To identify factors influencing the contrast sensitivity, contrast thresholds were first analyzed with a three-factor, repeated-measures ANOVA with one between-subject factor (refractive status) and two within-subject factors (contrast and background). The three factors were (1) refractive status with two levels (myopes and emmetropes), (2) contrast, with two levels (negative and positive), and (3) background luminance level with six levels (0.6, 1.6, 2.6, 3.6, 100, and 125 cd/m2). The ANOVA revealed significant main effects for all three factors: refractive status (F(2,78) = 1175.62; P < 0.0001), contrast (F(1,859) = 15.04; P < 0.0001), and background (F(5,859) = 1752.60; P < 0.0001) and significant interactions between refractive status and contrast (F(1,859) = 35.35; P < 0.0001) and refractive status and background (F(5,859) = 117.90; P < 0.0001). No interaction between contrast and background (F(5,859) = 0.41; P = 0.8441) and no three-way interaction (F(5,859) = 0.74; P = 0.5902) were found.
The ANOVA results are depicted in
Figure 1 , which shows mean contrast thresholds in myopic and emmetropic subjects, estimated separately for positive and negative contrast at the six background luminance levels. Emmetropes and myopes clearly differ in their average performance and, although the absolute differences become much less pronounced with an increasing background luminance level, these differences are all significant, according to Bonferroni-corrected two-sample
t-tests conducted separately for each contrast and background luminance level.
Myopic subjects conspicuously exhibit higher mean contrast thresholds for negative than for positive contrast, whereas in emmetropic subjects, the effect of contrast is reversed. To test the statistical significance of this phenomenon, we conducted Bonferroni-corrected paired t-tests for comparison of means, which were calculated separately for myopic and emmetropic subjects, at each of the six background luminance levels. Thus, the Bonferroni correction is given by the multiplication of each P-value by 6, which represents the number of tests conducted in each subject group. At all luminance levels, the tests revealed a significant difference (P < 0.0001) between the mean thresholds for negative and positive contrast, the difference being positive for myopes and negative for emmetropes.
Concentrating on the subsample of myopic subjects, we analyzed the relationship between the degree of myopia and contrast thresholds (
CT) by regressing the latter on the spherical equivalent refractive error (
D). To account for different intercept and slope coefficients for positive and negative contrast, we ran the regression:
\[CT_{i}{=}{\beta}_{0}{+}{\beta}_{1}I_{i}{+}{\beta}_{2}D_{i}{+}{\beta}_{3}D_{i}I_{i}{+}{\epsilon}_{i},\]
where the dummy variable
I takes on the value 1 for positive and 0 for negative contrast. This coding of the variable enables β
1 and β
3 to be viewed as differences in the intercept and the slope, respectively, which are associated with a change from negative to positive contrast. The regression model, which is thus analogous to ANCOVA (analysis of covariance), was estimated separately for each of the six background luminance levels: 0.6, 1.6, 2.6, 3.6, 100, and 125 cd/m
2.
The six scatterplots are shown in
Figure 2 . The solid and the dashed lines represent ordinary least squares (OLS) linear regressions for negative and positive contrast, respectively. In all subsamples, an increase in the refractive error led to an overall increase in the contrast threshold, although the slopes for positive contrast were lower than for negative contrast. The regression results are given in
Table 1 .
The slope coefficient β2, measuring the influence of the degree of myopia on contrast thresholds for negative contrast, was positive and significant (P < 0.001) at all six luminance levels. The slope for positive contrast, given by β2 + β3, was smaller than that for negative contrast at all luminance levels. β3, representing the difference in the two slopes, was negative and except at 0.6 cd/m2 (P = 0.084) significant at the 1% level. Overall, the regression models yielded adjusted coefficients of determination (R 2 adj) of ≥0.735. As expected, the intercept terms for negative contrast, β0, were all positive. The regression lines for positive contrast exhibited even higher intercepts in all subsamples; all coefficients β1, measuring the difference between the intercepts, were positive, although in three cases not statistically significant. This latter result is consistent with the previously discussed, Bonferroni-corrected paired t-tests for comparison of means, according to which emmetropes display higher thresholds for positive than for negative contrast.