Data analyses were performed using SPSS version 25 for Windows (IBM, Armonk, NY, USA). The VA and logCS values obtained with the three tests were characterized by median and interquartile range (IQR) (
Table 1). The normality of the data distributions was confirmed using the Shapiro-Wilks test. Because the logCS obtained with the CSV-1000E and quick CSF at four spatial frequencies, the logMAR VA, the estimated AULCSF, and cutoff frequency from the CSV-1000E test did not follow the normal distribution, the differences between the four simulated visual conditions at four spatial frequencies were compared using a 4 (spatial frequency) × 4 (condition) two-way nonparametric analysis of variance (ANOVA) (Scheirer-Ray-Hare test
42) and Friedman test, respectively. The cutoff and AULCSF obtained from the quick CSF followed the normal distribution, and a one-way repeated measure ANOVA was performed to evaluate the differences among the three simulated conditions and the BCVA condition. When the differences were statistically significant (with
P ≤ 0.05), the nonparametric Friedman test was followed by the Dunn-Bonferroni post hoc test to compare VA value, logCS at each spatial frequency from the CSV-1000E and the quick CSF tests, cutoff and AULCSF estimated from CSV-1000E, whereas a post hoc Bonferroni test was carried out to compare the cutoff and AULCSF from the quick CSF method. All α values were two-sided at a type I error rate of 0.05. Additionally, to quantitatively compare the two CSF methods in detecting small visual changes, a multivariate linear regression model was applied to test whether there were statistically significant differences in observed logCS differences between the simulated visual conditions and the BCVA condition measured with CSV-1000E and the quick CSF. The regression model takes the following form:
\begin{eqnarray*}{\rm{y}} &=& \alpha + {\beta _1}{{\rm{x}}_1} + {\beta _2}{{\rm{x}}_2} + {\beta _3}{{\rm{x}}_3} + {\beta _4}{{\rm{x}}_1} \cdot {{\rm{x}}_2} + {\beta _5}{{\rm{x}}_1} \cdot {{\rm{x}}_3}\nonumber\\
&& +\, {\beta _6}{{\rm{x}}_2} \cdot {{\rm{x}}_3} + {\beta _7}{x_1} \cdot {{\rm{x}}_2} \cdot {{\rm{x}}_3} + \varepsilon ,\end{eqnarray*}
where y is the logCS difference between the three simulated visual conditions and the BCVA condition, α was a constant, ε was a random error term, x
1 is the scale variable of SF, x
2, x
3 are nominal variables of visual conditions and methods, β
1, β
2, β
3 are the coefficients of the independent variables, β
4x
1 · x
2, β
5x
1 · x
3, β
6x
2 · x
3 are the pairwise interactions of the three independent variables, and β
7x
1 · x
2 · x
3 is the three-way interaction. The goodness of fit of the regression model was evaluated using the adjusted coefficient of determination, adjusted
R2, which adds precision and reliability by considering the impact of additional independent variables.