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'.
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 boxplots and post-hoc tests of each chemical measure across the different sites.
Scheffe post-hoc tests of the five variables seem to show that the Ashley Rails (A) and Island Thorns (I) sites share the same chemical composition, while the Llanederyn (L) and Caldicot (C) sites are similar to each other but different from the first two. This pattern holds for all of the chemical variables except 'Na' (sodium oxide). In this case there is still not significant difference within the two groups of sites mentioned above; however, there also is no significant difference between Caldicot and Ashley Rails or Island Thorns.
Boxplots of the five chemical variables by 'Site' agree with the results of the Scheffe post-hoc tests stated above. Boxplots for 'Al' and 'Na' by 'Site' are given below. The shaded areas on the boxplots correspond to 95% confidence intervals for the medians of each variable.
If we recode the 'Site' variable to combine Ashley Rails and Island Thorns into one group and Llanederyn and Caldicot into another, the MANOVA shows that there is a significant difference between these two groups.