Item response theory models and spurious interaction effects in factorial ANOVA designs
1996
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Item response theory models and spurious interaction effects in factorial ANOVA designs
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1996
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Abstract
In many psychological experiments, interaction
effects in factorial analysis of variance (ANOVA)
designs are often estimated using total scores derived
from classical test theory. However, interaction effects
can be reduced or eliminated by nonlinear monotonic
transformations of a dependent variable. Although
cross-over interactions cannot be eliminated by transformations,
the meaningfulness of other interactions
hinges on achieving a measurement scale level for
which nonlinear transformations are inappropriate (i.e.,
at least interval scale level). Classical total test scores
do not provide interval level measurement according to
contemporary item response theory (IRT). Nevertheless,
rarely are IRT models applied to achieve more optimal
measurement properties and hence more meaningful
interaction effects. This paper provides several conditions
under which interaction effects that are estimated
from classical total scores, rather than IRT trait scores,
can be misleading. Using derived asymptotic expectations
from an IRT model, interaction effects of zero on
the IRT trait scale were often not estimated as zero
from the total score scale. Further, when nonzero interactions
were specified on the IRT trait scale, the estimated
interaction effects were biased inward when
estimated from the total score scale. Test difficulty
level determined both the direction and the magnitude
of the biased interaction effects. Index terms: factorial
designs, interaction effects, interval measurement,
item response theory, level of measurement, measurement
scales, statistical inference.
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Embretson, Susan E. (1996). Item response theory models and spurious interaction effects in factorial ANOVA designs. Applied Psychological Measurement, 20, 201-212. doi:10.1177/014662169602000302
Suggested citation
Embretson, Susan E.. (1996). Item response theory models and spurious interaction effects in factorial ANOVA designs. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/119091.
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