?t?µ?s??µe t?? d?af???? t??
  ??.

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T?µata s?et???µe?a µe t? MANOVA

• ?p????? t?? ???
• Stat?st???? (ep????? ap? t?sse???)
• ?s???
• ? ?s??? e?a?t?ta? ap? t?? s?s?et?se?? µeta?? t??
  ???
• ????????µe?e? p????f???e? s?et??? µe t?? ??e???
  t?? ?s????

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?as???? p???p???se??

• 2 ? pe??ss?te?e? ??
• 1 ? pe??ss?te?e? ?at???????? ??
• St? MANCOVA ??e???esa? ep?s?? 1 ? pe??ss?te?e?
  s??e?e?? s??d?a??µa????se?

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???t?µata p??? ap??t?s?

• ???? ??t? ta ?d?a µe a?t? p?? ??t??µe st?? ANOVA.
  ???ad?
• ????e? ep?d??se?? ?a? a????ep?d??se??
• ??at??ta? ??a t?? ep?d??se?? sta?e???, e??a? ?
  d?af??? µeta?? t?? ?µ?d?? µe?a??te?? ap? t?? ?at?
  t??? p??sd???µe??
• ?????pt??? a??a??? st? s???et??? µetaß??t? t?? ??
  ??a µ?a ?? s??epe?a t?? d??s?? t?? ep?p?d??
  ??p??a? ????? ??

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? p???µetaß??t? Hotellings T2

• ?? ß???µe ?t? ? t?µ? Hotellings T2 e??a?
  s?µa?t??? p???????µe µe t?? ??e???, d?af??et???
  staµat?µe. St?? pe??pt?s? p?? ß???µe ?t? ?p???e?
  p???µetaß??t? ep?d?as? ?a p??pe? ?a a?a??s??µe
  pe?a?t??? t? s???et??? µetaß??t?.
• ????????µe µe ?e????st? t-tests x??s?µ?p????ta?
  t? d?????s? Bonferronni (a/p)
• Roy-Bargmann ß?µat??? a????s? /PRINT
  SIGNIF(STEPDOWN), ERROR(COR), HOMOGENEITY
  (BARTLETT, COCHRAN,BOXM)/METHODSEQUENTIAL

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??d??? ??µata

• ???e??? de??µat?? (se ???e ?e?? ?a ????µe a???µ?
  µe?a??te?? ap? t?? a???µ? t?? ?? ?, a??µ?
  ?a??te?a,t??????st?? 20 a?? ?e??)
• G?aµµ???t?ta, s????aµµ???t?ta p???µeta ß??t?
  ?a??????t?ta
• ?p??s?a a??a??? t?µ??
• ?µ??????e?a d?a??µa?s??-s??d?a??µa?s??

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Te???a ??a pa??de??µa

• ?p?te?esµat???t?ta t?? ?????e?ape?a? st??
  ???a?a??ast???-?ata?a??ast??? d?ata?a?? (?????)
• ??e?? ?µ?de?
• G??st??? s?µpe??f????? ?e?ape?a (GS?T)
• S?µpe??f????? ?e?ape?a (S?T)
• ?aµ?? ?e?ape?a (?OT)
• ??? e?a?t?µ??e? µetaß??t?? (???)
• ???a?a??ast???? e????e?e?
• ???a?a??ast???? s???e??

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?e????af??? stat?st???
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?? ???aµe d??f??e? ANOVA
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S????? G?
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?p??e?p?µe?a G?
GS?T
S?T
?OT
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?????sµata tet?a????? (Sums of Squares)
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??t?e? MANOVA s??????? SSCP (?)
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??t?e? MANOVA ?p??e?p?µe?? SSCP (E)
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??t?e? MANOVA ???t??? SSCP (M)
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?s?d??aµ? t?? F
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??a??????se?
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???a ap? t?? t?sse??? stat?st???? ?a d?a?????

• T?µata p??? a????s?
• Power (p?s? ??a?? e??a? ??a test ?a
• ap??a??pte? t?? s??se?? µeta?? t??
• µetaß??t??)
• Robustness (se p??? ßa?µ? ?s??e? ??a test
• pa?? t? ?e????? ?t? ????? pa?aß?aste?
  ??p??e? ap? t?? p???p???se?? t??)
• ?s?t?ta µe?????? de??µ?t??
• ?est Pillais Trace
• Robust ?ta? ta µe???? t?? de??µ?t?? e??a? ?sa.

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? MANOVA st? SPSS
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? MANOVA st? SPSS Contrasts
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? MANOVA st? SPSS Options
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? MANOVA st? SPSS ????? Output
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H MANOVA st? SPSS ANOVAs
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??a???t??? a????s? (Discriminant Function
Analysis)
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S?µp???????ta? t? MANOVA µe t? ??a???t??? ?????s?
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??a???t??? a????s? stat?st????
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??a???t??? a????s? stat?st????
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??a???t??? a????s? stat?st????
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??a???t??? a????s? stat?st????