Table 4. Tests of assumptions of the regression-based body condition indices (BCIs).
We used several tests to test the hypotheses that: 1) the data are linear; 2) the variance is constant (i.e., homoscedastic); and 3) the frequency distribution of residuals is normal. For clarity, only p-values are reported. Most assumptions are met for regressions of log-transformed mass on log-transformed length, but regressions of mass on length cubed exhibited neither homoscedasticity nor normality. Abbreviations for each of the BCIs are provided in Table 1.
| BCI | Regression | Ramsey’s RESET Test (linearity) | Breusch-Pagan Test (homoscedasticity) | Shapiro-Wilk Test (normality) | d’Agostino Test (skewness) | Anscombe-Glynn Test (kurtosis) | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| F | M | F | M | F | M | F | M | F | M | ||
| OLSres | OLS (logM~logL) | — | — | — | — | * | — | — | n/a | — | n/a |
| MAres | MA (logM~logL) | * | — | — | n/a | — | n/a | ||||
| SMAres | SMA (logM~logL) | * | — | — | n/a | — | n/a | ||||
| res(M~L^3) | SMA (M~L^3) |
— | — | ** | ** | ** | ** | ** | ** | ** | ** |
— p > 0.05
* p ≤ 0.05
**p ≤ 0.001