MANOVA

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'.

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.

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

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.