The psychometric function relates an observer's performance to an independent variable, typically a physical aspect of a stimulus. Even if a model fits data well, experimenters need estimates of parameter variability to assess differences across conditions. Traditional methods are unreliable due to small data sets. This paper and its companion suggest bootstrap methods for estimating variability. The bootstrap, a Monte Carlo resampling technique, is preferred over nonparametric methods. It tests the bridging assumption and considers sampling schemes' impact on confidence intervals. The choice of distribution function can affect confidence intervals, so recommendations are given to avoid this. Improved confidence intervals (bias-corrected and accelerated) are introduced. Software is available. Psychometric functions describe performance as a function of stimulus intensity. They are fitted using maximum-likelihood methods. The paper discusses the importance of sampling schemes and distribution functions in estimating variability. Bootstrap methods are used to estimate confidence intervals for thresholds and slopes. The paper shows that sampling schemes significantly affect confidence interval widths. The choice of distribution function can also influence confidence intervals, so recommendations are given to avoid this. The paper recommends bias-corrected and accelerated confidence intervals for more accurate estimates. Bootstrap methods are used to estimate variability in psychometric functions. They generate synthetic data sets and estimate parameters. The paper discusses the importance of sampling schemes and distribution functions in estimating variability. The paper shows that sampling schemes significantly affect confidence interval widths. The choice of distribution function can also influence confidence intervals, so recommendations are given to avoid this. The paper recommends bias-corrected and accelerated confidence intervals for more accurate estimates.The psychometric function relates an observer's performance to an independent variable, typically a physical aspect of a stimulus. Even if a model fits data well, experimenters need estimates of parameter variability to assess differences across conditions. Traditional methods are unreliable due to small data sets. This paper and its companion suggest bootstrap methods for estimating variability. The bootstrap, a Monte Carlo resampling technique, is preferred over nonparametric methods. It tests the bridging assumption and considers sampling schemes' impact on confidence intervals. The choice of distribution function can affect confidence intervals, so recommendations are given to avoid this. Improved confidence intervals (bias-corrected and accelerated) are introduced. Software is available. Psychometric functions describe performance as a function of stimulus intensity. They are fitted using maximum-likelihood methods. The paper discusses the importance of sampling schemes and distribution functions in estimating variability. Bootstrap methods are used to estimate confidence intervals for thresholds and slopes. The paper shows that sampling schemes significantly affect confidence interval widths. The choice of distribution function can also influence confidence intervals, so recommendations are given to avoid this. The paper recommends bias-corrected and accelerated confidence intervals for more accurate estimates. Bootstrap methods are used to estimate variability in psychometric functions. They generate synthetic data sets and estimate parameters. The paper discusses the importance of sampling schemes and distribution functions in estimating variability. The paper shows that sampling schemes significantly affect confidence interval widths. The choice of distribution function can also influence confidence intervals, so recommendations are given to avoid this. The paper recommends bias-corrected and accelerated confidence intervals for more accurate estimates.