Interpretation of the MATH-CPT
The Mathematics Continuous Performance Test (MATH-CPT) belongs to the category of mental testing called Continuous Performance Testing (CPT). The MATH-CPT is aimed at assessing attention levels. More specifically, it is aimed at identifying difficulties in attention, mainly in specific populations such as those with learning disabilities, brain damage and attention deficit hyperactivity disorder (ADHD). The MATH-CPT can be used for research with clinical groups as well as with non-clinical populations.
At present, the MATH-CPT is standardized for use with individuals between the ages of 12 and 90. The test is slightly more difficult than most CPT tests. For this reason, the test is unsuitable for children under the age of 12. Administering this measure to children younger than 12 may yield misleading results. Since the test is based on a learned skill, it should not be used with individuals with severe dyscalculia (defined as a mathematics learning disability). Individuals with mild dyscalculia may be tested without concern.
The results of the MATH-CPT provide a clear diagnosis of difficulties in attention. Such diagnoses (Attention Deficit Hyperactivity Disorder-ADHD) should not be based solely on the MATH-CPT. The tester should use other measures, such as IQ tests, other cognitive measures assessing attention, questionnaires distributed to teachers, questionnaires administered to parents and questionnaires administered to the examinees. Only a combination of such tests can yield a reliable diagnosis of difficulties in attention.
Assessing the intellectual ability of the examinee is essential for assessing attention level. MATH-CPT results within the normal range for individuals with high or very high IQs may change the final diagnosis for these individuals and lead the tester to diagnose them as having ADHD. The opposite may occur, with low final MATH-CPT scores for individuals with low IQs leading to a change in the final diagnosis. This may create a situation where a particular individual may not be diagnosed as having attention difficulties (or ADHD). Hence, an experienced and accredited clinician should interpret the scores since the diagnosis may not be reflected by the results of the MATH-CPT.
In the MATH-CPT results where all variables are reported in the test, higher scores on the normative measures (standard deviation, standard score, and percentile) indicate better performance or a better attention level, as can be seen in the graphs that use standard scores. Standard score, the measure used to assess most IQ tests, uses an average of 100 and a standard deviation of 15. With standard scores, a score above 100 signifies the individual is better than the population average, while a score below 100 signifies the individual is below the population average. Higher scores signify better performance on all the specific measures shown in the tables and in the graphs.
The following text explains the meaning of all the variables and measures used in the MATH-CPT:
Results Tables
Table of test’s main measures: This table appears after completing the test and confirming the coupon. The table shows the main variables of the test: total time (in minutes); standard deviation of response time; anticipatory responses; fast wrong responses; total impulsive responses; correct responses; sustained attention-time; sustained attention-standard deviation; sustained attention-impulsivity; and sustained attention-correct responses. Each variable includes the raw score, z-score, standard score and percentile score, as explained below.
Table Title – Main Test Measures
Raw score. This measure represents the raw score achieved by the person who took the test, without any processing of the scores. If you use the test for research, use the raw score for the statistical analysis.
Standard deviation (SD) or Z-Score. This measure represents the distance between the achieved score and the population average in standard deviation units, thus allowing a comparison of the score to the normal population. The SD measure reports the results relative to an average population score of 0.0. Scores above 0.0 are above average for this specific variable compared to the population average, while scores below 0.0 are below average. The SD scores on the MATH-CPT range from 3.1 to -3.1.
Standard score. This scale interprets the raw scores in a way that is different and easier to understand than the SD score. The standard score is a scale used by most intelligence tests, where the population mean is 100 and the SD is 15. The MATH-CPT has a maximum standard score of 146 and a minimum standard score of 54. Theoretically, it is possible to achieve higher and lower scores, but practically this does not improve understanding the results.
Percentile rank. This scale represents the ranking of an individual in the normal population with respect to a specific variable. The results reported on this scale are based on a mean of 50, where the lowest score is 1 and the highest score is 99. This scale is easier to understand for those who are less familiar with statistics. The percentile achieved represents the person’s standing in the normal population. For example, the 60th percentile signifies that the individual achieved a score better than 60 percent of the normal population on this specific variable, while this score is lower than 39 percent of the normal population.
Variables – Main Test Results
Total Time (in minutes). This measure reports the total time it took the individual tested to complete the answers for all 450 problems, it is reported in minutes (the time of anticipatory response is not count in the total time). This variable is also known as response rate, reaction time or hit rate. Other researchers have found response rate to be a very important measure in assessing attention level. On the MATH-CPT, the two most important variables in assessing attention level are the response rates (or total time) and the number of correct answers.
Standard deviation of reaction time. This measure assesses the standard deviation of the reaction time on all 450 problems of the test. The measure assesses the consistency of the examinee’s reaction time. Consistent performance is reflected in similar reaction times for the various problems. A lower SD raw score and a higher z-score, standard score and percentile indicate better performance. Inconsistent performance will result in a higher raw score and a lower z-score, standard score and percentile.
Anticipatory responses. A pilot study prior to the final construction of the MATH-CPT indicated that a simple arithmetical problem, such as those on the MATH-CPT, requires no less than 500 milliseconds (or half a second). This means that any answer given faster than 500 milliseconds is a guess or an anticipatory response or indicates that the respondent has held the key down longer. These responses are counted as anticipatory responses and not as correct or incorrect responses. Anticipatory responses are a major factor in assessing participants’ impulsivity, as with many other CPT-type tests.
Fast-wrong responses. This measure represents the number of wrong responses given faster than the average response rate of the individual performing the test. The average response rate is calculated by dividing the total time by 450 questions. In making this type of response, the examinee may have answered the wrong answer due to impulsivity. The fast-wrong responses are added to the anticipatory responses to yield the measure of total impulsivity. It is important to note that ‘Fast-Wrong-Responses’ is a weaker measure of impulsivity than anticipatory response. Therefore, it is better to describe it as light impulsivity.
Total impulsivity. This variable assesses the examinee’s overall impulsivity level. Total impulsivity comprises anticipatory responses and fast-wrong responses. Impulsivity is one domain in a diagnosis of ADHD. The other two are attention and hyperactivity.
Correct responses. This measure reports the number of correct answers out of the test’s 450 problems and serves as a measure of attention, one of the most important variables in a diagnosis of ADHD. The other two are hyperactivity and impulsivity. The underlying assumption of this variable is that any person answering the test should know the answers to the simple mathematical problems presented on the screen. The reason for giving a wrong response is lack of attention in answering regardless of the individual’s ability to answer correctly.
Overall attention formula. This number is the result of a combination of several of the test variables found to discriminate between a normal population and individuals with ADHD. The statistical procedure of discriminant function analysis was used to yield this number. This formula should indicate whether the individual being tested should be diagnosed as having ADHD. A raw score below 0.0 (or a negative number) is an indication of a normal score. A score of 0.0 or above (a positive number) is an indication of ADHD. If the number is positive, other variables should be examined in order to understand the nature of the problem. Considering the importance of this measure, we recommend that in deciding about any diagnosis you exercise caution in using the borderline raw scores of the overall attention formula, which ranged from 0.3 to ‑0.3.
Sustained attention – time. This variable reports the examinee’s performance by comparing the different parts of the test from beginning to end. This measure uses a special formula to calculate the response rate by comparing the nine parts of the test, each with 50 problems, from beginning to end. Improvement in the response rate indicates improved sustained attention. Taking more time to respond toward the end of the test indicates that the examinee has lower sustained attention. A lower raw score (and higher Z-score, standard score and percentile) indicates improved sustained attention, where the mean for a normal population is ‑7.30.
Sustained attention – standard deviation. This variable reports the examinee’s performance by comparing the different parts of the test from beginning to end. This measure uses a special formula to calculate the standard deviation by comparing the nine parts of the test from beginning to end. An improvement in the standard deviation indicates smaller raw score and improved sustained attention standard deviation. In such a case, performance toward the end of the test is more consistent. A larger raw score toward the end of the test indicates a lower sustained attention standard deviation or performance that is less consistent. A lower raw score (and higher Z-score, standard score and percentile) indicates better sustained attention—SD. The mean of a normal population is 0.02.
Sustained attention – impulsivity. This variable reports the examinee’s performance by comparing the different parts of the test from beginning to end. This measure uses a special formula to calculate total impulsivity, which is a combination of anticipatory responses and fast-wrong responses, by comparing the nine parts of the test (consists of the 50 problems) from beginning to end. A decrease in the number of impulsive responses (lower raw score) signifies improved sustained attention – impulsivity or less impulsive performance toward the end of the test. An increase in the number of impulsive responses toward the end of the test signifies lower sustained attention – impulsivity. A lower raw score (and higher Z-score, standard score and percentile) indicates better sustained attention – impulsivity. The mean of a normal population is 0.54.
Sustained attention-correct responses. This variable reports the way the person tested performed the task by comparing the different parts of the entire test from the beginning to the end. This measure uses a special formula to calculate the correct responses by comparison of the nine parts of the test, each one with 50 problems, from the start to the end. If the raw score of the correct responses increases (a larger number), it signifies a better sustained attention-correct responses at the end of the test, while a smaller number toward the end of the test signifies lower sustained attention-correct responses. A higher raw score (and higher Z-Score, Standard Score, and Percentile) indicates better sustained correct answers. The mean of a normal population is -0.24).
Graph showing Main Results
The main results are depicted as a graph below the Main Results table. This graph shows the results using standard scores (mean of 100 and standard deviation of 15). The purpose of this graph is to depict the results in clear graphical form and to enable comparing the examinee’s results to those of a normal population.
Tables and Graphs of Test Thirds
Performance tables and graphs for test thirds. The table titled Results Divided into Three Parts of 150 Problems Each (Raw Scores) shows the raw scores for six variables for three consecutive groups of 150 problems. The first third refers to questions 1 to 150; the second third refers to questions 151 to 300; and the last third refers to questions 301 to 450. The six variables are: total time (in minutes); standard deviation of the total time; anticipatory response; fast-wrong responses; total impulsivity; and correct responses. The purpose of this table is to show the examinee’s raw score performance throughout the test divided into three thirds and thus to estimate the progress during the course of the test.
Other graphs appear below this table: a) Results Divided into Three Parts of 150 Problems (Standard Score) and b) Thirds Graph, which depicts the results of the standardized performance scores for each third of the test. The graph uses the following colors to represent the different variables:
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Total time –blue
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Standard deviation of total time – green
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Total impulsivity – yellow
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Correct responses – black
A name describing the variable appears at the bottom of the graph to facilitate identification of the different variables.
Tables and Graphs of Test Ninths
Performance Table for Test Ninths. The table titled Results Divided into Nine Parts of 50 Problems Each (Raw Scores) presents the raw scores of six variables divided into nine parts of 50 problems each, as follows:
First ninth – problems 1 to 50
Second ninth – problems 51 to 100
Third ninth – problems 101 to 150
Fourth ninth – problems 151 to 200
Fifth ninth – problems 201 to 250
Sixth ninth – problems 251 to 300
Seventh ninth – problems 301 to 350
Eighth ninth – problems 351 to 400
Ninth ninth – problems 401 to 450
The variables are: total time (in minutes); standard deviation of the total time; anticipatory response; fast-wrong responses; total impulsivity; and correct responses. The purpose of this table is to show the examinee’s raw score performance throughout the test divided into nine ninths and to estimate the progress throughout the test. These raw scores are used to calculate one number to represent sustained attention in test performance.
Below this table is a graph titled Results Divided into Nine Parts of 50 Problems (Raw Scores). This graph depicts the results of the raw performance scores on the nine parts of the test. The graph uses the following colors to represent the different variables:
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Total time –blue
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Standard deviation of total time – green
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Total impulsivity – yellow
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Correct responses – black