ANF Adaptive Numerical Flexibility Test

The ANF is the first test on the market to provide an adaptive and fair assessment of cognitive flexibility in the area of mathematical problem solving.

Application
The Adaptive Numerical Flexibility Test is a tool for assessing flexibility in mathematical problem-solving as one of the important sub-dimensions of quantitative thinking as defined in the modified Gf-Gc theory (Horn & Noll, 1997). 

Theoretical background
Quantitative thinking is an important second-order factor both in the Three Stratum theory (Carroll, 1993) and in the modified Gf-Gc theory of Horn (1989; Horn & Noll, 1997). It covers not only number comprehension but also the understanding of basic arithmetical operations and mathematical principles and the ability to apply them. The Adaptive Numerical Flexibility Test assesses the ability to understand the basic arithmetical operations and apply them flexi-bly in solving abstract arithmetical problems.

Administration
Items are presented adaptively, so that after the initial phase the process of presenting only those items which are appropriate to the respondent’s ability is increasingly refined. It is not possible to omit an item or to return to a preceding one.
Each item presents the respondent with a series of unrelated operands and an answer which can be obtained by appropriate linking of the operands. The respondent has to insert the cor-rect arithmetical operators in the blank spaces, linking the operands in such a way that the given answer is achieved. Because any of the four basic arithmetical operations can be used as often as required the probability of arriving at the correct answer by guesswork is very low.

Test forms
There are two adaptive test forms which differ in their pre-set precision of measurement (stan-dard estimation error) of the person parameter estimate.

Scoring
The test yields an estimate of the respondent’s numerical flexibility. The estimate is made on the basis of the dichotomous logistical model of Rasch (1980) using an exact parameter esti-mation process (Fischer, 2000). In addition a percentile ranking is provided based on compari-son with a norm sample.

Reliability
Reliability in the sense of internal consistency as taken as given as a result of the validity of the Rasch model. Precision is represented for the short form by a critical standard estimate of error of 0.55, which corresponds to a reliability of 0.70. For the standard form the critical standard estimate of error is 0.50, corresponding to a reliability of 0.75. In contrast to linear test forms the quoted precision applies to all respondents across all parts of the range. This represents a decisive advantage over conventional psychometric tests constructed on the basis of classical test theory.

Validity
Studies are available both of the construct representation and of the convergent and discrimi-nant validity of the Adaptive Numerical Flexibility Test; these demonstrate the construct va-lidity of the test.

Norms
Norms are available (overall norm, and separated by gender and educational level) for a sam-ple of N=1362 individuals (585 men, 777 women; age range 15-52). The data was collected at the end of 2004 and beginning of 2005.