Editing G factor (psychometrics) (section)

=="Indifference of the indicator"==

Spearman proposed the principle of the ''indifference of the indicator'', according to which the precise content of intelligence tests is unimportant for the purposes of identifying ''g'', because ''g'' enters into performance on all kinds of tests. Any test can therefore be used as an indicator of ''g''.<ref name=":2">{{Cite journal |last1=Warne |first1=Russell T. |last2=Burningham |first2=Cassidy |date=2019 |title=Spearman's g found in 31 non-Western nations: Strong evidence that g is a universal phenomenon |url=http://psyarxiv.com/uv673/ |journal=Psychological Bulletin |volume=145 |issue=3 |pages=237–272 |doi=10.1037/bul0000184 |pmid=30640496 |s2cid=58625266}}</ref> Following Spearman, Arthur Jensen more recently argued that a ''g'' factor extracted from one test battery will always be the same, within the limits of measurement error, as that extracted from another battery, provided that the batteries are large and diverse.<ref>Mackintosh 2011, 151</ref> According to this view, every mental test, no matter how distinctive, calls on ''g'' to some extent. Thus a composite score of a number of different tests will load onto ''g'' more strongly than any of the individual test scores, because the ''g'' components cumulate into the composite score, while the uncorrelated non-''g'' components will cancel each other out. Theoretically, the composite score of an infinitely large, diverse test battery would, then, be a perfect measure of ''g''.<ref>Jensen 1998, 31</ref>

In contrast, [[Louis Leon Thurstone|L. L. Thurstone]] argued that a ''g'' factor extracted from a test battery reflects the average of all the abilities called for by the particular battery, and that ''g'' therefore varies from one battery to another and "has no fundamental psychological significance."<ref>Mackintosh 2011, 151–153</ref> Along similar lines, [[John L. Horn|John Horn]] argued that ''g'' factors are meaningless because they are not invariant across test batteries, maintaining that correlations between different ability measures arise because it is difficult to define a human action that depends on just one ability.<ref name="McGrew 2005">McGrew 2005</ref><ref>Kvist & Gustafsson 2008</ref>

To show that different batteries reflect the same ''g'', one must administer several test batteries to the same individuals, extract ''g'' factors from each battery, and show that the factors are highly correlated. This can be done within a confirmatory factor analysis framework.<ref name="Hunt 2011, 94"/> Wendy Johnson and colleagues have published two such studies.<ref>Johnson et al. 2004</ref><ref>Johnson et al. 2008</ref> The first found that the correlations between ''g'' factors extracted from three different batteries were .99, .99, and 1.00, supporting the hypothesis that ''g'' factors from different batteries are the same and that the identification of ''g'' is not dependent on the specific abilities assessed. The second study found that ''g'' factors derived from four of five test batteries correlated at between .95–1.00, while the correlations ranged from .79 to .96 for the fifth battery, the [[Cattell Culture Fair Intelligence Test]] (the CFIT). They attributed the somewhat lower correlations with the CFIT battery to its lack of content diversity for it contains only matrix-type items, and interpreted the findings as supporting the contention that ''g'' factors derived from different test batteries are the same provided that the batteries are diverse enough. The results suggest that the same ''g'' can be consistently identified from different test batteries.<ref name="deary2012"/><ref>Mackintosh 2011, 150–153. See also Keith et al. 2001 where the ''g'' factors from the [[Cognitive Assessment System|CAS]] and [[Woodcock–Johnson Tests of Cognitive Abilities|WJ III]] test batteries were found to be statistically indistinguishable, and Stauffer et al. 1996 where similar results were found for the [[Armed Services Vocational Aptitude Battery|ASVAB]] battery and a battery of cognitive-components-based tests.</ref> This approach has been criticized by psychologist [[Lazar Stankov]] in the Handbook of Understanding and Measuring Intelligence, who councluded "Correlations between the g factors from different test batteries are not unity."<ref>{{Cite web|url=https://www.researchgate.net/publication/285519372|title=G factor: Issue of design and interpretation}}</ref>

A study authored by [[Scott Barry Kaufman]] and colleagues showed that the general factor extracted from the [[Woodcock–Johnson Tests of Cognitive Abilities|Woodjock-Johnson]] cognitive abilities test, and the general factor extracted from the Achievement test batteries are highly correlated, but not isomorphic.<ref>{{cite journal | url=https://www.sciencedirect.com/science/article/pii/S0160289612000104 | doi=10.1016/j.intell.2012.01.009 | title=Are cognitive g and academic achievement g one and the same g? An exploration on the Woodcock–Johnson and Kaufman tests | year=2012 | last1=Kaufman | first1=Scott Barry | last2=Reynolds | first2=Matthew R. | last3=Liu | first3=Xin | last4=Kaufman | first4=Alan S. | last5=McGrew | first5=Kevin S. | journal=Intelligence | volume=40 | issue=2 | pages=123–138 | url-access=subscription }}</ref>