2.1

EABN

The EABN is an ecological test battery addressing the use of numbers in daily life; it consists of 8 tests ( Table 1 ) corresponding to common situations in everyday life involving numbers: telling time, going shopping, writing a cheque, writing down contact information, cooking etc. All tests and subtests are timed; however, subjects are asked not to take time measurement into account and to proceed as usual, thereby not being under pressure. The maximum total score is 40. The EABN material includes the rating sheet and the testing handbook, a chronometer, a calculator, a schedule, and play money. The complete test battery is completed individually by control subjects. The test generally takes place in a calm room and lasts 10 to 25 min. In most cases, professionals in charge of the EABN test went to the homes of control subjects.

2.2

Standardization of the EABN

The subjects included for the standardization phase were 20 to 79 years old with equal distribution by age (20–39, 40–59 and 60–79 years), sex and sociocultural level (SCL1: ≤ French certificate of higher education; SCL2, baccalaureate degree; SCL3, higher studies). Subjects had to understand and use the French language and have no abnormal neurological or psychiatric history. We produced descriptive (mean, SD, percentile 5) and inferential statistics using Student’s t test to estimate the effect of demographic variables on the EABN score and to establish standards according to the recorded effects. We preliminarily determined that if the score distribution were non-normal, the 5th percentile would be considered the pathological threshold.

2.3

Concurrent validity analysis

We performed a validity study with brain-injured patients who were hospitalized between September 2011 and December 2012 in the physical and rehabilitation medicine unit of La Pitié-Salpêtrière Hospital, Paris. Inclusion criteria were age 20 to 79 years, with no sensory or motor disability that disallowed taking the tests.

The patients were evaluated by both the EABN and a French analytical calculation test, the ECAN . The ECAN is an analytical battery designed to test abilities in calculation and number-processing. It was developed and standardized by Auzou et al. according to the French language adaptation of the Number-Processing and Calculation (NPC) battery . It includes 35 tasks assessing the different abilities in counting, the different aspects of number comprehension, numerical transcoding, calculation, arithmetic reasoning and conceptual knowledge. It assesses the calculation skills needed for 4 operations (simple fact retrieval, rule-based processing, mental calculation, written calculation) as well as problem resolution. The ECAN is more complete and provides more accurate evaluation of impaired processes than the EC301 and has been standardized with 423 healthy control subjects. It is based on 4 main areas: knowledge of numbers, transcoding, calculation and common knowledge of numbers. All tests are timed. They differ in several ways from the NPC: there are more items for the transcoding tests but some common items for different tasks, thereby allowing comparison of performance. Finally, the NPC approximate test, which practically all control subjects failed, has been replaced by a test derived from the Stanescu-Cosson test .

To study the degree of concordance between the ecological battery (EABN) and the analytical battery (ECAN), our reference battery, we calculated Kendall’s w coefficient . The Kendall w coefficient ranges from 0 to 1: the closer to 1, the greater the degree of concordance. The objective was to classify patients by rank on the test based on comparisons of the recorded grades.

2.4

Construct validity analysis

To establish construct validity, we analyzed the discriminatory power of each subtest. We calculated the discrimination indexes corresponding to the difference between the difficulty indexes of the 2 extreme groups, using the standardization data and the data collected from patients. The values for the P index for relative difficulty of the items range from 0 to 1: values close to 0 indicate an item for which few subjects successfully performed, and values close to 1 denote an item for which a high proportion of subjects successfully performed. When an item is rated on a scale containing several points, the difficulty index corresponds to the mean rating achieved for this item by the subjects as a whole. The mean rating for the item is divided by the maximum grade: for example, if the maximum grade for the item is 5, the mean grade for that item is divided by 5.

The P index equals the total sum of the ratings divided by the number of subjects. The item discrimination index D corresponds to the difference between the difficulty index for an item with regard to the “strong” group ( P +) and the difficulty index for the “weak” group ( P –). The larger the difference in D , the more the item discriminates between subjects with a high total score and those with a low total score. The “strong” group consists of subjects with a total score placing them in the upper 27% of the total population, and the “weak” group consists of those whose score places them in the lower 27% . To constitute these groups, we used the detailed standardization data ( n = 126) and the results recorded for patients ( n = 17), for a relatively large sample.

The discrimination index D can take on any value from –1 to +1. A value of zero means that a given item was as successfully negotiated by subjects with a low total score as by those with a high total score. A negative value means that with respect to an item, weaker subjects were more successful than stronger subjects. A discrimination index D > 0.4 is very good; 0.2 to 0.4, good; 0.1 to 0.2, average; and < 0.1 or negative, insufficient.

2.1

EABN

The EABN is an ecological test battery addressing the use of numbers in daily life; it consists of 8 tests ( Table 1 ) corresponding to common situations in everyday life involving numbers: telling time, going shopping, writing a cheque, writing down contact information, cooking etc. All tests and subtests are timed; however, subjects are asked not to take time measurement into account and to proceed as usual, thereby not being under pressure. The maximum total score is 40. The EABN material includes the rating sheet and the testing handbook, a chronometer, a calculator, a schedule, and play money. The complete test battery is completed individually by control subjects. The test generally takes place in a calm room and lasts 10 to 25 min. In most cases, professionals in charge of the EABN test went to the homes of control subjects.

2.2

Standardization of the EABN

The subjects included for the standardization phase were 20 to 79 years old with equal distribution by age (20–39, 40–59 and 60–79 years), sex and sociocultural level (SCL1: ≤ French certificate of higher education; SCL2, baccalaureate degree; SCL3, higher studies). Subjects had to understand and use the French language and have no abnormal neurological or psychiatric history. We produced descriptive (mean, SD, percentile 5) and inferential statistics using Student’s t test to estimate the effect of demographic variables on the EABN score and to establish standards according to the recorded effects. We preliminarily determined that if the score distribution were non-normal, the 5th percentile would be considered the pathological threshold.

2.3

Concurrent validity analysis

We performed a validity study with brain-injured patients who were hospitalized between September 2011 and December 2012 in the physical and rehabilitation medicine unit of La Pitié-Salpêtrière Hospital, Paris. Inclusion criteria were age 20 to 79 years, with no sensory or motor disability that disallowed taking the tests.

The patients were evaluated by both the EABN and a French analytical calculation test, the ECAN . The ECAN is an analytical battery designed to test abilities in calculation and number-processing. It was developed and standardized by Auzou et al. according to the French language adaptation of the Number-Processing and Calculation (NPC) battery . It includes 35 tasks assessing the different abilities in counting, the different aspects of number comprehension, numerical transcoding, calculation, arithmetic reasoning and conceptual knowledge. It assesses the calculation skills needed for 4 operations (simple fact retrieval, rule-based processing, mental calculation, written calculation) as well as problem resolution. The ECAN is more complete and provides more accurate evaluation of impaired processes than the EC301 and has been standardized with 423 healthy control subjects. It is based on 4 main areas: knowledge of numbers, transcoding, calculation and common knowledge of numbers. All tests are timed. They differ in several ways from the NPC: there are more items for the transcoding tests but some common items for different tasks, thereby allowing comparison of performance. Finally, the NPC approximate test, which practically all control subjects failed, has been replaced by a test derived from the Stanescu-Cosson test .

To study the degree of concordance between the ecological battery (EABN) and the analytical battery (ECAN), our reference battery, we calculated Kendall’s w coefficient . The Kendall w coefficient ranges from 0 to 1: the closer to 1, the greater the degree of concordance. The objective was to classify patients by rank on the test based on comparisons of the recorded grades.

2.4

Construct validity analysis

To establish construct validity, we analyzed the discriminatory power of each subtest. We calculated the discrimination indexes corresponding to the difference between the difficulty indexes of the 2 extreme groups, using the standardization data and the data collected from patients. The values for the P index for relative difficulty of the items range from 0 to 1: values close to 0 indicate an item for which few subjects successfully performed, and values close to 1 denote an item for which a high proportion of subjects successfully performed. When an item is rated on a scale containing several points, the difficulty index corresponds to the mean rating achieved for this item by the subjects as a whole. The mean rating for the item is divided by the maximum grade: for example, if the maximum grade for the item is 5, the mean grade for that item is divided by 5.

The P index equals the total sum of the ratings divided by the number of subjects. The item discrimination index D corresponds to the difference between the difficulty index for an item with regard to the “strong” group ( P +) and the difficulty index for the “weak” group ( P –). The larger the difference in D , the more the item discriminates between subjects with a high total score and those with a low total score. The “strong” group consists of subjects with a total score placing them in the upper 27% of the total population, and the “weak” group consists of those whose score places them in the lower 27% . To constitute these groups, we used the detailed standardization data ( n = 126) and the results recorded for patients ( n = 17), for a relatively large sample.

The discrimination index D can take on any value from –1 to +1. A value of zero means that a given item was as successfully negotiated by subjects with a low total score as by those with a high total score. A negative value means that with respect to an item, weaker subjects were more successful than stronger subjects. A discrimination index D > 0.4 is very good; 0.2 to 0.4, good; 0.1 to 0.2, average; and < 0.1 or negative, insufficient.