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Sources of variation

We appreciate that the observed variation in IVC may relate to differences in standing height. The illustration to the right shows the bell-shaped distribution of the independent variable, and tilted by 90 degrees, similarly of the dependent variable; the height of the bell corresponds to the number of observations. Clearly much of the variability in Y (the IVC) can be explained by differences in X (standing height). This does not account for all variability, however, otherwise all points would be on a straight line.

We previously addressed systematic and random measurement errors. Random errors in both IVC and length explain part of the scatter about the regression line. The remaining part is due to other ‘errors’, such as differences in body build, or in the properties of chest, lung parenchyma and airways, so that people of the same length do not have the same IVC. Also, for the same standing height males have a larger IVC than females. Similarly there are ethnic differences: Caucasians have a larger IVC for the same length than black people. These all represent sources of variability between subjects.

In the case of repeated measurements on the same person we do not get the same result. This may be due to subject co-operation, or the measurement influencing the respiratory system and hence the result of the next measurement. In addition the time of the day, or the season of the year, prior physical exercise, etc. may affect the results. In patients the disease process, or the use of drugs, may influence the IVC. These are all sources of biological variability within subjects.

Among the many other sources of measurement error are those due e.g. to
•	instruments,
•	calibrations, but also
•	reading errors,
•	the way the measurements are performed:
	how experienced and motivated is the person in charge of the measurements, is the IVC measured once or the largest of three efforts taken, are all maneuvers performed correctly, is the subject at rest and clearly informed of the purpose of the test and how it is performed, are measurements made in too rapid succession, is the subject naive (learning effect) or experienced in performing IVC maneuvers, etc.
Clearly the scatter depicted in the yellow dome-shaped bell along the Y-axis reflects
•	the IVC increasing with body size, but in addition
•	all other sources of variability in IVC listed above, and summarized as ‘errors’.

See also: Sources of variability between subject.

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