Suggested answers for case study 3


The long and short forms seem to be placed within a continuum of length/width ratios, and there does not seem to be any justification for splitting the sample at any particular point.

Graphical comparison of data sets

The three samples are overlapping in the plots, but the Swedish S. linnarssoni are usually larger than the S. glaber. In addition, aspect ratios are perhaps differing a little between the Norwegian S. linnarssoni and the S. glaber, at least for small specimens.

Principal Components Analysis

98.8 percent of the variation in the sample is accounted for by the first component. The other components are of minor significance.

Similar loadings of all variables on the first component means that as we go along the principal axis, all measurements are increasing similarly. This axis (component) is therefore a general size axis. The loadings on the second component show that as we go along the second axis, length is rapidly decreasing while the width values are increasing. The second component can therefore be described as a length/width ratio axis.

The scatter plot again shows some overlap between the groups, but the S. glaber and the Norwegian S. linnarssoni are now better separated than in the simple X/Y plots.

The 'typical long' (black dot 1) and 'typical short' (black dot 2) forms are positioned far down and far up on the second component axis, in accordance with our interpretation of this component.

Principal Coordinates Analysis

The groups are not really separated along the arch, and PCO does not seem to work well in this case.

Cluster Analysis

For the Euclidean distance measure, overall size will be all important for the clustering. As expected from our results above, the three samples do not form well separated clusters.

Discriminant analysis

The discriminant analysis histogram does not show really good separation of the two suggested species, but he Hotelling's t2 test reports a highly significant difference.

Conclusion

The analysis from these data alone is somewhat inconclusive. There is definitely a difference between the groups, but they are all within a continuously overlapping range. PCA analysis is perhaps the most revealing method for this data set.