Measurement Error Revisited: Its Importance for the Analysis of Size and Shape of Birds

Measurement error in morphological characters is an important issue for many ornithological studies (e.g. ecomorphology, quantitative studies of heritability, studies of systematic and geographic variation). The variation in external morphological characters, such as wing and tarsus length, is usually evaluated using multivariate statistical methods such as principal component analysis (PCA). These are often considered better than univariate statistical methods for explaining size and shape variation in bird populations because they reduce the ‘dimensionality’ of the data — the size of individual measures (wing etc.) are assumed to contain a component reflecting a general character ‘size’. However, the effect of measurement error on principal components has not been formally assessed with respect to such data. Here we report three examples in order to assess the importance of measurement error for analyses within and between bird populations. The effect of measurement error on PCA is also discussed in relation to the importance of levels of error in shape components. Our results indicate that, in relation to size (PC1), principal component scores are affected less by measurement error if the covariance matrix is used rather than the correlation matrix. However, the effects of relative measurement error were substantially greater in subsequent axes, which represent shape variation rather than size, than they were in the size axis (PC1). Measurement error may, therefore, be a more important issue for shape axes than for the size axis and this problem may be exacerbated further if very few characters are used in the PCA. Our results also indicate that PCA is especially sensitive to issues relating to sample size. We recommend that if reducing the measurement error in size and shape measures is not possible, and the sample size is small (≤ 30), principal component scores should be derived using the covariance matrix, as these are more likely to give more robust results.