Editing G factor (psychometrics) (section)

===Sampling theory===

The so-called sampling theory of ''g'', originally developed by [[Edward Thorndike]] and [[Godfrey Thomson]], proposes that the existence of the positive manifold can be explained without reference to a unitary underlying capacity. According to this theory, there are a number of uncorrelated mental processes, and all tests draw upon different samples of these processes. The inter correlations between tests are caused by an overlap between processes tapped by the tests.<ref>Mackintosh 2011, 157</ref><ref>Jensen 1998, 117</ref> Thus, the positive manifold arises due to a measurement problem, an inability to measure more fine-grained, presumably uncorrelated mental processes.<ref name="maas"/>

It has been shown that it is not possible to distinguish statistically between Spearman's model of ''g'' and the sampling model; both are equally able to account for inter correlations among tests.<ref>Bartholomew et al. 2009</ref> The sampling theory is also consistent with the observation that more complex mental tasks have higher ''g'' loading, because more complex tasks are expected to involve a larger sampling of neural elements and therefore have more of them in common with other tasks.<ref>Jensen 1998, 120</ref>

Some researchers have argued that the sampling model invalidates ''g'' as a psychological concept, because the model suggests that ''g'' factors derived from different test batteries simply reflect the shared elements of the particular tests contained in each battery rather than a ''g'' that is common to all tests. Similarly, high correlations between different batteries could be due to them measuring the same set of abilities rather than ''the'' same ability.<ref name="horn&mcardle"/>

Critics have argued that the sampling theory is incongruent with certain empirical findings. Based on the sampling theory, one might expect that related cognitive tests share many elements and thus be highly correlated. However, some closely related tests, such as forward and backward digit span, are only modestly correlated, while some seemingly completely dissimilar tests, such as vocabulary tests and Raven's matrices, are consistently highly correlated. Another problematic finding is that brain damage frequently leads to specific cognitive impairments rather than a general impairment one might expect based on the sampling theory.<ref name="maas"/><ref>Jensen 1998, 120–121</ref>