Bear Size ~

[tigerluver]

At the request of @peter, I have come up with a formula to describe the relationship between pad width and the weight of bears.

This was shared in the "Edge of extinction" thread:

*This image is copyright of its original author

I ran a linear regression based on the 9 specimens (did not use the 600 kg specimen) and the results were as follows:

*This image is copyright of its original author

In this dataset, the relationship was not significant (p = 0.235). For that reason, there is no point in elaborating on the formula on the top right as it is useless. Visually, it seems the two ~145 kg specimens with paw widths of 16 cm are outliers causing the issue, but I cannot remove the outliers unless I have some justification.

However, the lack of significance above seems to have been a type II error due to a lack of power. Blanchard published a study on Yellowstone bears which detailed bear weights and paw sizes in different age groups. While this is not as optimal as having individual weights, the foundation for estimation will still work as there are a good amount of datapoints. Here are the results (n = 21):

*This image is copyright of its original author

The association is very significant (p <<< 0.05). The relationship is also very significantly positively allometric as the 95% confidence interval for the scale factor of 3.9091 (95% CI 3.34-4.47) is significantly different from 3. This means a small change in pad width has great change in weight. 

In sum, the formula Mass = 3.9091log(Pad Width) - 6.1869 seems to be a powerful tool to estimate bear weight. There is a clear association between these two variables and bears get heavier quicker than their paws get wider. Reply