**Reading is a fundamental skill that can be significantly affected by visual disabilities. Reading performance, which typically is measured as reading speed with a reading chart, is a key endpoint for quantifying normal or abnormal vision. Despite its importance for clinical vision, existing reading tests for vision are time consuming and difficult to administer. Here, we propose a Bayesian adaptive method, the qReading method, for automated assessment of the reading speed versus print size function. We implemented the qReading method with a word/nonword lexical decision task and validated the method with computer simulations and a psychophysical experiment. Computer simulations showed that both the interrun standard deviation and intrarun half width of the 68.2% credible interval of the estimated reading speeds from the qReading method were less than 0.1 log10 units after 150 trials, with a bias of 0.05 log10 units. In the psychophysical experiment, reading functions measured by the qReading and Psi methods (Kontsevich & Tyler, 1999) in a word/nonword lexical decision task were compared. The estimated reading functions obtained with the qReading and Psi methods were highly correlated ( r = 0.966 ± 0.004, p < 0.01). The precision of the qReading method with 225 trials was comparable to that of the Psi method with 450 trials. We conclude that the qReading method can precisely and accurately assess the reading function in much reduced time, with great promise in both basic research and clinical applications.**

*speed*(

*size*) is in wpm,

*α*is the asymptote of reading speed in large print sizes, corresponding to the maximum reading speed,

*κ*is the print size at which the reading speed is

*γ*= 0.5 is the guessing rate in the word/non-word lexical decision task,

*β*was set to 2.0 based on pilot data collected on human observers.

^{1}Combined together, Equations 1, 2, and 3 can model the response accuracy of the observer in any print size and exposure duration condition in the lexical decision task.

*θ*= (

*x*= (

*size*,

*duration*).

*α*,

*κ*, and

*η*by updating their joint posterior distribution based on the observer's response via Bayes' rule. Because the performance of the observer in any print size and duration condition is jointly determined by these parameters, the qReading method can obtain information about the entire reading function in each trial instead of measuring reading speed at one print size at a time and therefore greatly improve test efficiency. As shown in Figure 2b, d, and f, the estimated reading speed versus print size curve is updated according to the responses made by observers (blue circles and red crosses). As trial number increases, the estimated reading speed versus print size function approaches the true function.

*α*, 15 values evenly sampled from 0.46 to 1.66 (log10 arcmin units) for the critical size

*κ*, and 15 values evenly sampled in log space from 0.079 to 1 (log10 arcmin units) for the ascending rate

*η*. The prior of the parameters is defined as a uniform distribution in the corresponding region of the three-dimensional space. The range of possible stimuli is 60 print sizes from 5.79 to 129 arcmin and 20 durations from 0.013 to 1 s. The stimulus space was sampled evenly in log units in both dimensions.

*α, κ*, or

*η*, in the

*j*th run, and

*θ*were sampled from the posterior distribution

*α, κ,*and

*η*, as well as the estimated reading speeds from the qReading method, are plotted as functions of trial number in Figure 3a through d, respectively. Both interrun standard deviation and intrarun HWCI decreased rapidly in about 50 trials. The interrun standard deviation for estimated

*α, κ,*and

*η*and reading speeds were 0.143, 0.044, 0.142, and 0.420 log10 units after 50 trials, respectively, and decreased to 0.065, 0.009, 0.068, and 0.084 log10 units after 150 trials, respectively. The intrarun HWCI for estimated

*α, κ,*and

*η*and reading speeds were 0.161, 0.051, 0.177, and 0.723 log10 units after 50 trials, respectively, and decreased to 0.060, 0.011, 0.075, and 0.090 log10 units after 150 trials, respectively.

*α, κ*, or

*η*in the

*j*th run, and

*k*th print size in the

*j*th run, and

*k*th print size.

*α, κ,*and

*η*and the AAB of the estimated reading speeds from the qReading method are plotted as functions of trial number in Figure 3a through d, respectively. The bias of the estimated

*α, κ,*and

*η*and the AAB of the estimated speeds were −0.064, 0.030, 0.100, and 0.099 log10 units after 50 trials, respectively, and decreased to −0.008, 0.010, 0.029, and 0.022 log10 units after 150 trials, respectively. The simulation results showed clearly that the qReading method could deliver very precise and accurate assessment of the reading speed versus print size function efficiently.

^{2}. Observers viewed the stimuli binocularly at a distance of 106.6 cm in a dark room.

^{2}) in the Arial font style. Fifty print sizes (evenly sampled in log space from 4.34 to 89.7 arcmin) and 33 exposure durations (evenly sampled in log space from 0.013 to 1 s) were used in the study. The sizes and durations were rounded to the nearest physically available values in the unit of pixels and refresh intervals, separately. The Psi method was applied to measure threshold reading speeds at six print sizes that were selected for each observer based on data collected in the practice session.

*α, κ,*and

*η*from the Psi method, were determined by the best-fitted parameter values, averaged across sessions and plotted against the average parameters measured directly from the qReading method in Figure 6a through c. The Pearson correlation coefficients between the estimated parameters from the two methods were 0.948 (

*p*= 0.052), 0.997 (

*p*= 0.003) and 0.975 (

*p*= 0.025) for

*α, κ,*and

*η*, respectively. No significant difference was found between the estimated

*α*,

*t*(3) = 2.76,

*p*= 0.067, and

*κ*,

*t*(3) = 1.97,

*p*= 0.144, from the two methods. The estimated

*η*from the qReading method was significantly smaller than that from the Psi method,

*t*(3) = 4.37,

*p*= 0.022.

*p*< 0.01 for all observers). A repeated-measure ANOVA with print size and method as factors was conducted on the estimated reading speeds obtained from the two methods. Method had no significant effect,

*F*(1, 15) = 0.036,

*p*= 0.862.

*β*of the psychometric function for the word/nonword lexical decision task is the same at different print sizes and can be fixed at 2.0 (Equation 3). It is important to know if the fixed slope assumption is valid in the real human experiment and if the true slope differs from the assumed value of 2.0.

^{2}test, all

*p*s > 0.05, Table 1). Model II, in which the thresholds are different but the slope is the same in different print size conditions, also provided good fits to the data for all observers (χ

^{2}test, all

*p*s > 0.05, Table 1). A nested model test showed that Model II is statistically equivalent to Model I (χ

^{2}test, all

*p*s < 0.05, Table 1), indicating that the fix slope assumption in the qReading method held true in our experimental data. From the best fitting Model II of each observer, we computed the averaged slope across observers. It was 2.06 ± 0.381, not significantly different from the assumed value in the qReading method,

*t*(3) = 0.312,

*p*= 0.776.

*α, κ,*and

*η*, as well as reading speeds from the qReading method, were highly correlated with those from the Psi method. The interrun standard deviation, intrarun HWCI, and average absolute bias of the estimated reading speeds from the qReading method were 0.109 ± 0.045, 0.058 ± 0.040, and 0.065 ± 0.012 log 10 units after 225 trials, respectively. Moreover, to achieve the same amount of precision, the qReading method only needs about half the number of trials of the Psi method. The test–retest reliability, as indicated by the OCCC of the reading speed measured by the qReading method was 0.891 ± 0.024.

*η*estimated from the qReading method was smaller than that derived from the Psi method,

*t*(3) = 4.37,

*p*= 0.022. However, it should not be considered as an inaccuracy issue for qReading method. In our experiment, reading speed was only sampled at six print sizes in the Psi test. It is possible that the number of data points was not sufficient to obtain an accurate estimate of

*η*from the Psi test.

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*Journal of Vision*^{1}In the current implementation of the qReading method, we assume that the shape of the underlying psychometric function is known. It has been demonstrated that the shape of the psychometric function was largely invariant in contrast detection (Chen et al., 2014; Hou et al., 2010) and letter identification (Hou, Lu, & Huang, 2014). This assumption was tested and validated in the psychophysical experiment in this study.

^{2}[In Appendix A] The Psi method (Kontsevich & Tyler, 1999) is based on minimizing expected entropy, which is equivalent to maximizing the expected change of entropy

*r*. The mutual information is symmetric (Cover & Thomas, 1991):

*θ*= (

*x*= (

*size*,

*duration*) and a psychometric function in each stimulus condition, conditioned on the parameters of the reading curve:

*λ*represent the guessing rate, lapse rate of the observer when performing the task, and

*β*is slope of the psychometric function. The probability of an incorrect response is

*x*. The equations also provide the conditioned joint probability of the parameter

*x*. In this way, the qReading test directly estimates the entire reading speed curve define by three parameters, instead of measuring reading speed at one print size once a time, therefore greatly improving the testing efficiency.

^{2}(Cover & Thomas, 1991; Kujala & Lukka, 2006) for each possible stimulus

*x*,

*t*= 1, 2, 3… is the prior knowledge about

*t*th trial, and

*p*. A one-step-ahead search determines the optimal stimulus

*x*condition to be used in the next (

_{t}*t*th) trial, by maximizing the expected information gain over the entire stimulus space:

*t*, the posterior distribution of the reading function parameters

*size*,

*duration*) in the trial and the prior knowledge about parameters