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Assessment of Normative Statements Through Measures of Central Tendency
(RESEARCH FOR THE CLINICIAN)
Assessment of Normative Statements Through Measures of Central Tendency n derstan din g "normal" is the base from which all clinicians proceed when evaluU ating and treating patients. In order to identify dysfunction, predict rehabilitative potential, assess progress, and define final functional level, it is important to be able to relate a patient's performance in a given area to that of an unimpaired individual of the same sex, age, and general background. This process of comparison is usually based on observation or a com bination of observation and measurement. While the presence of a fracture, disrupted tendon, or open wound is an obvious departure from normal, many problems facing clinicians are not so apparent, necessitating more sophisticated approaches. Also, in this age of accountability, clinicians are being required to substantiate their actions through documentation and review. Being able to numerically document patient performance to that of "normal" performance is essential. Ostensibly, this process seems easy enough. The phenomenon in question is measured and the resultant scores are compared to established normal values for that particular phenomenon. While this may sound elemental, closer scrutiny reveals a very sophisticated process based on specific criteria. First, an instrument whose reliability and validity have been statistically established (see previous Research for the Clinician columns) must be used to measure the given event, and second, for comparison, this instrument must also have accompanying normative data appropriate to the event being measured. By what criteria may clinician consumers judge the efficacy of normative statements? All too often one is presented with an assessment instrument that has as its normative statement one or two "average" values. Noting another source of potential confusion, both clinical and research studies often report findings in terms of statistical "averages." What do these statements reflect in terms of the issues being studied? Are they meaningful and how may they be evaluated? Given a sufficiently large group of subjects, data from a normal population are distributed in a relatively predictable manner that is graphically represented by a symmetrical bell-shaped curve. Three measures of central tendency (mean, median, and mode) are fundamental to evaluating the shape or configuration of a group of values, whether they represent a statement derived from a large normal population, from a specific diagnostic entity, or from a smaller sample population that has been studied. One of the easiest methods of determining whether a group 198
JOURNAL OF HAND THERAPY
of scores conforms to the shape of the theoretical normal bell-shaped curve is to compare the three measures of central tendency to each other. In a normal curve, all three (mean, median, and mode) will have the same numeric value. The further apart these values are found to be, the less the group of scores as a whole is likely to be representative of a normal population. Each of the three statements of central tendency is a different measure of "average." The mean of a group of scores may be mathematically computed by dividing the sum of all the scores by the total number of scores. For example, the following pinch strengths are found for a group of 11 patients: 9, 10, 10, 10, 11, 11, 12, 12, 18, 20, and 21 pounds; the sum of all the scores is 144. When divided by the total number of scores, 11, the mean for the group is found to be 13.09 pounds. The median of a group of scores is that score which, when all the scores are rank-ordered from lowest to highest in a frequency distribution, lies at the 50th percentile level. In the above distribution the median or 50th percentile value is the sixth score from either the top or bottom of the distribution: 11 pounds. The third measure of central tendency, the mode, is that score which most often appears in the distribution. For the above distribution the mode value is 10 pounds. For the above example, the three measures of central tendency are dissimilar (13.9 pounds. . 11 pounds, and 10 pounds), indicating that the sample population is skewed and probably not representative of a normal population. In light of such circumstances, one should not put much trust in the accuracy of the sample scores as being an appropriate statement of normalcy. While many reasons may be cited for lack of agreement of measures of central tendency, one of the most frequently encountered problems is that of too small a sample population. It is for this reason that studies carried out on relatively small numbers must be viewed with caution. It is possible that the scores of the sample population may fall somewhere toward a tail of the normal bell curve, resulting in potentially aberrant information. Additionally, it is imperative that normal values be gathered with instruments which have been proven to be both reliable and valid. If instruments are used that lack either of these criteria, countless hours will be wasted in the collection of meaningless and
untruthful data that could be extremely misleading and even dangerous when used to assess or direct patient treatment. This is sobering in light of the relatively few instruments currently available to us that meet these two basic criteria. Directly influencing the direction and scope of patient treatment, statements of normal are critical to our understanding of pathology and to the measurement of dysfunction. It is therefore essential that we
as clinicians understand and be able to assess the efficacy of these statements. After meeting instrument criteria of reliability and validity, comparison of the mean, median, and mode is one method of several by which we as clinicians may assess the accuracy of normative statements. Elaine Ewing Fess, MS, OTR, FAOTA Research Editor
A group of hand therapists met with Professor Kesslerin Rehovat, Israel in February 1988 in preparation for the Fourth International Congress of the International Federation of Societies for Surgery of the Hand and the International Federation of Societies of Hand Therapy, which are planned for April 1989 in Tel Aviv. All hand therapists are encouraged to attend. For further information, contact the Secretariat, P.O. Box 50006, Tel Aviv 61500 Israel. In the photograph are therapists of the IFSHTScientific Committee and therapists working with the IFSSH organizing committee. From left to right are: Ruth Levy, Rosalie Kupfer-Halstuch, Judy Leonard, Barbara Sumech, Tsofia Rosen, Leah Fostick, and Ozi Van Straten. Committee member Moshe Wise was n~t available for the meeting. Watch for further informati on about the meeting in future issues of Journal of Hand Therapy.
October-December 1988
199
Assessment of Normative Statements Through Measures of Central Tendency n derstan din g "normal" is the base from which all clinicians proceed when evaluU ating and treating patients. In order to identify dysfunction, predict rehabilitative potential, assess progress, and define final functional level, it is important to be able to relate a patient's performance in a given area to that of an unimpaired individual of the same sex, age, and general background. This process of comparison is usually based on observation or a com bination of observation and measurement. While the presence of a fracture, disrupted tendon, or open wound is an obvious departure from normal, many problems facing clinicians are not so apparent, necessitating more sophisticated approaches. Also, in this age of accountability, clinicians are being required to substantiate their actions through documentation and review. Being able to numerically document patient performance to that of "normal" performance is essential. Ostensibly, this process seems easy enough. The phenomenon in question is measured and the resultant scores are compared to established normal values for that particular phenomenon. While this may sound elemental, closer scrutiny reveals a very sophisticated process based on specific criteria. First, an instrument whose reliability and validity have been statistically established (see previous Research for the Clinician columns) must be used to measure the given event, and second, for comparison, this instrument must also have accompanying normative data appropriate to the event being measured. By what criteria may clinician consumers judge the efficacy of normative statements? All too often one is presented with an assessment instrument that has as its normative statement one or two "average" values. Noting another source of potential confusion, both clinical and research studies often report findings in terms of statistical "averages." What do these statements reflect in terms of the issues being studied? Are they meaningful and how may they be evaluated? Given a sufficiently large group of subjects, data from a normal population are distributed in a relatively predictable manner that is graphically represented by a symmetrical bell-shaped curve. Three measures of central tendency (mean, median, and mode) are fundamental to evaluating the shape or configuration of a group of values, whether they represent a statement derived from a large normal population, from a specific diagnostic entity, or from a smaller sample population that has been studied. One of the easiest methods of determining whether a group 198
JOURNAL OF HAND THERAPY
of scores conforms to the shape of the theoretical normal bell-shaped curve is to compare the three measures of central tendency to each other. In a normal curve, all three (mean, median, and mode) will have the same numeric value. The further apart these values are found to be, the less the group of scores as a whole is likely to be representative of a normal population. Each of the three statements of central tendency is a different measure of "average." The mean of a group of scores may be mathematically computed by dividing the sum of all the scores by the total number of scores. For example, the following pinch strengths are found for a group of 11 patients: 9, 10, 10, 10, 11, 11, 12, 12, 18, 20, and 21 pounds; the sum of all the scores is 144. When divided by the total number of scores, 11, the mean for the group is found to be 13.09 pounds. The median of a group of scores is that score which, when all the scores are rank-ordered from lowest to highest in a frequency distribution, lies at the 50th percentile level. In the above distribution the median or 50th percentile value is the sixth score from either the top or bottom of the distribution: 11 pounds. The third measure of central tendency, the mode, is that score which most often appears in the distribution. For the above distribution the mode value is 10 pounds. For the above example, the three measures of central tendency are dissimilar (13.9 pounds. . 11 pounds, and 10 pounds), indicating that the sample population is skewed and probably not representative of a normal population. In light of such circumstances, one should not put much trust in the accuracy of the sample scores as being an appropriate statement of normalcy. While many reasons may be cited for lack of agreement of measures of central tendency, one of the most frequently encountered problems is that of too small a sample population. It is for this reason that studies carried out on relatively small numbers must be viewed with caution. It is possible that the scores of the sample population may fall somewhere toward a tail of the normal bell curve, resulting in potentially aberrant information. Additionally, it is imperative that normal values be gathered with instruments which have been proven to be both reliable and valid. If instruments are used that lack either of these criteria, countless hours will be wasted in the collection of meaningless and
untruthful data that could be extremely misleading and even dangerous when used to assess or direct patient treatment. This is sobering in light of the relatively few instruments currently available to us that meet these two basic criteria. Directly influencing the direction and scope of patient treatment, statements of normal are critical to our understanding of pathology and to the measurement of dysfunction. It is therefore essential that we
as clinicians understand and be able to assess the efficacy of these statements. After meeting instrument criteria of reliability and validity, comparison of the mean, median, and mode is one method of several by which we as clinicians may assess the accuracy of normative statements. Elaine Ewing Fess, MS, OTR, FAOTA Research Editor
A group of hand therapists met with Professor Kesslerin Rehovat, Israel in February 1988 in preparation for the Fourth International Congress of the International Federation of Societies for Surgery of the Hand and the International Federation of Societies of Hand Therapy, which are planned for April 1989 in Tel Aviv. All hand therapists are encouraged to attend. For further information, contact the Secretariat, P.O. Box 50006, Tel Aviv 61500 Israel. In the photograph are therapists of the IFSHTScientific Committee and therapists working with the IFSSH organizing committee. From left to right are: Ruth Levy, Rosalie Kupfer-Halstuch, Judy Leonard, Barbara Sumech, Tsofia Rosen, Leah Fostick, and Ozi Van Straten. Committee member Moshe Wise was n~t available for the meeting. Watch for further informati on about the meeting in future issues of Journal of Hand Therapy.
October-December 1988
199