Aptitude skill lesson
Reaction-time exercises: skill lesson
Reaction-time exercises measure how long the loop from stimulus to response takes, and how much longer it gets when a decision is inserted into that loop. Simple reaction time uses one signal and one response; choice reaction time adds alternatives; discriminative tasks add a go/no-go decision. Novus Learn reports this construct separately from the rest of the battery for an honest reason: a browser measurement carries your display's refresh interval, your input device's polling rate and your operating system's scheduling on top of you, and those alone can move a score by ten milliseconds or more between devices. That makes it excellent for tracking your own change over time on one device, and poor for comparing yourself with anybody else. Results stay on this device unless you export them.
Published · last reviewed
Applies to Novus Learn 0.1.0
What changed, and when
- , Replaced the body of all 27 non-judgement lessons with construct-specific material: six worked examples each, carrying the actual arithmetic, the actual inference or the actual procedure, plus expanded objectives, practice tips and glossary. Every 'Related Learn topics' link now points at a real page on this site rather than a generic search. The eight workplace-judgement lessons are unchanged.
- , Rebuilt the lesson page around a sticky contents rail, per-section links, previous/next lesson navigation, and two graded checkpoints drawn from the open practice bank.
- , Repaired the aptitude integrations behind the lessons so each one links to skill-specific practice instead of the unscoped fixture engine.
- , Published one lesson for each of the 35 aptitude skill constructs: objectives, worked examples, practice tips, glossary, Learn topic links, and sources.
These 35 skill lessons are authored and revised as one set, so they share one revision history rather than 35 identical dates.
Objectives
Copy link- Report a reaction-time block with the median rather than the mean, and justify the choice from the shape of the distribution.
- Apply Hick's law to predict how much a task slows when the number of response alternatives grows, and recognise that doubling alternatives adds a roughly constant increment rather than doubling the time.
- Estimate how much of a between-device score gap is display refresh and input polling rather than the person, and refuse to compare across hardware.
- Distinguish an anticipation from a genuine response using a physiological floor, and explain why a fixed foreperiod invites false starts.
- Convert speed and error rate into correct responses per minute so a fast, sloppy strategy can be compared honestly against a slower, accurate one.
- Use Donders' subtraction logic to attribute added milliseconds to discrimination or to response selection, and state the assumption that logic rests on.
Checkpoint: does the idea land?
Copy linkBefore the worked examples, check that the objectives above actually landed.
Two questions from the open practice bank, answered here and scored on this device. Untimed, ungraded, and not added to your practice history, the full bank is where attempts are recorded.
Examples
Copy linkOne lapse ruins the mean and barely touches the median
Eight simple-reaction trials, in milliseconds: 245, 262, 231, 258, 249, 812, 240, 255. The 812 is a lapse - attention wandered, or a notification stole a frame. The mean is the sum, 2552, divided by 8, which is 319 ms. Sort the trials: 231, 240, 245, 249, 255, 258, 262, 812. The median is the average of the two middle values, 249 and 255, which is 252 ms. One trial out of eight moved the mean 67 ms and moved the median by almost nothing. Reaction-time distributions are right-skewed by construction - there is a hard physiological floor below which you cannot go, and no ceiling at all on how late a lapsed trial can be - so the mean is dragged upward by the tail on every block, and comparing two blocks by their means largely compares how many lapses each contained. Report the median. If you want the lapse information too, report it separately as a lapse count rather than letting it contaminate the central estimate.
Hick's law: what four more options actually cost
Choice reaction time grows with the logarithm of the number of alternatives, the relationship Hick described in 1952 and Hyman in 1953, usually written as RT = a + b x log2(n + 1). Take a = 200 ms and b = 150 ms per bit and compute three cases. With 2 alternatives, log2(3) is about 1.585, so RT is 200 + 238 = 438 ms. With 4, log2(5) is about 2.322, so RT is 200 + 348 = 548 ms. With 8, log2(9) is about 3.170, so RT is 200 + 475 = 675 ms. Doubling from 2 to 4 costs 110 ms; doubling again from 4 to 8 costs 127 ms. The increments are nearly equal rather than doubling, and they would be exactly equal at 150 ms if the formula used log2(n) instead of log2(n + 1). The wrong intuition is that twice the options means twice the time, which would predict 876 ms at 4 alternatives; the real cost of adding options is far gentler, which is why an eight-way keypad is workable at all. It also tells you where design effort pays: removing two options from a six-option interface saves much less than people expect, whereas making the mapping between signal and key more natural saves a great deal.
How much of the gap is your hardware
A stimulus can only appear when the display draws a frame. At 60 Hz a frame is 1000/60 = 16.7 ms, so the true onset falls somewhere inside that window and adds 8.3 ms on average, up to 16.7 ms at worst. At 240 Hz the frame is 4.2 ms and the average addition is about 2.1 ms. Input adds its own: a 125 Hz USB keyboard reports at 8 ms intervals, roughly 4 ms on average, while a 1000 Hz gaming mouse reports at 1 ms intervals, about 0.5 ms. Add them up. A 60 Hz laptop with a standard keyboard carries roughly 8.3 + 4 = 12.3 ms of hardware overhead. A 240 Hz monitor with a high-polling mouse carries about 2.1 + 0.5 = 2.6 ms. That is a gap of nearly 10 ms between two identical people, before browser timer resolution, background processes or battery-saver frame throttling are considered. So a 248 ms score on one machine and a 239 ms score on another are not evidence about the two people. Fix one device, one browser, one input method and one posture, and read only your own trend.
Anticipation: the trial that is too fast to be real
Nerve conduction, sensory processing and muscle activation impose a floor. Published simple visual reaction times for healthy young adults commonly fall in the low 200s of milliseconds, with auditory reaction a little faster because the auditory pathway is shorter, so a logged trial of 120 ms is not a fast response - it is a movement launched before the signal, which happened to land near it. This is why foreperiod design matters. If the delay between 'ready' and the signal is fixed at exactly 2.0 seconds, you learn the rhythm within a handful of trials and begin timing your press to the clock rather than the stimulus, which produces a beautiful-looking block full of anticipations. Randomising the foreperiod - uniformly between about one and four seconds - removes the rhythm to lock onto. When you review a block, discard trials below roughly 150 ms as anticipations and count them, rather than keeping them and admiring the improvement. A block with a 190 ms median and six discarded anticipations is a worse block than one with a 240 ms median and none, because the first one shows you were guessing.
Fast and wrong loses to slow and right
Two candidates on a two-choice task. Candidate A averages 420 ms with a 4 percent error rate. Candidate B averages 350 ms with a 25 percent error rate. Speed alone says B by 70 ms per trial. Convert to correct responses per minute instead. A completes 60,000/420 = 142.9 trials a minute and 96 percent are correct, giving 137.1 correct per minute. B completes 60,000/350 = 171.4 trials a minute and 75 percent are correct, giving 128.6. A is ahead despite being visibly slower on every single trial. If the task also penalises errors one for one, A nets 137.1 minus 5.7 equals 131.4 while B nets 128.6 minus 42.9 equals 85.7, and the gap becomes enormous. This is the speed-accuracy trade-off with numbers on it, and it is the reason a reaction-time result should never be reported as a bare millisecond figure. A median with no accompanying error rate is not a result; it is half of one, and it is the half that can be improved by simply caring less.
Subtracting the stages, and the assumption underneath
Run the same participant on three tasks. Simple reaction, one signal and one key: 220 ms. Go/no-go, press for green and withhold for red: 290 ms. Two-choice, green to the left key and red to the right: 350 ms. Donders' subtractive method, proposed in 1868, attributes the differences to inserted stages. Adding the requirement to discriminate green from red costs 290 minus 220 equals 70 ms. Adding the requirement to select between two responses costs a further 350 minus 290 equals 60 ms. That is a genuinely useful decomposition - it tells you whether your own slowness is perceptual or decisional, and therefore whether to practise signal discrimination or response mapping. But state the assumption honestly: subtraction only works if inserting a stage leaves the other stages untouched, the 'pure insertion' assumption, and later work has shown stages overlap and interact rather than queueing cleanly. Treat the 70 and the 60 as informative estimates of where your time goes, not as measurements of separate mental modules.
Checkpoint: can you apply it?
Copy linkNow apply it. These come from a later section of the bank, so they are not more of the same.
Two questions from the open practice bank, answered here and scored on this device. Untimed, ungraded, and not added to your practice history, the full bank is where attempts are recorded.
Practice tips
Copy link- Report the median and the error rate together, every time, and log lapses as their own count. A millisecond figure with no accuracy figure alongside it cannot be interpreted and can always be improved by being careless.
- Change one variable at a time and keep everything else fixed - same device, same browser, same input method, same seating, similar time of day. Because hardware differences alone are worth about ten milliseconds, an uncontrolled comparison tells you about your equipment, not about you.
- Warm up with five to ten discarded trials before recording. The first few responses of any block are systematically slower, and including them makes every session look like it improved partway through.
- Make the foreperiod unpredictable and set yourself a false-start rule. If you can feel a rhythm, you are practising rhythm-following rather than responding, and the score stops meaning anything.
- Practise choice tasks with the response mapping you will actually use and keep it stable. A large part of choice reaction time is response selection, so most early improvement comes from the mapping becoming automatic, not from you getting faster.
- Sleep, alcohol, illness and fatigue move reaction time far more than a practice session does. Note your state with each block, and never read a single bad block as a change in ability - and never read any of this as clinical information about yourself.
Glossary
Copy link- Simple reaction time
- One signal, one response, no decision. It is the closest available estimate of the sensing-to-moving loop and the baseline that other conditions are compared against.
- Choice reaction time
- Multiple signals mapped to multiple responses. It adds discrimination and response selection to the loop and grows with the logarithm of the number of alternatives.
- Hick's law
- The relationship RT = a + b x log2(n + 1) between the number of equally likely alternatives and reaction time, described by Hick in 1952 and extended by Hyman in 1953.
- Foreperiod
- The interval between the ready cue and the signal. A fixed foreperiod becomes predictable and invites anticipations, so it is normally randomised across a range.
- Anticipation
- A response launched before the signal was processed, showing up as an implausibly short trial. It is discarded and counted, never averaged in.
- Lapse
- An unusually long trial caused by a momentary attention failure. Lapses form the right tail that drags the mean upward and is the reason the median is the fairer summary.
- Refresh interval
- The time between drawn frames - 16.7 ms at 60 Hz, 4.2 ms at 240 Hz. A stimulus can only appear on a frame boundary, so half a frame of unmeasured delay is built into every browser-based trial.
- Speed-accuracy trade-off
- The systematic relationship whereby responding faster raises the error rate. It makes any speed figure uninterpretable on its own and is why throughput - correct responses per minute - is the fairer comparison.
Sources
Copy link- Trial sets, Hick's law worked values, hardware-latency arithmetic and throughput comparisons above are written for Novus Learn. All numbers are original worked examples, not measured data from any population.
- Concepts follow widely published work: Donders (1868) on the subtractive method, Hick (1952) and Hyman (1953) on choice reaction time, and the standard treatment of skewed reaction-time distributions. The stated range for simple visual reaction time is given as a commonly reported approximation, not as a norm, and no percentile or cut-score is implied.
- Refresh-interval and polling-rate figures are arithmetic from the stated rates (1000/60 ms per frame at 60 Hz, 8 ms per report at 125 Hz) and are illustrative of magnitude, not a benchmark of any specific device.
- Novus Learn aptitude construct registry (catalog seed), which records reaction time separately because device hardware and latency affect results.
- Public educational framing only - not affiliated with any official exam board, publisher or employer, and not a clinical, diagnostic, fitness-to-drive or fitness-to-work measure.
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