3　Discussion　　Our results of mean stereoacuity are generally similar to those from other studies that used selected normal subjects and similar methods. Heron and co-workers［9］ found similar median stereoacuity values of 8.0″ and 20.0″ in young adults for the Frisby and Randot tests respectively, and Simmerman［12］ found a mean value for young adults on the Frisby stereotest of 10.7″. Obviously, much poorer level of stereoacuity can be obtained if the subject group is unselected and includes subjects with strabismus or poor binocular vision. For example, Frisby and colleagues obtained a mean stereothreshold of 79″ in an unselected group of young adults, some of whom had stereothresholds of 800″ and 400″［10］. These data were also truncated in that the best score a subject could gain was 40″［10］. Brown and colleagues measured stereoacuity using a Howard-Dolman apparatus and found an average stereoacuity slightly higher than ours of 16.8″ in a group of subjects aged 21-28 years［13］. Although they selected only patients with healthy eyes and good binocular vision as we did, they used a complicated psychophysical procedure to measure threshold with a minimum step size of 3.55″ which may have led to a higher threshold.

　　The stereothresholds from the three tests were similar at 7-11″. However, the range of stereoacuities was much greater for the Howard-Dolman and Randot compared with the Frisby test (Table 1). The 95% confidence ranges for the three tests can be calculated as follow:the lower 95% confidence limit=mean-(1.96 times SD),the upper 95% confidence limit=mean+(1.96 times SD). These ranges from the test results were 0″ to 19.6″ (Howard-Dolman),2.2″ to 19.6″ (Randot) and 1.2″ to 13.7″. These findings are similar to those of Heron and colleagues［9］. They measured stereoacuity in normal children and adults, and concluded that among the Frisby, TNO, Titmus, and Randot tests, the Frisby stereotest showed the least variability. The Frisby stereotest is therefore more likely to detect subtle deviations from normality compared to the other two tests. The larger 95% confidence ranges of values for the Randot and Howard-Dolman tests compared to the Frisby test from normal subjects is likely due to their greater inherent variability (Table 2).

　　The Frisby test was shown to have the best repeatability (COR of ±2.7″) and the highest test-retest correlation (r=0.91) in the study. This is similar to previous findings of Frisby and co-workers who found a higher test-retest correlation for the Frisby test (0.76) compared to the Titmus circles (0.51) and TNO stereotests (0.29)［10］. The better repeatability is also shown in the smaller inter-subject variability as discussed above. No previous studies have reported the 95% confidence limits for change for stereotests. We found values of ± 9.3″ (Howard-Dolman),±8.0″ (Randot) and ±2.7″ (Frisby)(Table 2). This indicates that for a change in stereoacuity to be 'real' (meaning not just due to chance variability) it must be greater than 9.3″ for the Howard-Dolman, greater than 8″ for the Randot and greater than only 2.7″ for the Frisby test. Obviously, these figures are only valid if the tests are measured using the methodology described here and for a young adult group. It is highly likely, for example, that the 95% confidence limits for change would be much larger for all three tests for a group of young children (Heron et al.) If a value for a 'real' change in stereoacuity for children of a certain age were required,the experiment described would have to be repeated with children of that age group with normal healthy eyes and binocular vision. It should also be noted that the technique used here with both the Frisby and Randot tests of varying the working distance is only practical for non-presbyopic subjects. With presbyopic subjects,such as when assessing stereopsis before and after cataract surgery［14］, a different reading add would be required for each new distance used. The Frisby test is particular affected in this regard as it only has three step sizes (340″,170″ and 85″ at 40cm with a PD of 64 mm) if working distance is not varied.

　　Generally the three clinical tests used in the study are poorly correlated, with correlation coefficients of around 0.30(Table 3). This is similar to the findings of earlier results［7～10］, and is likely due in part to different design characteristics and psychophysical methods in each test［9］. In addition, the poor correlations are due to the tests' variability, for example, if the Randot and Howard-Dolman provide relatively low test-retest correlations (0.56 and 0.60 respectively, i.e. they correlate moderately with themselves), how can they correlate highly with another test? Previous authors have also suggested that the tests might measure different aspects of stereo performance, which resulted in a poor correlation between the tests. Therefore, they have argued against judging stereoacuity on the basis of one test alone.

　　In summary, among the three stereotests used in the study, the Frisby test showed the best repeatability and smallest range of normal values. Furthermore, it has several other advantages: no glasses needed, independent on visual acuity (large dot size) and impossible to solve in the absence of binocular single vision［5］. A disadvantage is that it is difficult to use with presbyopic patients, such as before and after cataract surgery［14］, because of the practical difficulties of changing reading add for each change in working distance. For young adults, the 95% confidence limits for change were calculated to be ±2.7″. If a young adult's stereoacuity measured with the Frisby test changes by more than this amount, then this should be considered a significant clinical change.

　　Biography:Ping Situ(1962-), B.Med.MSc. centre for contact lens research,Scool of Optometry,University of Waterloo.

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