MANOVA

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MANOVA
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Samples of Romano-British pottery were taken at
four sites in the United Kingdom. A chemical
analysis of the pottery was performed to measure
the percentage of five metal oxides present in
each sample. The purpose of the analysis was to
determine if different sites produced pottery
with different chemical compositions. Since we
have five different measures of chemical
composition, we should perform a multivariate
analysis of variance (MANOVA) analysis to
determine if there is a significant difference
between sites considering all five variables
simultaneously. The dependent variables
(Y-variables) for the MANOVA are the five
chemical variables the predictor variable
(X-variable) is 'Site'.
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• Twenty-six samples of Romano-British pottery were
  found at four different kiln sites in Wales,
  Gwent and the New Forest. The sites are
  Llanederyn (L), Caldicot (C), Island Thorns (I),
  and Ashley Rails (A). The other variables are the
  percentage of oxides of various metals measured
  by atomic absorption spectrophotometry. The data
  were collected to see if different sites
  contained pottery of different chemical
  compositions.

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• Al Percentage of aluminum oxide in sample
• Fe Percentage of iron oxide in sample
• Mg Percentage of magnesium oxide in sample
• Ca Percentage of calcium oxide in sample
• Na Percentage of sodium oxide in sample
• Site Site where pottery sample was collected

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• The MANOVA analysis shows that there is a
  significant difference between the sites when
  considering all five measures simultaneously and
  when considering each individually. This is
  convincing evidence that a difference exists
  however, it does not tell us which group(s) were
  different from the others. To determine this, we
  must rely on post-hoc tests of each chemical
  measure across the different sites.

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