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  • Print publication year: 2016
  • Online publication date: April 2016

5 - Measurement error and latent variables


Ambient temperature affects the metabolic rate of animals. When it is cold a homeothermic animal has to burn stored energy reserves – first glycogen and fat and then, when these are exhausted, protein – in order to generate heat and maintain its body temperature. The scaling of surface area (the site of heat loss to the atmosphere) to body volume (where the heat is generated) means that small homeothermic animals, such as songbirds, can lose up to 15 per cent of their body fat in one cold night. To burn this fat the bird must increase its metabolic rate, which increases its oxygen consumption. Imagine that we conduct an experiment in which we place small birds inside metabolic chambers overnight and vary the air temperature. The hypothesised causal process is shown in Figure 5.1.

Unfortunately, we can't directly measure any of these three variables; they are unmeasured, or latent, and so I have enclosed them in circles following the conventions of path diagrams. If we measure the air temperature using a thermometer then we aren't directly measuring temperature – the average kinetic energy of the molecules in the air. Instead, we are measuring the height of a column of mercury in a vacuum and enclosed in a hollow glass tube. In fact, we can't even measure the actual height of the mercury exactly, since our observed height will include some measurement error. Nor can we directly measure metabolic rate. Typically, one measures the rate of gas exchange (oxygen decrease or carbon dioxide increase) between the air entering and leaving the metabolic chamber. If we measure oxygen consumption using an infrared gas analyser then we aren't even directly measuring oxygen consumption. Instead, we are measuring differences in the amount of light of particular wavelengths that is absorbed as the light passes through the air. Again, even this variable is not perfectly measured, since the observed values will also contain measurement error. When we measure the fat reserves that are burned by the birds we might actually be measuring the difference in body weight over the course of the experiment, and this too will include measurement error. One simplified representation of the actual causal process is depicted in Figure 5.2.