An example Nomon application for selecting between 16 points on screen (screenshot).

<p>The horizontal and vertical positions of the option points were chosen uniformly at random in the box shown to illustrate the flexibility of the method.</p

Entropy of the estimated probability distribution over clocks for two Nomon applications.

<p>Entropy is shown as a function of clicks remaining to selection. Each solid line represents a single selection process. Dotted lines decreasing to zero at respective rates of (lower) and (upper) bits per click are illustrated for reference. <i>Left</i>: 25 selections on the Nomon Keyboard: 30 clocks, non-trivial prior , clock period seconds, switch input from joystick button. <i>Right</i>: 25 selections on another Nomon application: 401 clocks, uniform prior , clock period seconds, switch input from space bar. Data was generated by the experienced user (TB).</p

Mean entry rate (<i>left</i>) and click load (<i>right</i>) across interface blocks.

<p>Mean entry rate is measured in words per minute, and click load is measured in clicks per output character. In both panels, error bars represent 95% confidence intervals for the novice user means, and the average experienced user (TB) performance is illustrated by horizontal lines for comparison.</p

Subjective ratings of the two interfaces by novice participants.

<p>Each response to the lefthand statements was on a scale from 1 (strongly disagree) to 7 (strongly agree). In the questionnaires, the interface name was substituted for X. Mean responses are shown with standard deviations in parentheses. Boldface is used to highlight the means corresponding to a more positive user experience.</p

The scanning grid from The Grid 2 used in this comparison study (screenshot).

<p>The six long rectangles on the left hold word completions. The remaining options are fixed and include letters, an underscore for space, a period, a character-deletion function, and a word-deletion function.</p

The Nomon Keyboard, a writing application (screenshot).

<p>Words that are prefixed by the concatenation of the current context and the letter X appear next to the letter X. Underscore represents a space. Options for period, a character-deletion function, and an undo function are also available.</p

Confidently Comparing Estimates with the c-value

Modern statistics provides an ever-expanding toolkit for estimating unknown parameters. Consequently, applied statisticians frequently face a difficult decision: retain a parameter estimate from a familiar method or replace it with an estimate from a newer or more complex one. While it is traditional to compare estimates using risk, such comparisons are rarely conclusive in realistic settings. In response, we propose the “c-value” as a measure of confidence that a new estimate achieves smaller loss than an old estimate on a given dataset. We show that it is unlikely that a large c-value coincides with a larger loss for the new estimate. Therefore, just as a small p-value supports rejecting a null hypothesis, a large c-value supports using a new estimate in place of the old. For a wide class of problems and estimates, we show how to compute a c-value by first constructing a data-dependent high-probability lower bound on the difference in loss. The c-value is frequentist in nature, but we show that it can provide validation of shrinkage estimates derived from Bayesian models in real data applications involving hierarchical models and Gaussian processes.</p